Multilayer innovation network resilience: A framework for digital economy vulnerability assessment

Summary

Innovation networks drive technological progress, yet their multilayer structures remain poorly understood in digital economy vulnerability contexts. This study develops a comprehensive framework for assessing multilayer innovation network resilience, analyzing interdependencies and disruption scenarios using China’s digital economy as a representative empirical context. We construct coupled multilayer networks implementing four integrated attack strategies to identify cascading vulnerability mechanisms. Results reveal asymmetric patterns: collaboration networks show significant fragility to targeted attacks, while knowledge networks demonstrate higher resilience, especially during mature stages. Cascade failure analysis establishes that knowledge network disruptions propagate severe ecosystem-wide effects, whereas collaboration network perturbations generate limited cross-layer impacts. This asymmetry advances multilayer innovation network theory and provides practical insights for vulnerability assessment. The framework indicates that protecting critical technological knowledge should prioritize over maintaining collaborative arrangements when resources are limited, as knowledge networks constitute the essential integrative mechanism within innovation systems.

Graphical abstract

Highlights

• •Framework assesses multilayer innovation network resilience in digital economy
• •Knowledge networks show higher resilience than collaboration networks to attacks
• •Knowledge disruptions cause severe cascading effects across innovation ecosystems
• •Protecting technological knowledge prioritizes over maintaining collaborations

Environmental science; Economics

Introduction

In today’s global economy, innovation networks function as critical infrastructures propelling technological advancement and economic competitiveness.¹ These complex adaptive systems connect organizations, institutions, and knowledge domains, facilitating collaborative innovation across boundaries.² The resilience of these multilayer networks has become increasingly important amid escalating global uncertainties, as digital transformation accelerates across industries and various disruption scenarios expose structural vulnerabilities in innovation ecosystems. Recent examples include geopolitical tensions such as the recent implementation of up to 145% tariffs on Chinese imports by the Trump administration, which has triggered retaliatory measures targeting critical technology sectors including semiconductors and rare earth materials.³ These trade disruptions reveal the inherent vulnerability of innovation ecosystems to external perturbations and emphasize the necessity for robust analytical frameworks to systematically assess network vulnerability and enhance systemic resilience.^4,5

Digital economy industries represent particularly crucial contexts for developing comprehensive frameworks for multilayer innovation network vulnerability assessment, due to their foundational role in contemporary economic systems and their inherently networked innovation processes.^6,7 As digital technologies increasingly permeate traditional industries and facilitate the emergence of entirely new sectors, understanding the vulnerabilities of digital innovation networks becomes essential for sustainable technological development and economic resilience.⁸ This imperative has become pronounced across rapidly developing digital economies globally, where accelerated growth trajectories and evolving governance frameworks generate unique multilayer structural dynamics. Using China’s digital economy as a representative case, it has experienced unprecedented expansion, increasing from approximately 21.6% of GDP in 2012 to 41.5% by 2023.⁹ The characteristics of major digital economy industries, including their scale, accelerated development trajectory, and evolving position within global technology value chains, make them exceptionally valuable contexts for investigating multilayer innovation network resilience amid intensifying international competition and technological restrictions.¹⁰ Analyzing how these complex, multilayered innovation networks respond to targeted disruptions provides insights applicable to digital economy development globally, given the heightened prominence of “technological decoupling” in contemporary international relations and industrial policy discourse.¹¹

Scholarly investigation into innovation network vulnerabilities has evolved along several complementary trajectories: empirical assessments examining real-world vulnerability patterns and their socioeconomic implications, and simulation-based approaches that model systematic responses to diverse disruption scenarios. However, these research streams have yet to converge into unified frameworks capable of addressing the multilayer nature of contemporary innovation networks. While each research direction offers distinct strengths, they collectively inform our investigation of multilayer innovation network dynamics in digital economy industries.

A significant stream of literature addresses the empirical assessment of innovation network vulnerability and the consequent impacts on socio-economic systems. Regarding network vulnerability evaluation, Tóth et al.¹² conducted a comprehensive analysis of technological capability network resilience across 269 European metropolitan areas, establishing quantitative metrics for regional innovation vulnerability. Tsouri et al.¹³ analyzed the knowledge network of the Trentino ICT innovation system from the perspective of network resilience and examined the consequences of network failures. Guo et al.¹⁴ conducted a social network analysis of technology transfer in strategic emerging industries along the G60 innovation corridor and found that the scale of technology transfer from core cities to relatively less-developed corridor cities is increasing. This research domain extends to examining the robustness of diverse specialized networks, including venture capital,¹⁵ energy systems,¹⁶ technology transfer networks,¹⁷ trade networks,¹⁸ and mobility networks.¹⁹ These studies collectively provide valuable methodological frameworks for evaluating resilience across distinct socio-technical systems, though they remain limited by single-layer analytical approaches.

Regarding innovation networks’ socio-economic impacts, a substantial body of research investigates their influence on economic resilience and innovation elasticity under various conditions. For example, Du et al.⁸ studied the impact of cross-regional collaborative innovation networks on economic resilience in China at different intervals after a shock. This research stream has systematically identified critical mediating and moderating factors influencing innovation network-resilience relationships, including environmental turbulence,²⁰ digital transformation,²¹ knowledge diffusion,²² and knowledge network embeddedness.²³ These studies collectively advance theoretical understanding of how network structural properties translate into tangible socio-economic resilience outcomes, yet have not addressed how these factors operate differently across multiple network layers.

A parallel stream of literature focuses on computational simulations examining innovation network vulnerability under diverse perturbation scenarios. Kou et al.²⁴ constructed a two-layer coupled city network incorporating risk propagation and cooperative recovery, and modeled the impact of public health disaster emergencies in different cities on regional resilience using a network of Chinese cities. Drawing on complex network cascade failure theory, Shi et al.²⁵ constructed an industrial cluster innovation network and developed a cascade propagation model of collaborative innovation risk. Focusing on knowledge network dynamics specifically, Zhao et al.²⁶ also simulated the impact of various malicious attacks on the robustness of the knowledge network. Building on this research trajectory, the robustness of innovation networks in China’s electric vehicle industry and low-carbon technology industry has also been studied.^27,28 Collectively, these simulation-based studies establish methodological foundations for quantitatively assessing vulnerability patterns in innovation networks, though they predominantly rely on theoretical network models that may not capture the structural complexities of real-world innovation systems. In addition, recent advancements in network robustness and cascading failure analysis have extended beyond traditional network models to incorporate higher-order structures, particularly through hypergraph-based approaches.^29,30 Studies examining cascading dynamics in double-layer hypergraphs with higher-order inter-layer interdependencies,³¹ higher-order interdependent percolation on hypergraphs,³² and hypergraph-based modeling of cascading failures with probabilistic node-to-group interactions³³ have contributed valuable methodological frameworks for understanding failure propagation in complex systems. These hypergraph approaches provide deeper insights into analyzing systems with group-level interactions and multi-node dependencies, and reveal the effectiveness of network science methods for analyzing vulnerability patterns and cascading failures.

Despite these valuable contributions, three critical research gaps persist in developing comprehensive frameworks for multilayer innovation network vulnerability assessment. First, existing studies have predominantly analyzed innovation networks as isolated, single-layer structures, overlooking the inherently multilayered nature of innovation ecosystems where collaboration and knowledge networks operate simultaneously and interdependently. Second, most computational simulation studies employ abstract network models (e.g., small-world or scale-free networks) with generic attack strategies disconnected from real-world innovation system perturbations. While theoretically elegant, these approaches often fail to capture the complex structural realities and evolutionary dynamics of actual innovation systems, limiting their practical applicability for policy formulation and strategic management. Third, comprehensive frameworks that integrate empirical network construction with theoretically grounded vulnerability assessment methodologies remain underdeveloped, particularly for digital economy innovation networks.

This study addresses these gaps by developing a comprehensive framework for multilayer innovation network vulnerability assessment, using China’s digital economy industries as a representative empirical context. China’s digital economy industries, characterized by rapid growth, increasing technological sophistication, and strategic significance within global innovation networks, provide an ideal empirical setting for framework development and testing. We construct a coupled two-layer network from extensive patent data: a collaboration network and a knowledge network. Our approach combines empirical network analysis with targeted simulations to reflect the real-world challenges facing innovation ecosystems. We develop contextually relevant attack strategies and conduct experiments across four meaningful scenarios, revealing cascading mechanisms by which layer-specific vulnerabilities propagate between the collaboration and knowledge networks.

Through this approach, this study advances multilayer innovation network theory and vulnerability assessment methodology through three contributions. First, we enhance methodological approaches by analyzing empirically constructed coupled innovation networks from digital economy industries, moving beyond theoretical abstractions to capture real-world structural complexities and evolutionary dynamics. Second, our contextually relevant attack scenarios provide practical insights into vulnerability patterns, enabling the identification of critical nodes whose failure would trigger significant system-wide impacts. Third, we reveal a fundamental asymmetry in multilayer innovation resilience: knowledge networks maintain substantial functionality despite collaborative disruptions, while knowledge network perturbations generate severe cascading effects throughout the entire innovation ecosystem. Together, these contributions offer a comprehensive framework for vulnerability assessment in digital innovation systems with implications extending beyond the specific empirical context to inform multilayer network analysis in diverse digital economy settings.

Results

Temporal dynamics of two-layer networks

The innovation ecosystem of digital economy industries demonstrates significant transformation patterns over extended development periods, as evidenced by our empirical analysis. To visualize this evolutionary trajectory, Figure 1 presents snapshots of the two-layer digital economy network across three distinct periods (2004–2012, 2013–2018, and 2019–2023). These visualizations capture both the collaboration network (bottom row) and knowledge network (top row) dynamics, revealing the changing structure and interconnections that characterize digital innovation system.

Figure 1.

Time-dynamic snapshot of the two-layer digital economy network

The figure displays network snapshots of the constructed two-layer network at different time periods.

The knowledge network exhibits a clear pattern of increasing density and complexity over time. During the emergent period (2004–2012), the knowledge network appears relatively sparse with a discernible core-periphery structure, where a small set of central knowledge elements (indicated by larger red nodes) connects to numerous peripheral elements. Moving to the growth period (2013–2018), we observe significant expansion in both the number of knowledge elements and their interconnections. By the maturity period (2019–2023), the knowledge network has developed a more balanced and densely connected structure.

The collaboration network demonstrates even more dramatic transformation. In the emergent period, the network appears highly fragmented with minimal collaboration density, characterized by numerous isolated nodes and small connected components. This fragmentation reflects early-stage digital economy development, when innovation activities were primarily conducted by individual entities with limited inter-organizational collaboration. The growth period witnesses a remarkable shift toward a more cohesive structure with the emergence of a clear giant component and significantly increased collaborative ties. The maturity period (2019–2023) reveals further consolidation and stratification within the collaboration network, with discernible layers of connectivity and a robust core of highly collaborative innovators surrounded by an extensive periphery of less-connected entities.

Table 1 provides statistical indicators of both network layers across the three time periods, offering quantitative evidence of the structural evolution visualized in Figure 1.

Table 1.

Statistical indicators of networks over time

Layer type	Year	Node	Edge	Average degree	Average path length	Clustering coefficient	Community	Density
Collaboration network	2004–2012	675	924	2.7378	5.3634	0.2425	21	0.0041
	2013–2018	6761	13829	4.0908	4.3890	0.3581	55	0.0006
	2019–2023	23290	50817	4.3638	4.5752	0.3102	87	0.0002
Knowledge network	2004–2012	350	1906	10.8914	2.8254	0.4674	8	0.0312
	2013–2018	489	5192	21.2352	2.4048	0.4719	7	0.0435
	2019–2023	567	13134	46.3280	2.1307	0.5818	4	0.0819

The collaboration network exhibits dramatic growth in scale, with the number of nodes increasing from 675 in the emergent period to 23,290 in the maturity period. Similarly, the number of collaborative ties grew exponentially from 924 to 50,817. The average degree nearly doubled from 2.7378 to 4.3638 across the three periods, suggesting that innovators are forming more collaborative relationships over time. Interestingly, despite this densification of connections, the network density decreased from 0.0041 to 0.0002, revealing that the network’s growth in nodes outpaced its growth in edges. This is a pattern typical of scale-free networks in rapidly expanding innovation systems. The clustering coefficient initially increased from 0.2425 to 0.3581 during the growth period before slightly decreasing to 0.3102 in the maturity period, indicating a trend toward more structured collaboration patterns followed by a slight moderation as the network matured. The number of communities increased consistently from 21 to 87, reflecting greater specialization and diversification within digital innovation ecosystem.

The knowledge network displays equally significant but distinct evolutionary patterns. While exhibiting more modest growth in nodes, the knowledge network experienced dramatic intensification in interconnections, with edges increasing from 1,906 to 13,134, nearly a 7-fold rise. This disparity between node and edge growth rates suggests substantial knowledge recombination and integration rather than merely the emergence of new knowledge domains. The average degree rose remarkably from 10.8914 to 46.3280, indicating that knowledge elements became increasingly interconnected across technological domains. The average path length decreased considerably from 2.8254 to 2.1307, demonstrating enhanced efficiency in knowledge flow and recombination potential. The clustering coefficient increased steadily from 0.4674 to 0.5818, revealing stronger localized knowledge clustering and specialization. The network density increased significantly from 0.0312 to 0.0819, confirming the intensified interconnectedness of knowledge elements within the innovation system.

The data presented in Table 2 reveal the intensifying interconnections between the collaboration and knowledge layers in the digital economy innovation network across the three developmental periods.

Table 2.

Evolution of interlayer coupling in China’s digital economy innovation network

Year	Interlayer edge	Average number of knowledge elements per applicant	Average number of applicants connected to each knowledge element
2004–2012	8661	2.9231	24.6752
2013–2018	54036	3.3974	110.2776
2019–2023	181104	4.3655	319.4074

The interlayer edges have grown dramatically from 8,661 in the emergent period (2004–2012) to 181,104 in the maturity period (2019–2023), representing a nearly 21-fold increase. This exponential growth outpaces even the substantial expansion in the number of actors and knowledge elements observed in Table 1, indicating that the coupling between the two network layers has strengthened considerably. The average number of knowledge elements per applicant has increased steadily from 2.9231 to 4.3655, suggesting that innovation entities are engaging with a broader range of knowledge domains. Simultaneously, the average number of applicants connected to each knowledge element has surged remarkably from 24.7752 to 319.4074, nearly a 13-fold increase. This pattern indicates the formation of denser technological communities around key knowledge elements. Based on the empirically constructed two-layer network, we next conducted simulation experiments for the four vulnerability assessment scenarios designed within our framework.

Single-layer vulnerability assessment

Scenario 1: Collaboration network vulnerability

Figure 2 illustrates the robustness changes of digital economy industry collaboration networks under three attack strategies across the three developmental periods. The top row presents the structural robustness measured by the relative size of the maximal connected subgraph, while the bottom row displays the functional robustness indicated by network efficiency.

Figure 2.

Robustness changes of collaboration networks under attack

This figure illustrates the impact of different attack strategies on structural and functional robustness within collaboration networks across three periods. Data are represented as mean values from simulation results.

The results reveal significant vulnerability patterns characteristic of collaboration networks in digital innovation systems. Across all three periods, both targeted attack strategies (degree-based and innovative capacity-based) demonstrate devastating effects on network robustness compared with random attacks. When removing just 10% of the highest-degree nodes, the maximal connected subgraph size drops precipitously to below 0.2 in all periods, indicating that over 80% of the network’s connectivity is disrupted. Similarly, removing the top 10% of nodes based on innovative capacity produces comparable catastrophic effects. In contrast, random attacks show a much more gradual decline in network connectivity, requiring removal of approximately 70–80% of nodes to achieve similar disruption levels.

The functional robustness results (bottom row) exhibit similar patterns but with even more pronounced vulnerability to targeted attacks. Network efficiency collapses almost immediately under both targeted attack strategies, dropping to near-zero values after removing just 10% of nodes. This indicates that the collaboration networks’ ability to efficiently transmit information or knowledge is severely compromised by the removal of either well-connected actors or highly productive innovators.

Notably, there is minimal difference between the impacts of degree-based and innovative capacity-based attacks, suggesting a strong correlation between collaborative connectivity and innovation productivity in this ecosystem. This correlation indicates that the most productive entities in terms of patent output also tend to be the most central in the collaboration network, functioning as keystone actors whose removal severely compromises the entire innovation ecosystem.

Scenario 2: Knowledge network vulnerability

Figure 3 presents the robustness changes of knowledge networks under different attack strategies across the three time periods. The contrast with collaboration networks reveals distinct vulnerability patterns in the knowledge dimension of digital economy innovation systems.

Figure 3.

Robustness changes of knowledge networks under attack

This figure illustrates the impact of different attack strategies on structural and functional robustness within knowledge networks across three periods. Data are represented as mean values from simulation results.

Unlike the collaboration networks, the knowledge networks demonstrate considerably higher resilience against all attack strategies. For structural robustness (top row), even under targeted degree-based attacks, the maximal connected subgraph maintains over 60% of its size until approximately 20% of nodes are removed. While degree-based attacks eventually cause significant disruption, the threshold for catastrophic failure is substantially higher than in collaboration networks. Knowledge classification-based attacks show impact patterns similar to random attacks, indicating that technological categories do not necessarily align with critical connectivity patterns in the knowledge network.

The functional robustness results reveal important insights about knowledge network evolution and resilience. In the earliest period (2004–2012), the knowledge network’s efficiency under degree-based attacks deteriorates rapidly, but in subsequent periods, its resilience improves markedly. By the maturity period (2019–2023), the network shows substantially enhanced robustness against all attack types, with efficiency maintaining relatively high values even after significant node removal. This evolution suggests a maturation process where knowledge interdependencies become more distributed and redundant over time, creating multiple pathways for knowledge recombination and reducing reliance on specific technological components. Particularly noteworthy is the growing divergence between random attacks and knowledge classification-based attacks in the maturity period. While initially these attack strategies produced similar effects, by 2019–2023, knowledge classification-based attacks show intermediate impact between random and degree-based strategies.

The comparison between collaboration and knowledge networks reveals asymmetric vulnerability patterns in the digital economy innovation system. While the collaboration network exhibits high vulnerability consistent with scale-free network properties, the knowledge network has evolved toward greater resilience, particularly in terms of functional robustness. This asymmetry suggests that technological knowledge becomes more widely distributed and integrated across innovation systems, even as collaborative activities remain concentrated around key actors. Understanding such structural differences has important implications for vulnerability assessment and strategic planning in digital economy industries.

Multilayer vulnerability assessment

Scenario 3: Vulnerability under collaboration attacks

Building upon our single-layer vulnerability assessment, we now examine how attacks on the collaboration network propagate through the coupled two-layer innovation system. We set the failure threshold ($\theta$) to 0.5 to conduct the simulation. Figures 4 and 5 illustrate the structural and functional robustness changes, respectively, when attacks target the collaboration layer but affect both layers through cascade failure mechanisms.

Figure 4.

Structural robustness changes of two-layer networks under collaboration network attacks

This figure illustrates the impact of different collaboration network attack strategies on structural robustness across three periods within the networks. Data are represented as mean values from simulation results.

Figure 5.

Functional robustness changes of two-layer networks under collaboration network attacks

This figure illustrates the impact of different collaboration network attack strategies on functional robustness across three periods within the networks. Data are represented as mean values from simulation results.

The structural robustness results (Figure 4) reveal critical cross-layer vulnerability patterns in multilayer innovation systems. When collaboration networks are subjected to targeted attacks (degree-based or innovative capacity-based), not only does the collaboration layer itself experience catastrophic disruption as observed in scenario 1, but also this disruption propagates to the knowledge layer through interlayer dependencies. This cascade effect is particularly pronounced in the later development periods (2013–2018 and 2019–2023), where removing just 5–10% of critical collaboration nodes triggers disconnection in the knowledge network. The knowledge network’s maximal connected subgraph size decreases to approximately 0.6–0.8 after targeted removal of 10% of collaboration nodes, despite no direct attacks on knowledge elements themselves. This demonstrates vulnerability transfer from the collaboration to the knowledge layer, highlighting how disruptions to key innovative entities can indirectly compromise technological knowledge connectivity.

The functional robustness analysis (Figure 5) provides insights into cross-layer cascade effects in multilayer innovation systems. While the collaboration network’s efficiency collapses rapidly under targeted attacks as seen in scenario 1, the knowledge network initially maintains its efficiency despite these attacks. However, as more critical collaboration nodes are removed (beyond approximately 20%), the knowledge network’s efficiency also begins to deteriorate, albeit more gradually than the collaboration network. This pattern suggests that, while immediate knowledge flow disruption is concentrated in the collaboration layer, continued removal of key collaborative entities eventually compromises the knowledge network’s functional capacity through cascade failures.

The evolution across time periods reveals important dynamics in multilayer innovation system interdependence: while both network layers have grown more extensive and complex over time, their interdependence has also strengthened. The most recent period (2019–2023) shows the most pronounced cascade effects, with knowledge network robustness more tightly coupled to collaboration network integrity than in earlier periods. This suggests that, as digital economy industries mature, the resilience of technological knowledge bases becomes increasingly dependent on the stability of key collaborative entities.

The comparative impact of different attack strategies on the two-layer system offers additional insights into multilayer vulnerability patterns. While both targeted strategies (degree-based and innovative capacity-based) produce similar catastrophic effects on the collaboration layer, their cascade impacts on the knowledge layer show subtle differences, particularly in the functional robustness domain. This suggests that the mechanisms by which collaborative disruptions propagate to knowledge structures may vary depending on whether the targeted entities are selected based on their connectivity or their innovative output, highlighting the complex interdependencies that characterize digital economy innovation ecosystems.

Scenario 4: Vulnerability under knowledge attacks

Figures 6 and 7 present the counterpart to scenario 3, examining how attacks targeting the knowledge layer propagate through the coupled two-layer system to affect both knowledge and collaboration networks. This scenario simulates disruptions to technological foundations and their ripple effects on innovation ecosystems.

Figure 6.

Structural robustness changes of two-layer networks under knowledge network attacks

This figure illustrates the impact of different knowledge network attack strategies on structural robustness across three periods within the networks. Data are represented as mean values from simulation results.

Figure 7.

Functional robustness changes of two-layer networks under knowledge network attacks

This figure illustrates the impact of different knowledge network attack strategies on functional robustness across three periods within the networks. Data are represented as mean values from simulation results.

The structural robustness results (Figure 6) reveal asymmetric cross-layer effects that provide fundamental insights into multilayer innovation system vulnerability. When knowledge networks are subjected to degree-based attacks, both network layers experience significant disruption, but with distinct patterns. The knowledge layer itself shows substantial vulnerability to degree-based attacks, with its maximal connected subgraph size decreasing rapidly as high-degree knowledge elements are removed. More striking is the pronounced cascade effect on the collaboration network, where removing just 10–20% of high-degree knowledge elements causes catastrophic disruption to the collaboration structure, particularly in the maturity period (2019–2023). This demonstrates that critical knowledge elements serve as foundational pillars for collaborative activities, and their removal can trigger widespread disconnection among innovation entities. In addition, knowledge classification-based attacks show interesting temporal evolution in their impact on the two-layer system. In the earliest period (2004–2012), these attacks produce moderate effects on both layers, comparable to random attacks. However, in later periods, particularly 2019–2023, their impact intensifies, especially on the collaboration network.

The functional robustness analysis (Figure 7) reveals nuanced cross-layer dynamics that illuminate fundamental principles of multilayer innovation system vulnerability. Degree-based attacks on knowledge elements cause immediate and severe efficiency loss in both network layers across all time periods. The collaboration network’s efficiency collapses more rapidly than the knowledge network itself in response to high-degree knowledge element removal, particularly in the maturity period. This counterintuitive pattern suggests that while knowledge networks maintain some functional pathways even after losing critical nodes, collaboration network functionality becomes severely compromised when key knowledge foundations are removed.

Knowledge classification-based attacks show relatively moderate impacts on functional robustness in the early period but increasingly disruptive effects in later periods. By 2019–2023, removing knowledge elements based on classification causes substantial efficiency loss in both network layers, though still less severe than degree-based attacks. This evolution indicates growing technological specialization within digital economy industries, where innovation entities become increasingly dependent on specific technological domains rather than diverse knowledge foundations.

Comparing scenarios 3 and 4 reveals fundamental asymmetries in the vulnerability structure of digital economy innovation systems that have important implications for our multilayer vulnerability assessment framework. While collaboration network attacks primarily affect the collaboration layer with more moderate cascade effects on the knowledge layer, knowledge network attacks trigger severe disruptions in both layers. This asymmetry suggests that knowledge layers serve as more critical foundations for entire innovation ecosystems than collaboration layers. In practical terms, this indicates that protecting key technological foundations may be more crucial for maintaining system-wide resilience than preserving specific collaborative arrangements. Moreover, the temporal evolution across the three periods highlights changing interdependencies between collaboration and knowledge in digital economy industries. As the system has matured, the cascade effects between layers have intensified, particularly from knowledge to collaboration, suggesting increasing technological specialization and dependency patterns that are characteristic of maturing digital innovation ecosystems.

Framework extensions

Sensitivity analysis of failure threshold

The main analysis assumes a fixed failure threshold (θ = 0.5) to model cascade failures from the knowledge layer to the collaboration layer. To ensure our findings are not dependent on this specific parameter, we conducted a sensitivity analysis by varying the failure threshold from a low value of 0.3 to a high value of 0.7. This extension allows us to assess how the vulnerability patterns change as innovation entities become more or less resilient to the loss of their knowledge foundations. The results, presented in Figure 8, illustrate the impact of different thresholds on the robustness of both network layers under the three knowledge network attack scenarios.

Figure 8.

Sensitivity analysis of robustness to the failure threshold

This figure illustrates a sensitivity analysis of the failure threshold. Data are represented as mean values from simulation results.

The analysis reveals that the failure threshold is a critical parameter that significantly mediates the intensity of cascade failures, particularly on the collaboration network. For both degree-based and classification-based attacks, a lower failure threshold results in a much more rapid collapse of the collaboration network’s structure and function. For instance, under a degree-based attack with a low threshold (θ = 0.3), the collaboration network’s maximal connected subgraph disintegrates almost immediately. As the threshold increases, the network demonstrates greater resilience, with the collapse occurring at a higher percentage of node removal. This pattern confirms that the model is sensitive to the assumed resilience of the innovation entities: as firms become more tolerant to knowledge loss (higher θ), the system-wide disruption is less severe.

In contrast, the robustness curves for the knowledge network remain largely unaffected by the failure threshold parameter. This is an expected result, as θ governs the cascade from knowledge to collaboration, not the direct impact of attacks on the knowledge layer itself. The stability of the knowledge network’s decay curves across all threshold values reinforces the validity of the underlying attack simulations. While the precise rate of the collaboration network’s collapse is dependent on the chosen threshold, the fundamental finding of the system’s profound vulnerability to knowledge layer attacks holds true across all tested parameter values. The severe, asymmetric impact, where disruptions to the knowledge layer trigger catastrophic failures in the collaboration layer, is a robust feature of the system’s dynamics.

Dynamic analysis of network structures

Our main analysis treats the three time periods as independent snapshots. This comparative static approach is informative but does not capture the continuous evolution of innovation networks. To address this, we developed a dynamic validation framework to test if our findings are robust against plausible network changes, such as those driven by learning and adaptation.

The validation method uses the empirical 2013–2018 collaboration network as a starting point. We then simulated minor structural changes using two established mechanisms: Preferential Attachment and Triadic Closure.^34,35 Preferential Attachment models the tendency for new ties to form around already well-connected entities, while Triadic Closure models the densification of clusters as partners of a common partner connect directly. For each mechanism, we generated an ensemble of 100 “evolved” networks by rewiring 5% of the original network’s edges. Finally, we applied our three attack scenarios to the original network and all 200 evolved networks to compare their robustness.

Figure 9 presents the results of this validation. It compares the robustness score of the original network (red star) with the distribution of scores from the evolved networks (boxplots). The analysis reveals that the effect of network evolution on vulnerability depends heavily on the type of attack. First, the validation confirms our static assessment against random shocks. As shown in Figure 9, the original network’s robustness score consistently falls within the typical range of the evolved networks under random attacks. This indicates that resilience to non-specific failures is a stable property of the network, not significantly altered by minor evolutionary changes.

Figure 9.

Validation of robustness assessment using dynamic network simulation

This figure illustrates the use of different dynamic network simulations to validate the robustness of the framework. Data are represented as mean values from simulation results.

In contrast, a different pattern emerges for targeted attacks. The original network is consistently less robust to degree-based attacks than the evolved networks. This suggests that common topological evolution processes, such as increased redundancy from Triadic Closure or diversified connectivity from Preferential Attachment, naturally generate structures that are more resilient against attacks on core nodes. Most notably, the results reveal a critical trade-off when considering classification-based attacks. Here, the original network is significantly more robust than the evolved networks. This finding suggests that purely topological evolution, which is blind to the knowledge content of nodes, can degrade resilience to domain-specific shocks. By optimizing for connectivity alone, these mechanisms may create vulnerable concentrations of knowledge. The superior performance of the real-world network suggests it was shaped by forces that balance both structural efficiency and functional diversity.

Cross-regional generality analysis

To test the cross-regional generality of our multilayer vulnerability framework, we extend the analysis beyond a single national context. We selected patent data for Japan and the United States in the Himmpat database, which are two of the world’s five largest intellectual property offices, and constructed their respective two-layer innovation networks for the 2013–2018 period. By comparing the vulnerability patterns of these three major digital economies, we can assess whether the identified mechanisms are unique to one country or represent more general features of multilayer innovation systems. The comparative results for collaboration and knowledge network attacks are presented in Figures 10 and 11.

Figure 10.

Cross-regional comparison of robustness under collaboration network attacks

This image illustrates changes in the robustness of networks from different countries under collaboration network attacks. Data are represented as mean values from simulation results.

Figure 11.

Cross-regional comparison of robustness under knowledge network attacks

This image illustrates changes in the robustness of networks from different countries under knowledge network attacks. Data are represented as mean values from simulation results.

The analysis of attacks on the collaboration network (Figure 10) confirms the general applicability of the framework. While minor variations in resilience levels exist, the innovation systems of all three countries exhibit a shared, extreme vulnerability to targeted attacks (degree-based and innovative capacity-based). In all cases, the collaboration layers collapse rapidly after the removal of just a few central nodes. This result demonstrates that the principle of high vulnerability to targeted attacks on key collaborative entities is a general and critical feature of these systems, validating our framework’s ability to identify this core risk.

The comparison under knowledge network attacks (Figure 11) provides even stronger evidence for the framework’s generality. Critically, the fundamental finding of asymmetric vulnerability, that is, attacks on the knowledge layer induce severe, systemic collapse, holds true for all three countries. The catastrophic impact of degree-based attacks on both the knowledge and collaboration layers is a universal feature across these distinct national ecosystems, reinforcing the foundational role of key knowledge elements. Although the precise decay rates under random and classification-based attacks show some regional variation, the overarching pattern of the knowledge layer serving as the critical foundation of the entire system remains consistent.

In conclusion, this cross-regional analysis strongly supports the general validity of our multilayer vulnerability framework. Despite differences in their specific industrial structures, the innovation ecosystems of China, Japan, and the United States all exhibit the same fundamental vulnerability patterns when analyzed through our framework. Core findings such as the critical role of the knowledge layer, the disproportionate threat posed by targeted attacks, and the existence of asymmetric cascade failures are not idiosyncratic to a single country but appear to be general principles governing mature digital innovation ecosystems. This demonstrates the framework’s effectiveness as a robust tool for analyzing systemic risks in multilayer innovation networks across different national contexts.

Discussion and conclusion

Discussion

Our findings reveal critical insights into the structural dynamics and vulnerability patterns within multilayer digital economy innovation ecosystems, providing theoretical foundations for comprehensive vulnerability assessment frameworks. Specifically, our results offer a quantitative validation of core tenets from multilayer network theory, while also extending these concepts to the specific domain of innovation systems. The observed asymmetric robustness profiles between collaboration and knowledge networks align with theoretical perspectives on multilayer network interdependence³⁶ particularly the theories of cascading failures in interdependent networks developed by Buldyrev et al.³⁷ and further elaborated by Gao et al.³⁸ Our work extends understanding of how innovation systems specifically demonstrate layer-specific vulnerability patterns grounded in their unique coupling characteristics.

The dramatic vulnerability of collaboration networks to targeted attacks, wherein removing merely 10% of high-degree nodes resulted in over 80% connectivity disruption, empirically validates the characteristic vulnerability of scale-free networks as theorized by Barabási and Albert.³⁴ However, within a multilayer context, this fragility is significantly amplified. Established theory on interdependent networks predicts that when a node in one network fails, it can trigger the failure of dependent nodes in another network, leading to a cascade of failures that can result in an abrupt, first-order phase transition and complete system collapse.³⁶ Our findings suggest that the collaboration network acts as the primary initiator of such cascades under targeted attacks. This is because the failure of a collaborative hub (e.g., a major company or research institution) not only fragments the collaboration layer but also removes the functional support for all knowledge nodes exclusively linked to that hub. This initiates a feedback loop of failures that is far more destructive than what would be observed in a single-layer analysis. From a structural perspective, this pronounced fragility stems from the inherent architecture of patent collaboration networks, where co-application relationships create concentrated connectivity patterns with relatively few alternative pathways. When key collaborative entities are removed, entire clusters of innovation actors become disconnected because collaboration requires direct, active partnerships that cannot be easily substituted. This principle extends to other innovation-driving ecosystems, such as venture capital, where the network position of central institutions is a critical conduit for knowledge spillovers and resource allocation that fuel green technology innovation.¹⁵

Real-world evidence of this vulnerability is demonstrated in cases where regulatory restrictions on specific companies' collaborative activities have rapidly disrupted entire innovation consortiums, such as restrictions on Huawei’s partnerships that immediately severed multiple collaborative research projects across the telecommunications sector.³⁹ This substantiates the proposition that innovation networks typically evolve through preferential attachment mechanisms, simultaneously generating both efficiency advantages and critical vulnerability points characteristic of digital economy innovation systems. The collaboration layer’s pronounced fragility exemplifies the “robust-yet-fragile” paradigm characteristic of complex socio-economic systems,⁴⁰ highlighting how structural properties create latent vulnerabilities that manifest under pressure, whether from targeted disruptions or external environmental shocks like extreme weather events that have been shown to inhibit firms' innovation persistence.^41,42

Conversely, the knowledge network’s significantly higher resilience, particularly evident during the maturity period (2019–2023), indicates evolution toward enhanced structural redundancy and technological robustness. Theoretically, the resilience of the knowledge layer can be explained by its different network topology and the nature of its interlayer coupling. Unlike the sparse, hub-and-spoke structure of collaboration, knowledge networks often exhibit a more distributed, clustered topology where knowledge is replicated and shared across multiple actors.³⁵ This creates inherent redundancy. Structurally, knowledge networks constructed from patent technological similarity exhibit dense interconnectedness where multiple entities possess related technological capabilities, creating redundant pathways for knowledge diffusion. This structural redundancy means that removing specific knowledge nodes has limited impact because alternative knowledge carriers with similar technological profiles maintain system connectivity. This resilience reflects the distributed nature of technological knowledge, which can be embedded across multiple entities and domains. Empirical evidence of this resilience is observed in quantum computing development, where despite restrictions on international research collaborations, domestic knowledge networks have maintained functionality through independent parallel development efforts across multiple research institutions.⁴³ The observed divergence between knowledge classification-based and degree-based attack impacts in later developmental periods further suggests progressive technological domain specialization while maintaining substantial cross-domain knowledge integration potential. This may represent a characteristic of maturing digital innovation ecosystems globally.

Real-world cases from various digital economy contexts illustrate these theoretical insights. For example, in the semiconductor sector amid technological competition, despite comprehensive export controls specifically targeting collaboration networks through restrictions on interactions between firms and advanced manufacturers, knowledge networks have demonstrated remarkable resilience through accelerated domestic capacity building and development of alternative technological pathways.⁴⁴ This empirical pattern precisely exemplifies our central finding that knowledge networks can maintain substantial functionality even when corresponding collaboration networks experience severe targeted disruptions.

Our study provides additional insights into the existing literature on the robustness of innovation networks. Zhao et al.²⁷ modeled the robustness of Chinese electric vehicle knowledge networks under targeted attacks and found that targeted attacks can cause significant damage to knowledge networks. They also found that knowledge networks at different stages of development are affected by malicious attacks to different degrees.²⁶ Our study extends their single-layer network framework and finds that the damage is not limited to knowledge networks, but is even greater for collaboration networks, a finding that highlights the critical importance of incorporating multilayer perspectives to avoid underestimating systemic risk.

A fundamental contribution of our vulnerability assessment framework lies in quantifying the asymmetric cascading effects between innovation network layers. This asymmetry is a key phenomenon in multilayer systems, often stemming from non-identical interlayer degree correlations and asymmetric dependency relationships.^45,46 Recent theoretical work further suggests that the strength of these asymmetric couplings is critical: strong, rigid dependencies heighten vulnerability, whereas a higher proportion of weak couplings can act as a buffering mechanism that disperses the impact of cascading failures and enhances overall system robustness.⁴⁷ Our simulation results demonstrate that, when collaboration networks suffered targeted attacks, knowledge networks maintained moderate functionality until approximately 20% of critical collaboration nodes were removed. In contrast, attacks on the knowledge network triggered immediate and severe disruptions that propagated rapidly across both network layers. This pronounced asymmetry validates the foundational role that technological knowledge plays in sustaining entire innovation ecosystems, aligning with established theoretical perspectives that posit that shared knowledge bases constitute the fundamental integration mechanism within innovation systems.⁴⁸ Theoretically, this suggests an asymmetric dependency structure: a collaboration entity is existentially dependent on its underlying knowledge base, whereas a knowledge concept is supported by, but not absolutely dependent on, a single collaborative entity. When a core knowledge node is removed, all collaborating entities that rely solely on that knowledge fail, triggering a catastrophic cascade that immediately impacts the collaboration layer. This powerful, unidirectional dependency explains the severe, system-wide impact of knowledge network disruptions. This finding corroborates research from other domains, such as energy systems, where enhanced innovation capacity has been empirically identified as a primary mechanism for strengthening systemic resilience, reinforcing the conclusion that the knowledge base is a critical foundation for the adaptability and stability of complex systems.¹⁶

The temporal evolution of these cascade effects substantially enriches theoretical understanding of multilayer innovation network dynamics. The progressively strengthening interdependence across developmental periods, particularly the intensified vulnerability transfer from knowledge to collaboration networks during the maturity period (2019–2023), empirically demonstrates accelerating technological specialization within digital economy industries. Moreover, our finding that knowledge classification-based attacks grew increasingly disruptive over time provides compelling evidence of heightened technological stratification within the innovation ecosystem, wherein specific technological domains have become disproportionately central to system-wide innovation activities and value creation processes.

Strategic cases from emerging technology development provide compelling illustrations of this asymmetric vulnerability phenomenon. Substantial investments in quantum information science have systematically established robust knowledge foundations that demonstrate resilience despite increasingly stringent restrictions on international research collaborations.⁴⁹ Conversely, when comprehensive restrictions are implemented on access to critical technological knowledge domains through targeted export controls on advanced manufacturing equipment, the resulting cascade effects propagate rapidly through multiple interconnected layers of innovation networks, disrupting both knowledge development trajectories and collaborative arrangements across numerous dependent technological sectors.⁵⁰ These patterns suggest universal principles of multilayer vulnerability that extend beyond specific geographic or institutional contexts, aligning with broader assessments that find the overall resilience of regional innovation ecosystems to be a critical yet often underdeveloped area requiring policy intervention.⁵¹ Furthermore, our framework contributes to vulnerability assessment methodology by employing multiple metrics (including network efficiency), a practice supported by recent studies that caution that relying solely on the size of the largest connected component can mask underlying fragilities in network integrity.⁵²

Conclusion

As digital economies become increasingly interconnected and complex globally, understanding the vulnerability patterns of multilayer innovation networks has become critical for sustainable technological development. This study develops and validates a comprehensive framework for multilayer innovation network vulnerability assessment, using China’s digital economy industries as an empirical testing ground. Through comprehensive patent data analysis, we constructed a coupled two-layer network structure: (1) a collaboration network based on patent co-application relationships and (2) a knowledge network based on knowledge element co-occurrences. We systematically analyzed vulnerability patterns across three developmental periods using our framework’s network-based robustness measurement techniques, employing four distinct assessment scenarios and six targeted attack strategies.

Our empirical validation reveals significant structural transformation patterns in multilayer innovation networks over time, characterized by dramatic increases in scale and interconnectedness that parallel digital economy industry maturation. Most significantly, we identified asymmetric robustness profiles between the two layers: the collaboration network exhibited extreme vulnerability to targeted attacks, whereas the knowledge network demonstrated considerably higher resilience, particularly during the mature development period. This structural asymmetry was further illuminated through our cascade failure analysis, which revealed that disruptions to knowledge networks propagate severe effects across both layers, while collaboration network disruptions generate more limited cross-layer impacts.

This research makes several theoretical and methodological contributions to multilayer innovation network analysis and vulnerability assessment. First, we advance methodological approaches by developing a framework that constructs empirically grounded coupled innovation networks based on comprehensive patent data from digital economy industries. Unlike previous studies that rely predominantly on abstract simulations using small-world or scale-free network models, our approach captures the actual structural complexities and evolutionary dynamics of real-world innovation ecosystems, thereby substantially enhancing both theoretical validity and practical relevance.

Second, we develop contextually embedded attack strategies and realistic scenario simulations that substantially advance the existing vulnerability assessment literature. Previous innovation network studies have typically employed generic node removal strategies divorced from real-world contexts. In contrast, our attack strategies and four scenario simulations explicitly correspond to realistic innovation system perturbations, including export restrictions on semiconductor technologies, market withdrawals of key partner entities, and targeted restrictions on specific technology areas. This real-world methodological approach facilitates deeper understanding of vulnerability patterns compared to traditional theoretical analyses, enabling more precise identification of critical nodes whose failure would trigger catastrophic cascading impacts throughout innovation ecosystems.

Third, we reveal practical cascade failure mechanisms that demonstrate how disruptions propagate between collaboration and knowledge networks in real innovation systems. While previous research typically examined innovation networks as isolated systems, our integrated approach demonstrates how perturbations in one subsystem generate multifaceted impacts across the entire innovation ecosystem. Our analysis reveals a critical asymmetry with broad theoretical implications: when key knowledge elements are disrupted, both knowledge structures and collaborative relationships suffer severe degradation; conversely, when collaborative relationships are disrupted, knowledge bases demonstrate substantially greater resilience. This finding yields direct practical implications for innovation policy across diverse digital economy contexts, suggesting that protecting critical technological knowledge should take priority over maintaining specific collaborative arrangements when resources are limited. For regions facing technological competition or restrictions, strategic investment in knowledge foundation development offers superior long-term resilience compared with policies primarily focused on collaborative network building.

Policy implication

Our findings yield significant implications for innovation policy and strategic management within digital economy contexts globally. First, the high vulnerability of collaboration networks to targeted disruptions indicates that policymakers should prioritize fostering redundant collaborative pathways rather than merely maximizing network density. Implementing incentives for diverse partnership formation, particularly involving peripheral actors, could enhance system-wide resilience by reducing dependency on keystone collaborators. Second, the foundational role of knowledge networks revealed through our cascade failure analysis demonstrates that protecting and nurturing critical technological knowledge domains should constitute a primary focus in innovation policy frameworks across digital economy contexts. Third, the increasing interdependence between collaboration and knowledge layers over time necessitates that innovation policies adopt holistic, integrated perspectives rather than addressing technological development and collaborative innovation as separate domains. Supporting initiatives that simultaneously enhance knowledge creation and collaborative capacity building would generate greater systemic benefits compared with isolated interventions in either domain.

Strategic approaches to AI development in various national contexts exemplify these principles in practice. Comprehensive policy frameworks that strategically promote industry agglomeration through coordinated governmental action demonstrate effective implementation of our vulnerability assessment insights. For instance, the cultivation of specialized enterprises through targeted support programs, combined with robust local knowledge base development through coordinated investment initiatives, illustrates how protecting knowledge foundations while building collaborative capacity can enhance innovation ecosystem resilience.⁵³ These examples demonstrate the practical applicability of our framework across diverse institutional and policy contexts.

Limitations of the study

While our framework provides valuable insights into multilayer innovation network dynamics, several limitations suggest promising avenues for future research and framework enhancement. First, our analysis relies primarily on patent data, which effectively captures formalized innovation activities but may under-represent informal innovation and the broader innovation ecosystem context. Future framework development should integrate complementary data sources to more carefully characterize the innovation ecosystems in which innovation agents are embedded, such as energy and environmental systems, to develop a more comprehensive multilayer network characterization. Second, our attack simulations focused exclusively on node removal rather than edge disruption mechanisms. Future research could systematically investigate how the targeted removal of specific collaborative ties or knowledge connections, rather than entire nodes, affects system-wide resilience. This refined methodological approach would more accurately simulate realistic disruptions such as partnership dissolutions, knowledge transfer restrictions, or technological obsolescence within innovation ecosystems, further enhancing the framework’s practical applicability across diverse digital economy contexts. Third, our cascade failure model relies on a deterministic, threshold-based rule. While our sensitivity analysis confirms our findings are robust across a range of thresholds, this approach simplifies the complex processes of knowledge persistence. Future work could incorporate stochastic failure models to more accurately capture the probabilistic nature of how innovation entities withstand the loss of specific knowledge assets.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Rongkai Chen (rongkaichen@ruc.edu.cn).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •All the data and information are within the manuscript.
• •All original code has been deposited at Zenodo and is publicly available at Zenodo: https://doi.org/10.5281/zenodo.15776326 as of the date of publication.
• •Any additional information required to reanalyze the data reported in this study is available from the lead contact upon request.

Acknowledgments

This work was supported by the National Social Science Fund Project of China (No. 23BGL026).

Author contributions

Conceptualization: H.Z. and R.C.; Writing-original draft: H.Z. and R.C.; Investigation: H.Z. and H.L.; Methodology: H.Z.; Writing - review and editing: H.Z.; Supervision: H.L. and R.C.; Project administration: H.L. and R.C.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Patent data	Himmpat database	https://www.himmpat.com/
Software and algorithms
Python	Python 3.9	https://www.python.org/
Gephi	Gephi 0.10.1	https://gephi.org/
The code to analyze the data is available at Zenodo: https://doi.org/10.5281/zenodo.15776326	–	https://doi.org/10.5281/zenodo.15776326

Method details

Data description

Patent data are widely used to measure innovation and to gauge innovation linkages. Joint patent applications demonstrate collaborative relationships among innovation participants and are detailed and timely evidence of collaborative innovation. Therefore, this study utilizes joint patent application data to construct multilayer innovation networks for developing and testing our vulnerability assessment framework, using China’s digital economy industry as the empirical context. We used patent data from the Himmpat database, a database of publicly available commercial patents containing more than 200 million patents around the world. Database access was conducted between March 12-19, 2025, ensuring data consistency and completeness for our analytical timeframe.

For specific extraction criteria, the first step is to identify the most relevant patents to China’s digital economy industry. The Digital Economy Core Industry Classification and International Patent Classification Reference Relationship Directory (2023) published by the State Intellectual Property Office of China provide valuable CNIPA.⁵⁴ It categorizes digital economy industries into four categories and establishes International Patent Classification (IPC) references for 15 intermediate categories and 86 subcategories within these four categories. Since this catalog is used for various digital economy industry measurements and statistics in China, and is widely used by the central and local levels of government, we used the directory to identify the required IPC codes for the 86 subcategories, and used these codes to search for patents in the Himmpat database.

We then identified 2004-2023 as the period for data retrieval. The selection of the 2004-2023 timeframe is grounded in both policy evolution and data availability patterns. Although China connected to the international internet in 1994, the period from 2004 onwards represents the high-speed growth phase of internet development. Notably, in January 2005, the State Council issued “Several Opinions on Accelerating E-commerce Development,” China’s first policy document specifically guiding e-commerce development, which established the guiding principles and six major initiatives for promoting e-commerce. This marked the beginning of systematic policy support for internet development. Subsequently, the government introduced various regulations to promote e-commerce growth. Industries related to the digital economy, although not clearly defined at the time, began to grow and evolved into key catalysts for social and economic transformation.⁵⁵ From a data perspective, we observe that the number of joint patent applications matching the 86 subcategory IPC codes was only 129 in 2004, representing the initial phase of such patent applications. Then, the number exceeded 1,000 by 2008 and 10,000 by 2014, showing an exponential growth pattern. Thus, 2004 approximates the actual starting point for such patents, capturing the complete evolution from emerging collaborative innovation to mature ecosystem development. The timeframe concludes in 2023 rather than extending to more recent years due to the inherent publication lag in patent systems, where patent applications typically require approximately three years from filing to public disclosure.

Our extraction criteria followed a systematic three-stage process: (1) Primary filtering based on IPC codes corresponding to the 86 subcategories within four main digital economy categories in the selected timeframe; (2) Secondary screening to ensure that the number of patent applicants is greater than or equal to two and includes at least one Chinese entity; (3) Tertiary validation to confirm patent relevance through keyword matching with digital economy terminology. We excluded utility model patents and design patents because invention patents undergo more rigorous examination processes and better reflect substantial technological innovations rather than incremental improvements. Patents with incomplete bibliographic information were excluded through systematic filtering: missing applicant information and absent or incomplete IPC classification were removed to ensure network construction accuracy. Finally, patent data with complete bibliographic information were obtained in plaintext format. After screening, a total of 126,529 patents were finally eligible and included in the subsequent network construction.

Two-layer network construction

Innovation processes in digital economy industries are simultaneously embedded in both knowledge and collaboration contexts,^56,57 requiring a sophisticated multilayer network approach to capture their complex interactions and enable comprehensive vulnerability assessment. To address this dual embedding nature, we construct a coupled collaboration-knowledge two-layer network using patent data from digital economy industries. The collaboration network represents interactions between innovating entities, where nodes are patent applicants (individuals, firms, research institutions, and universities), and edges denote co-application relationships established when two or more applicants jointly file a patent.

Complementary to the collaboration layer, we establish a knowledge network that captures the technological structure underlying digital innovations. In this layer, nodes represent knowledge elements defined by the first four positions of the IPC codes (e.g., G06F), which provide standardized categorization of technological domains at the subclass level. Following established approaches in innovation studies,^58,59 we create intra-layer connections based on the co-occurrence of these knowledge elements across different patents, indicating technological proximity or complementarity between knowledge components.

The coupling between these two network layers is established through the correspondence between patent applicants and the knowledge elements they utilize. Specifically, we create inter-layer edges when an applicant in the collaboration layer employs a specific knowledge element (four-digit IPC code) in the knowledge layer. This network construction process provides the empirical foundation for our multilayer vulnerability assessment framework, as shown in Figure S1. Figure S1A represents the two-layer network structure, Figure S1B illustrates the construction process of the knowledge network, and Figure S1C shows the real structure of the two-layer digital innovation network that we constructed. The network data were processed in Python software and subsequently visualized by Gephi software.

Measurement of robustness

Network robustness is a critical property that reflects a system’s ability to maintain its structural integrity and functional performance when subjected to various perturbations or attacks.^4,60 In this study, we evaluate the robustness of digital economy innovation networks through two complementary dimensions as core components of our vulnerability assessment framework: structural robustness and functional robustness.²⁷ Our selection of these specific quantitative metrics is grounded in established innovation network research literature that has validated these indicators for assessing collaborative network integrity and knowledge diffusion capacity in innovation ecosystems.

Structural robustness measures the network’s ability to maintain connectivity when nodes are removed, which is particularly important in understanding how innovation networks respond to the departure of key actors or knowledge components.⁵ This metric has been extensively employed in innovation network studies to assess the vulnerability of collaborative relationships and the persistence of innovation ecosystem connectivity under various disruption scenarios.⁶¹ We quantify structural robustness using the relative size of the maximal connected subgraph (also known as the giant component) after node removal:

$$R_S\left(q\right)=\frac{N^{\prime }\left(q\right)}{N}$$

where $N^{\prime }\left(q\right)$ represents the size of the maximal connected subgraph after removing a fraction $q$ of nodes, and $N$ is the original number of nodes in the network. As nodes are progressively removed according to different attack strategies, the value of $R_S\left(q\right)$ decreases, with a more gradual decline indicating greater structural robustness. This indicator effectively captures the fragmentation patterns of innovation networks and provides quantitative assessment of how collaborative relationships deteriorate under targeted or random disruptions.

While structural robustness captures the network’s connectivity, functional robustness addresses the efficiency of information or knowledge flow through the network, which is crucial for understanding innovation diffusion capacity.²⁷ Prior innovation network research has demonstrated that network efficiency serves as a critical indicator of knowledge transfer effectiveness and innovation ecosystem performance, making it an appropriate metric for assessing functional vulnerability.⁶² We measure functional robustness using network efficiency,⁶³ which evaluates how efficiently nodes can communicate across the network:

$$E=\frac{1}{N\left(N-1\right)}\sum _{i\ne j}\frac{1}{d_{ij}}$$

where $d_{ij}$ is the shortest path length between nodes $i$ and $j$. When nodes are removed, the network efficiency typically decreases as paths become longer or disconnected. We quantify functional robustness as the relative efficiency after node removal:

$$R_F\left(q\right)=\frac{E\left(q\right)}{E\left(0\right)}$$

where $E\left(q\right)$ is the network efficiency after removing a fraction $q$ of nodes, and $E\left(0\right)$ is the initial network efficiency. This metric provides quantitative assessment of how innovation networks maintain their diffusion capabilities under various attack scenarios, complementing structural robustness measures by capturing performance degradation beyond simple connectivity loss.

Cascade failure mechanism

The robustness of multilayer networks is significantly influenced by interdependencies between layers, which can lead to cascade failures where disruptions in one layer propagate to another. Understanding these cascade mechanisms is essential for comprehensive vulnerability assessment in digital innovation systems. For our two-layer digital innovation network, we design two directional cascade failure mechanisms to simulate real-world innovation system vulnerabilities.

We define the cascade failure mechanism in terms of both bottom-up and top-down mechanisms:

First, we implement a bottom-up mechanism where the failure of innovation entities in the collaboration network leads to the failure of their associated knowledge elements in the knowledge network (as illustrated in Figure S2A). The failure propagation follows a deterministic rule: when an innovation entity $i$ fails in the collaboration network, all knowledge elements $k$ that are exclusively connected to entity$i$ immediately fail in the knowledge network. This mechanism simulates realistic scenarios where organizational failures directly eliminate proprietary technologies from the innovation ecosystem. Real-world examples include recent semiconductor company bankruptcies such as Japan’s JS Foundry in 2024, which specialized in power semiconductor production and whose bankruptcy resulted in the loss of related proprietary technologies and production capabilities. Similarly, when research teams disband due to funding cuts or institutional restructuring, specialized knowledge that exists only within those teams becomes inaccessible to the broader innovation community. When an innovation entity fails, all knowledge elements exclusively connected to that entity also fail, while knowledge elements shared across multiple entities remain active in the system.

Second, we establish an up-down mechanism where failures in the knowledge network can trigger failures of innovation entities in the collaboration network (as illustrated in Figure S2B). This mechanism employs a threshold-based failure rule where an innovation entity $i$ fails when the proportion of its associated knowledge elements that have failed exceeds a critical threshold $\theta$:

$$Fi=1,if\frac{\left(\sum kFk\times Aik\right)}{\left(\sum kAik\right)}>\theta$$

$$Fi=0,otherwise$$

where $Fk$ represents the failure state of knowledge element $k$ (1 = failed, 0 = active), $Aik$ represents the connection between entity $i$ and knowledge element $k$ in the bipartite network, and $\theta$ is the failure threshold parameter. This reflects situations where technological obsolescence or access restrictions to critical knowledge components can compromise the viability of entities heavily dependent on those technologies. For instance, export controls restricting access to advanced semiconductor manufacturing equipment and associated technical knowledge have forced companies to adopt less efficient alternatives. Since 2019, ASML has been prohibited from selling advanced EUV equipment to China under U.S. pressure, forcing Chinese companies like SMIC to rely on more costly and less efficient methods such as double patterning techniques to achieve advanced process nodes. This technological knowledge restriction has significantly impacted the operational capabilities of entities heavily dependent on these technologies.

We assess cascade severity by measuring the change in network robustness metrics before and after cascade propagation. Specifically, we compare the structural robustness $R_S\left(q\right)$ and functional robustness $R_F\left(q\right)$ of both network layers after the initial attack versus after cascade completion. The magnitude of additional robustness loss due to cascade effects quantifies the severity of cross-layer failure propagation, enabling systematic comparison of cascade impacts across different attack scenarios and threshold parameters. These cascade failure mechanisms enable us to simulate how perturbations propagate through the coupled innovation system and to identify critical vulnerabilities where targeted disruptions could trigger widespread system failures.

Attack strategies and scenario design

To comprehensively evaluate multilayer network robustness within our vulnerability assessment framework, we implement distinct node removal strategies for each network layer, each simulating specific real-world scenarios in digital innovation ecosystems.

Collaboration network attack strategies

• 1.Random attacks: Nodes are removed randomly, simulating the natural attrition or random exit of innovators from the ecosystem. This represents unpredictable events such as personnel turnover, company closures due to market fluctuations, or retirement of key researchers.
• 2.Degree-based attacks: Nodes are removed in descending order of their degree centrality. This simulates disruptions to key collaborative entities, such as when major digital corporations face mergers, acquisitions, or market exits. A real-world example is the global financial crisis of 2008, which led to the collapse of several highly connected financial technology firms that maintained extensive collaboration networks in digital payment innovations.
• 3.Innovative capacity-based attacks: Nodes are removed based on their innovative capacity, which we operationalize as the total number of patent applications filed by each innovation entity. This strategy is designed to simulate targeted attacks on the functional core of the innovation ecosystem, i.e., its most productive and influential innovators.

The theoretical justification for this approach is rooted in foundational management and innovation theories. From the perspective of the Resource-Based View (RBV), patents are tangible outcomes of a firm’s critical intangible resources, such as technological knowledge and R&D capabilities, which are central to its competitive advantage. Furthermore, Schumpeterian innovation theory posits that highly innovative firms drive economic progress through “creative destruction.” Therefore, targeting entities with high patent output simulates a direct assault on the ecosystem’s primary drivers of technological advancement.

Our operationalization of innovative capacity via patent counts is a well-established and validated proxy in innovation economics literature as reliable indicators of an organization’s research productivity and technological capabilities.^64,65 The validity of this proxy is supported by two key arguments. First, patent applications represent formal documentation of novel technological solutions, requiring substantial R&D investment and technical expertise to develop. Second, the patent application process involves rigorous novelty assessments, ensuring that counted innovations meet minimum standards for technological advancement. Consequently, this attack strategy simulates scenarios where highly productive entities face targeted restrictions or resource constraints that impair their innovative capabilities. Real-world examples include targeted sanctions against leading technology companies, which significantly impair their ability to access critical components and technologies necessary for continued innovation.^11,66 Companies like Huawei, previously among major patent applicants, experienced substantial challenges in maintaining their innovation momentum following these restrictions,⁶⁷ demonstrating how targeting functionally core entities can impact innovation networks.

Knowledge network attack strategies

• 1.Random attacks: Knowledge elements are removed randomly. This simulates the unpredictable obsolescence of technological components or the random abandonment of certain knowledge domains due to shifting market demands.
• 2.Degree-based attacks: Knowledge elements are removed in order of their degree centrality. This represents scenarios where core technological foundations face disruption. A prominent real-world example is export controls on advanced semiconductor technologies, which restricted access to critical foundational technologies that were highly connected to numerous other knowledge domains in digital innovation networks. The impact of these restrictions on key chip manufacturing technologies, particularly in advanced nodes below 14 nm, illustrates how removing highly-connected knowledge nodes can impair multiple innovation pathways simultaneously across AI, telecommunications, and high-performance computing sectors.⁶⁸
• 3.Knowledge classification-based attacks: Knowledge elements are removed according to their hierarchical classification. This strategy simulates a critical and fundamentally different class of vulnerability: systematic, domain-specific disruptions. This approach is not only justified from a macro-level perspective of strategic competition, but is also strongly grounded in the micro-level characteristics of the knowledge elements (IPC codes) themselves.

The theoretical justification rests on the fact that the International Patent Classification (IPC) system is not an arbitrary set of labels. Instead, it is a structured taxonomy that reflects technological proximity, complementarity, and dependence. Knowledge elements sharing the same IPC class (e.g., all codes starting with 'G06F' for Digital Data Processing) represent a coherent body of synergistic knowledge. Innovation within a specific domain, such as developing a new computer, requires the integration of multiple, complementary technologies from this shared knowledge base (e.g., processing, input or output, memory). Therefore, removing nodes based on their classification is not a random act, it is a targeted attack on a complete “technological toolkit” necessary for innovation within that specific paradigm.

This approach is fundamentally different from a degree-based attack. A degree-based attack removes central nodes regardless of their technological domain, simulating a disruption to the network’s overall structural integrity. In contrast, a classification-based attack leverages the intrinsic logic of the knowledge structure itself. It simulates the crippling of an entire innovation pathway by removing a whole cluster of related and often mutually reinforcing knowledge components. This captures a more sophisticated threat where the objective is not just to remove the most connected components, but to dismantle the entire knowledge foundation of a specific technological capability.

A notable example is targeted restrictions on access to quantum computing and artificial intelligence technologies through measures such as the U.S. CHIPS and Science Act and related export controls implemented in 2022-2023.^69,70 Unlike semiconductor manufacturing restrictions that targeted highly-connected nodes, these measures specifically targeted entire classifications of emerging technologies by controlling access to both hardware and software components within specific IPC classifications related to quantum information science and AI model development. The logic behind these policies precisely mirrors our attack strategy: policymakers understand that strategic technologies are not built on a few central patents, but on a comprehensive and interdependent knowledge ecosystem. This case illustrates how policy interventions targeting entire technological domains based on their classification can systematically impact innovation capabilities in strategic technologies.

Scenario design

Based on these attack strategies, we design four comprehensive scenarios within our vulnerability assessment framework to examine robustness from multiple perspectives:

Scenario 1

Single-layer collaboration network vulnerability assessment. In this scenario, we focus exclusively on the collaboration network layer, applying three attack strategies (random, degree-based, and innovative capacity-based) to assess how the structural and functional robustness of the collaboration network changes when subjected to different types of perturbations.

Scenario 2

Single-layer knowledge network vulnerability assessment. This scenario examines the knowledge network layer in isolation, applying random attacks, degree-based attacks, and knowledge classification-based attacks to evaluate the structural and functional robustness of the knowledge system. The results reveal which knowledge elements serve as critical foundations for the digital innovation landscape.

Scenario 3

Multilayer vulnerability assessment under collaboration network attacks. Moving beyond single-layer analysis, this scenario investigates how attacks on the collaboration network propagate through the coupled two-layer network system. By removing entities from the collaboration layer according to our three attack strategies and measuring the impact on both layers, we assess the interdependencies between collaborative relationships and knowledge structures in the digital innovation ecosystem.

Scenario 4

Multilayer vulnerability assessment under knowledge network attacks. In our final scenario, we examine how targeted removals of knowledge elements affect the coupled two-layer network system. This analysis reveals how disruptions to specific knowledge domains can cascade through the innovation ecosystem, potentially affecting collaborative structures even when the collaborative entities themselves remain intact.

Through these four complementary scenarios, our vulnerability assessment framework provides comprehensive evaluation of digital economy innovation networks' vulnerabilities and resilience mechanisms, accounting for both the individual characteristics of each network layer and the complex interactions between them.

Published: December 1, 2025