Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2019 Jul 23;9:10692. doi: 10.1038/s41598-019-47119-2

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

PMC Copyright notice

Robustness of seven real-world complex weighted networks under different strategies of nodes-links removals. The robustness of real-world complex weighted networks was analyzed under different nodes-links removals strategies and using different measures for the system functioning. (a) Efficiency of the system (Eff) as a function of the fraction of nodes or links removed (q). The network efficiency (Eff) decreases under nodes-links removal; in this example the red strategy produced a sharper decrease in the network efficiency meaning that is more harmful than the black strategy. (b) Example of the complex networks robustness (R) for the two strategies of nodes or links removal of the outcomes in (a). The robustness (R) of the removal strategy is the area below the curve produced by the removal strategy in (a). The robustness (R) produced by the removal strategy is normalized on the max value of the strategy robustness for that system functioning measurement; in this way we can easily compare the robustness of the network under different nodes-links removal strategies. (c,d) The real-world networks robustness (R) under different nodes-links removal strategies. (c) Links removal strategies. (d) Nodes removal strategies. Eff indicates the weighted system efficiency computed on the real-world networks; Eff_ran is the weighted efficiency computed on the real-world network after the randomization of the link weights, i.e. the real link weights are randomly re-assigned on the network links. LCC indicates the largest connected cluster in the network; LCC_ran is the largest connected cluster measurements computed on the real-world network after the randomization of the link weights; TF is the total flow in the network, i.e. the sum of the all link weights; TF_ran is the total flow on the real-world networks after the randomization of link weights. The random removal (Rand) and the randomized link weights network counterparts (LCC_ran, EFF_ran and TF_ran) outcomes are the average of 10⁴ simulations.