Table 2:

Structural covariance network studies on schizophrenia and related psychotic disorders that applied graph theoretic methods

Author	Sample size and goals of the study	Field strength/Acquisition scheme/Atlas used/Analysis software used	Methods	Main findings
Studies examining gray matter volume SCNs
Bassett et al. (2008)	203 chronic SZ patients and 259 HC. To identify commonalities and differences in network organization of the principal cortical divisions, namely unimodal, multimodal and transmodal (connectivity between unimodal and multimodal networks) cortices(connectivity between unimodal and multimodal networks) networks based on definitions by Mesulam (1998). Second goal was to assess whether these divisions are impacted by SZ.	T1-weighted MRI data from a 1.5 Tesla GE Signa scanner at 1.5 mm thick slices. SPM2 was used to preprocess the scans. Pick Atlas-defined 104 brain regions corresponding to the Brodmann areas + amygdala, hippocampus, striatum, and thalamus were grouped into 28 unimodal, 32 multimodal and 42 transmodal regions.	Partial correlation networks were constructed from residuals of brain regional volumes after regressing out age, sex, and total gray volumes. Fully connected networks over a pre-calculated small-worldness threshold range were examined. Networks examined at global, divisional, and regional scales. Network measures were averaged over the small worldness threshold range for the divisional and regional networks. Compared graph metrics with random networks.	Both HC and SZ networks showed degree distribution that followed exponential truncated power law, and fully connected networks within the cost range. HC showed hierarchical organization in the multimodal network only. Transmodal network was the only cortex that showed significant assortativity. Connection distance was the smallest for the transmodal, intermediate for the unimodal and greatest for the multimodal networks among HC. The right premotor cortex, orbitofrontal cortex, middle temporal cortex, retrosplenial, bilateral DLPFC, and insula were identified as hubs of the HC network by two of the four (degree or centrality) parameters considered. SZ patients showed qualitatively different hubs in the bilateral insula, right inferior temporal cortex, left premotor area, left temporopolar region, left pars opercularis, and right thalamus. less hierarchical multimodal network throughout the small world regime, and greater mean connectional distance of multimodal network compared to HC. No significant differences in in hierarchy, assortativity and connection distance in the unimodal and transmodal cortices. Clustering coefficient was different in 23 nodes at the regional level between SZ and HC.
Zugman et al. (2015)	Examined 143 chronic SZ, 32 first episode SZ and 82 HC. Examined a proposed paradox where structural disconnection may lead to reduced structural covariance whereas reduced volume due to the disease may result in increased covariance	1.5 Tesla Siemens scanner data on structural MRI with 1 mm slice thickness examined. GM volumes of DKT atlas based parcellations for 68 regions was used for SCN.	Integrity-closeness (absolute values of the correlation coefficient between two nodes) and connectivity-closeness (inverse of the absolute values of correlation coefficients between two nodes) were estimated for the groups	Integrity-closeness and connectivity closeness were negatively correlated as expected by their definitions. No significant difference in connectivity-closeness between groups Reduced integrity-closeness in pars orbitalis and insula in SZ compared to HC. Higher degree nodes in patients compared to controls. First episode cases did not differ from chronic schizophrenia.
Liu et al. (2019)	95 chronic SZ patients and 95 HC To identify voxel-level GM volume SCN differences between SZ and HC Whether these differences were related to SZ risk genes (not discussed in this review)	MRI data acquired at 3 Tesla GE scanner with a slice thickness of 1 mm. A GM mask of 32,164 voxels created with the removal of subcortical and cerebellar AAL regions removed. Software used for graph theoretic analysis not stated.	Voxelwise SCN was built using Pearson correlation tests after regressing out the effects of age, sex and ICV using linear regression. Structural covariance/connectivity strength for each voxel was calculated by the weighted sum of correlations r>0.2 with other voxels. Permutation test was used to compare the group level SCS False discovery rate correction was applied for multiple test correction	Degree centrality was the main measure used and structural hubs were also examined. Spatial distribution of high SCS was similar in both groups observed in the medial PFC, posterior cingulate cortex/cuneus, insula, and lateral PFC and temporal regions. SZ showed Increased structural covariance strength in the right orbital part of superior frontal gyrus and bilateral middle frontal gyrus and decreased SCS in the bilateral superior temporal gyrus and the precuneus. Validation with weighted network at raw resolution (1.5×1.5×1.5 mm3), weighted network with r=0.1 and r=0.3 and binarized network at a resolution of 3×3×3 mm3 did not alter the findings None of the genes survived multiple test corrections. A trend was noted for altered pattern of SCS correlation with expression of gene classes involved in therapeutic target and neurodevelopment
Palaniyappan et al. (2019)	41 chronic SZ and 40 HC The goal was to identify if the observed pattern of GM volume loss conforms to coordinated pattern of structural reorganization	MPRAGE data at 1 mm slice thickness acquired; field strength not provided. AAL-90 atlas for parcellation of regions. Graph theoretical approach using Graph Analysis Toolbox, a MATLAB package that integrates with the Brain Connectivity Toolbox.	Group level Pearson correlation matrix of residuals of volumes weighted for age, sex and ICV was generated. Range of density function cut off used (0.3 – 0.5 at increments of 0.025) 3 groups of graph measures examined: integration (shortest pathlength, characteristic pathlength and global efficiency), segregation (clustering coefficient, both local and global) and centrality (degree of a region or a node). Small world index calculated as a ratio of clustering coefficient to characteristic pathlength of the study network with that of the null network. Resilience of the network examined through random and targeted removal (“attack”) on nodes	SZ showed higher global clustering coefficient than HC. SZ connectome showed reduced resilience to targeted attack but not random attack relative to HC. A simulated removal of high centrality nodes resulted in significant loss of overall covariance pattern. Random attack led to ≈1.5% reduction in the greatest connected component (GCC) and global efficiency whereas targeted attack led to ≈10 times greater reduction in these measures in SZ SCN compared to HC SCN. Reduced local clustering coefficient in right middle temporal region, reduced local efficiency in right hippocampus and right ACC. Nodal degree reduced in right insula and left middle DLPFC. SZ had reduced centrality in ACC and insula but increased centrality in fusiform cortex. Hub regions were in the frontal lobe in both groups. Within the frontal region, ACC and gyrus rectus showed high degree in controls not patients. Among non-frontal hubs, insula was prominent in controls and fusiform in patients. Controls had 5 modules (fronto-insular, temporal, occipital, parietal and subcortical). SZ had 7 modules
Kuo et al. (2020)	26 chronic SZ, 30 MDD, 19 AD and 909 HC from 2 cohorts; 80 subjects were training subjects and 109 was the testing cohort. To estimate the brain aging profile in these disease states compared to HC using large-scale GM volume SCNs.	3D-MPRAGE data on Siemens 3 Tesla TIM Trio using 12-channel phased-array head coil for HC, SZ and MDD. Fast-SPGR data on GE 3 Tesla scanner with 8-channel phased-array head coil for AD patients. Multivariate ICA selected highly correlated GM voxel components. Various software platforms used: SPM8 and MELODIC on FSL.	Voxelwise GM volume maps were estimated followed by multivariate spatial independent component analysis (ICA) and estimated the network integrity index (β coefficients). Network integrity indices were used to construct brain age estimators at different ICA model orders. Multiple large SCNs were divided into distinct subnetwork systems after hierarchical clustering analysis: (1) the cerebellar and subcortical network system; (2) the posterior default-mode network, posterior fronto-parietal network, and motor network system; (3) visual network, salience network, anterior fronto-parietal network, and anterior default-mode network system; and (4) temporal network system.	Cerebellar and subcortical network system components played major role in brain age estimation. Brain age gap for the AD and the SZ group was significantly higher compared to the testing healthy control cohort. MDD subjects did not differ significantly from HC. Brain age gap did not correlate with cognitive performance among AD patients. Similarly, brain age gap did not correlate with cognitive, psychopathology severity scores and mood severity among SZ and MDD patients. SZ patients showed lower integrity index in hippocampus, posterior frontal parietal, visual, parietal operculum, and salience regions but higher integrity index in the caudate compared to controls. AD patients showed lower network integrity index in the hippocampus, posterior default mode network, posterior frontoparietal, visual, and parietal operculum regions and higher indices in the thalamus, posterior frontal parietal, and motor regions compared to controls. MDD patients showed lower indices in the hippocampus, thalamus, posterior frontal parietal, visual, parietal operculum, and salience network regions
Studies examining cortical thickness SCNs
Zhang et al. (2012)	101 chronic SZ and 101 HC. Goal was to examine topological organization of large-scale structural brain networks built using cortical thickness between SZ and HC.	1.5 Tesla MRI data with 1.5 mm slices were examined for cortical thickness measured using the Freesurfer. Regions were parcellated using Freesurfer based on the AAL atlas. 39 regions per hemisphere were labeled and extracted. Software used for network analysis not mentioned.	Partial correlation networks were constructed after regressing out the effects of age, gender, and brain volume. Pathlength, clustering coefficient, small worldness, and nodal centrality were calculated, and hubs were identified.	Betweenness centrality was reduced in primary, association cortices and increased centrality in primary and paralimbic cortices. Characteristic path length and clustering coefficient were higher in patients than in controls. Patients had altered small-worldness. Slightly higher number of hubs (17) were identified in patients compared to controls (13). Control hubs were mainly in the association cortex whereas patient hubs were distributed across primary, association and paralimbic cortices.
Wannan et al. (2019)	3 cohorts (FEP=70, HC=57; chronic SZ=153, HC=168; treatment resistant SZ=47, HC=54) To identify extent and location of cortical thickness differences among the groups Examine whether cortico-cortical connectivity inferred from SCN could explain topographic distribution of thickness changes	1.5 Tesla GE Signa-acquired T1-weighted images at 1.5 mm slice thickness. Freesurfer 5.1 package for chronic SZ, 5.3 for FEP and treatment-resistant SZ used for cortical thickness estimation. The Destriex atlas was used for cortical surface parcellation.	Pearson correlation matrix was built after regressing the covariates (age, agê2, sex, and acquisition site) Permutation tests used to compare the structural covariance within the regions with cortical thickness reduction and randomly selected regions. SCN in each patient group, control group and the differences between the groups were examined. Mean structural covariance of top regions that showed thickness reductions and random set of nodes was computed	34, 79, and 106 regions showed significant reductions in cortical thickness in the first-episode psychosis, chronic schizophrenia, and treatment-resistant schizophrenia groups. All 4 groups showed increased structural covariance for the SCN of regions with reduced cortical thickness. First episode SCN, but not chronic or treatment resistant SZ, showed significant covariance difference with HC, especially in the subnetwork comprising of temporal and frontal regions. Mean structural covariance for the top n regions that showed highest thickness reduction was reduced compared to the random region SCN. In the SCN of regions with thickness reductions, FEP network showed weaker covariance compared to chronic and treatment resistant group that showed stronger covariance compared to HC
Kim et al. (2020)	39 chronic SZ, 37 bipolar type I and 32 HC subjects Examined global and local cortical thickness-based network alterations among the 3 groups	1.5 Tesla MRI data acquired on Siemens Magnetom scanner at 1.2 mm thickness using East Asian version of ICBM template. Surface-based morphometry performed using CAT-12 implemented in SPM12. Cortical thickness of the regions was extracted using the Destrieux atlas defining 74 cortical areas in each hemisphere.	Weighted network analysis using graph theoretic approaches. Strength, pathlength, clustering coefficient and efficiency at the global level was examined, along with clustering coefficient for each node.	Strength, pathlength, clustering coefficient and efficiency at the global level were decreased in both SZ and BD patients compared to HC. At the local level, left suborbital sulcus, right superior frontal sulcus, right long insular gyrus and central insular sulcus and left superior occipital gyrus showed lower CC in patients. The former two regions were reduced in volumes in SZ compared to bipolar and HC whereas the latter two were reduced in volume in both patient groups compared to HC. Pathlength inversely correlated with delusion and hallucinations whereas strength and clustering coefficient positively correlated with delusion severity. Nodal clustering coefficient in the right long insular gyrus and the central insular sulcus positively correlated with PANSS positive and general symptoms, conceptual disorganization, suspiciousness/persecution, and hostility in SZ. Bipolar patients showed lower CC at the insular and superior occipital gyrus. Bipolar disorder patients showed positive correlation of nodal CC of the left superior occipital gyrus with the mania severity score on the Young’s Mania Rating Scale (YMRS). CC correlated with psychotic and mood symptoms separately in each of the disorders. Only HC showed positive correlation of the right long insular gyrus and the central insular sulcus clustering coefficient with the Korean version of verbal learning test
Studies examining Gyrification Index-based SCNs
Palaniyappan et al. (2015)	41 SZ/SZA patients and 40 HC Goal was to examine regional gyrification topology in the insula and prefrontal cortex and to test that the degree of correlation to increase with greater severity of illness.	3 Tesla MRI data with 1 mm slice thickness. LGI was obtained for 148 regions parcellated using the Destrieux atlas. Graph Analysis Toolbox that uses computational algorithms from the Brain Connectivity Toolbox was used.	Gyrification was obtained through Freesurfer 5.1. Local gyrification index (LGI) calculated as a ratio between the surface area of the buried surface and the visible surface within 25 mm radius spheres. Gyrification-based networks using a 3-dimensional index. Methods were very similar to (Palaniyappan et al., 2019). Networks were visualized using the BrainNet Viewer (http://www.nitrc.org/projects/bnv/).	No significant difference in small worldness index, overall segregation (clustering coefficient, local efficiency), integration (pathlength) measures and hubness of cingulate Regional topographies were significantly different between the groups. Local clustering coefficient was increased in insula and efficiency in frontal middle gyrus in SZ. Somatosensory and occipital regions showed reduced segregation in SZ. Hubness in the cingulate was observed in controls but not in patients. The abnormal segregated folding pattern in the right peri-sylvian regions (insula and fronto-temporal cortex) was associated with greater severity of illness.
Nelson et al. (2018)	22 unmedicated or 12 off-antipsychotic SZ subjects (n=34) and 23 HC scanned at baseline and at 6 weeks To examine morphological covariance of cortical gyrification and impact of 6-week treatment with Risperidone at variable doses.	3 Tesla MRI at 1 mm slice thickness Freesurfer used for cortical surface generation; 25 mm spherical ROI at each vertex of the outer surface mesh to calculate ratio of cortical surface area to outer surface area to estimate local gyrification index and propagate to generate heat maps at each timepoint. For graph analysis, DKT atlas was used for parcellation on which average gyrification index was calculated.	Network integration (shortest pathlength, global efficiency), segregation (clustering coefficient, local efficiency), and betweenness centrality and modularity were assessed in a 68 × 68 matrix. 20 null hypothesis networks were generated to test group by time changes	Local gyrification index was higher in HC compared to SZ. Small world index showed significant group by time interaction. Path length and global efficiency did not show differences over 6 weeks. Clustering coefficient, local efficiency and modularity were different at baseline but not at 6 weeks
Ajnakina et al. (2021)	53 nontreatment resistant (NTR) and 17 treatment-resistant (TR) SZ. No HC recruited. Goal was to examine the structural covariance of gyrification index between TR and NTR SZ	3-Tesla GE Signa HDx scanner used to acquire structural data at 1.2 mm thickness. The Destriex atlas was used to parcellate 148 cortical regions. Schaer’s automated vertex-wise method used to compute Zille’s gyrification index. Graph Analysis Toolbox to generate binary undirected graph with a range of 0.050-.25, intervals of 0.01.	84 SZ patients at first contact with psychiatric service were followed up. Final sample was 70. 148×148 correlation matrix built and then individual contributions were estimated using jack-knife method. Five core symptoms of TR SZ were defined by conducting confirmatory factor analysis. Small worldness, characteristic pathlength and clustering coefficient were calculated at the global level.	TR SZ showed reduction in small worldness and clustering coefficient but increased pathlength compared to NTR SZ. Positive symptom dimension positively correlated with small worldness after controlling for age, sex, and the TR status. Direct comparison of the local gyrification index of all 148 regions between the TR and NTR SZ did not identify any between group differences after applying false discovery rate correction. Authors interpret this as disturbance in covariance pattern to be more pronounced than any inter-regional alteration in local gyrification index.
Study examining SCN built using GM values
Cauda et al. (2018)	198 HC, 5236 SZ, 1738 OCSD and 1719 ASD. HC data from the Beijing dataset within the 1000 Functional Connectomes Project that obtained MRI data on 3 Tesla Siemens Trio scanner at 1.33 mm thickness.	Coordinates and imaging metadata from 203 studies that reported GM and WM changes in standard stereotactic space from the Brainmap database consisting of coordinates and meta-data from 3076 publications and 15243 neuroimaging experiments (www.brainmap.org).	Anatomical co-alteration network analysis that examined co-alteration of brain regions as networks in SZ, ASD and OCSD Clusters of co-alterations in a morphometric co-alteration network were examined. Used Patel’s k (ranges from −1 to 1), a measure of the probability that the 2 nodes co-alter as opposed to independently alter. Values close to 1 reflect high connectivity. Statistical significance tested through Monte Carlo algorithm	In these 3 disorders, brain alterations follow network-like patterns of co-alteration that involved 33 nodes spread across prefrontal, temporal and parietal along with thalamus. Insulo-insular, insulo-frontal, insulo-cingulate, insulo-temporal, and interhemispheric connection were common across the disorders. The network of co-atrophy was similar between SZ and ASD and SZ and OCSD but less so between ASD and OCSD. SZ SCN contributed the most to the edges in a combined analysis of the sample. Also conducted ALE estimation on the rsfMRI (not discussed in this review)
Studies examining SCNs of GM volumes and White matter data
Griffa et al. (2015)	16 chronic SZ and 15 HC To examine damages to the core of the connectome and topological disruption that underlies such damage. Specifically, to test decentralization of a distributed set of nodes as a mechanism contributing to SZ pathophysiology. Structural SCN was built on GM volumes	MPRAGE data on 3 Tesla Siemens Magnetom Tim Trio scanner using 32-channel head coil obtained at 1.2 mm thickness. DSI data was also obtained on the same scanner. DKT atlas used for parcellation of GM volumes. Connectome mapping toolkit used to combine morphometric and diffusion data.	Examined SCN from 68 cortical regional volumes and Diffusion Spectrum Imaging (DSI). From the DSI data, 32 streamline propagation per voxel per direction Two metrics of network integration (global efficiency, nodal closeness centrality) and segregation (network transitivity, nodal local efficiency) properties were examined for structural topology. Generalized fractional anisotropy (gFA) and average diffusion coefficient and used weighted gFA and inverse of ADC as size of the tract in terms of stream count. To identify the brain regions contributing to the loss of global topological properties, the single nodes were tested for decreased closeness centrality and local efficiency. Hubs were defined as nodes with closeness centrality >1 SD over the mean closeness centrality of all 82 nodes examined.	Global efficiency and the transitivity measures were both decreased in patients compared to controls. Affected core regions comprised of 30% of the whole network and they were: fronto-basal (bilateral medial orbitofrontal and left lateral orbitofrontal), middle frontal (bilateral caudal middle frontal and right rostral middle frontal), and inferior frontal (right pars triangularis, left pars orbitalis and left pars opercularis) cortices, left precentral cortex, parietal (bilateral postcentral region, right supramarginal, and precuneus, left superior parietal) and left temporal-occipital (lateral occipital, middle temporal, and inferior temporal) areas, basal ganglia (bilateral caudate, pallidum, and accumbens areas, right putamen), and left thalamus. Among these affected core nodes, 40% were considered hubs. These core networks had a significant role in global efficiency. Number of paths passing through the affected core nodes was decreased and paths not passing through the nodes was increased in SZ. Weighted gFA and the weighted inverse ADC (measure of tract size) were altered in patients compared to controls when averaged within the core but not outside these core edges

Abbreviations used: AAL, Automated Anatomic Labeling; ACC: Anterior Cingulate Cortex; AD, Alzheimer’s disease; ASD, Autism Spectrum Disorder; DKT, Diffusion Kurtosis Imaging; DLPFC, Dorsolateral Prefrontal Cortex; FEP, First Episode Psychosis; GM, Gray Matter; ICA, Independent Component Analysis; HC, Healthy Controls; OCSD, Obsessive Compulsive Spectrum Disorder; PANSS, Positive and Negative Syndrome Scale; PFC, Prefrontal cortex; ROI, Region-of-Interest; SCN, Structural Covariance Network; SPM, Statistical Parametric Mapping; SZ, Schizophrenia; SZA, Schizoaffective Disorder