Figure 1.
Main GUI of the graph analysis toolbox (GAT).
The toolbox allows topological assessment of morphometry, functional, diffusion, and behavioral data.
Figure 2.
GUI for graph theoretical analysis of morphometry data.
The toolbox facilitates construction of structural correlation networks, extraction of network measures, statistical analysis, regional network analysis, network failure and attack analysis, modularity analysis, AUC and FDA analyses and visualization.
Figure 3.
GUI for graph theoretical analysis of functional data.
The toolbox facilitates construction of functional networks, extraction of network measures, statistical analysis, regional network analysis, modularity analysis, AUC and FDA analyses and visualization.
Figure 4.
Association and adjacency matrices.
Association matrices for A) ALL and B) CON groups; the color-bar shows the strength of the connections. Binary adjacency matrices for C) ALL and D) CON groups; red color represents presence of connection. These matrices are the maps thresholded at Dmin (22%) in which all nodes became fully connected in the structural networks of both groups. For clarity, only the regions in the left hemisphere are labeled. Abbreviations are used as follow: L: left hemisphere; AMYG: amygdala; ANG: angular gyrus; CALC: calcarine fissure; CN: caudate nucleus; ACC: anterior cingulate; MCC: mid-cingulate; PCC: posterior cingulate; CUN: cuneus; IFOp: inferior frontal gyrus, opercular part; IFOr: inferior frontal gyrus, orbirtal part; IFTr: inferior frontal gyrus, triangular part; MedFOr: medial fronal gyrus, orbital part; MFG: middle frontal gyrus; MFOr: middle frontal gyrus, orbital part; SFG: superior frontal gyrus; MedSF: superior frontal gyrus, medial part; SFOr: superior frontal gyrus, orbital part; FG: fusiform gyrus; HSHL: heschl gyrus; HIPP: hippocampus; INS: insula; LNG: lingual gyrus; IOG: inferior occipital gyrus; MOG: middle occipital gyrus; SOG: superior occipital gyrus; OFB: olfactory cortex; PLD: lenticular nucleus, pallidum; PCL: paracentral lobule; PHIP: parahippocampal gyrus; IPL: inferior parietal lobule; SPL: superior parietal lobule; PoCG: postcentral gyrus; PrCG: precentral gyrus; PCUN: precuneus; PUT: putamen; REC: gyrus rectus; RLN: rolandic operculum; SMA: supplementary motor area; SMG: supramarginal gyrus; ITG: inferior temporal gyrus; MTG: middle temporal gyrus; MTP: middle temporal pole; STP: superior temporal pole; STG: superior temporal gyrus; THL: thalamus.
Figure 5.
Changes in global network measures as a function of network density.
Normalized clustering (top), normalized path length (middle), and small-world index (bottom) of both the ALL and CON networks. Both the networks follow a small-world organization, i.e. normalized clustering of greater than 1 and normalized path length of close to 1.
Figure 6.
Between-group differences in global network measures as a function of network density.
The 95% confidence intervals and between-group differences in normalized clustering (top), normalized path length (middle) and small-world index (bottom). The + marker shows the difference between CON vs. ALL networks; the + signs falling out of the confidence intervals indicate the densities in which the difference is significant. The positive values indicate CON > ALL and negative values indicate CON < ALL. Relative to CON network, the small-world index in ALL network was significantly lower in various network densities. The AUC of the small-world index was also significantly lower in the ALL network.
Figure 7.
Between-group differences in regional network topology.
Regions that showed significant between-group differences in nodal betweenness mapped on ICBM152 surface template. Hot color identifies the regions that have significantly higher nodal betweenness in CON compared to ALL while cold color identifies regions with significantly higher nodal betweenness in ALL compared to CON. The regional differences were quantified based on AUC analysis in the density range of 0.22∶0.01∶0.45.
Figure 8.
Constructed networks and corresponding hubs for ALL (top) and CON (middle) groups. Nodes that are labeled represent network hubs (nodes with nodal betweenness of 2SD greater than network mean betweenness). The volume of the spheres represents the betweenness of the corresponding brain region. Green color highlights hubs specific to CON network; yellow color represents hubs specific to ALL network; Orange color represents hubs that are common in both groups; blue color represents non-hub regions. The hubs were quantified based on AUC analysis in the density range of 0.22∶0.01∶0.45.
Figure 9.
Between-group differences in network resilience to random failure and targeted attack.
Changes in the size of the largest component of the networks after cascading random failure (A) and targeted attack (B). Stars show where the difference in the size of the largest remaining components between groups is significant. The ALL network shows less tolerance to random failure and targeted attack. The AUC analysis revealed a significantly lower tolerance to random failure in the ALL network compared to CON.
Figure 10.
Between-group differences in network modularity.
The 95% confidence intervals and between-group differences in network modularity (A). The + marker shows the difference between CON vs. ALL networks; the + signs falling out of the confidence intervals indicate the densities in which the difference in global modularity is significant. The positive values indicate CON > ALL and negative values indicate CON < ALL. The modular structures of the CON and ALL networks are also shown (B). While both the networks had the same number of modules (five modules color-coded for each network separately), the degree of modularity is significantly lower in the ALL group in various network densities relative to CON group.
Figure 11.
The log-log plot of cumulative degree distributions of ALL (A) and CON (B) networks thresholded at Dmin. The solid line indicates the exponentially truncated power-law curve fitted to the cumulative degree distribution of the networks (dotted line). The estimated exponent was 1.19 for ALL and 1.27 for CON, the cut-off degree was 2.65 for the ALL and 2.52 for the CON network. These parameters resulted in R-square value of 0.97 for both distributions (value close to one represents a good fit).