Altered Topological Properties of Brain Networks in Social Anxiety Disorder: A Resting-state Functional MRI Study

Recent studies involving connectome analysis including graph theory have yielded potential biomarkers for mental disorders. In this study, we aimed to investigate the differences of resting-state network between patients with social anxiety disorder (SAD) and healthy controls (HCs), as well as to distinguish between individual subjects using topological properties. In total, 42 SAD patients and the same number of HCs underwent resting functional MRI, and the topological organization of the whole-brain functional network was calculated using graph theory. Compared with the controls, the patients showed a decrease in 49 positive connections. In the topological analysis, the patients showed an increase in the area under the curve (AUC) of the global shortest path length of the network (Lp) and a decrease in the AUC of the global clustering coefficient of the network (Cp). Furthermore, the AUCs of Lp and Cp were used to effectively discriminate the individual SAD patients from the HCs with high accuracy. This study revealed that the neural networks of the SAD patients showed changes in topological characteristics, and these changes were prominent not only in both groups but also at the individual level. This study provides a new perspective for the identification of patients with SAD.

Small-world analysis.
The small-world parameters of a network (clustering coefficient p C , and characteristic path length p L ) were originally proposed by Watts and Strogatz 1 .
Briefly, the p C of a network was the average of the clustering coefficients over all nodes, where the clustering coefficient i C of a node i was defined as the ratio of the number of existing connections among the node's neighbors and all their possible connections. p C quantified the local interconnectivity of a network. p L of a network was the shortest path length (number of edges) required to transfer from one node to another averaged over all pairs of nodes. p L was an indicator of the overall routing efficiency of a network. In our study, we calculated the p L as the "harmonic mean" distance between all possible pairs of regions to deal with the disconnected graphs dilemma 2 . To estimate the small-world properties, we scaled p C and p L derived from the brain networks with the mean s p C  and s p L  of 100 random networks (i.e.,  = p C / s p C  and  = p L / s p L  ) that preserved the same number of nodes, edges and degree distributions as real brain networks. Typically, a small-world network should fulfill the conditions of  > 1 and  ≈ 1 1 , and therefore, the small-worldness scalar    /  will be more than 1 2 . Of note, in the present study the "harmonic mean" distance was employed to calculate the characteristic path length to deal with the possible disconnected graphs dilemma 3 .

Network efficiency.
Efficiency is a more biologically relevant metric to describe brain networks from the perspective of parallel information flow that can deal with either the disconnected or nonsparse graphs or both 4 . Network efficiency measures how efficiently information is exchanged over the network. For a network G with N nodes and K edges, the global efficiency (Eglob) of G can be computed as 5,6 : where ij d is the shortest path length between node i and node j in G .
Global efficiency measures the ability of parallel information transmission over the network. The local efficiency of (Eloc) G is measured as 5,6 : where ) ( The nodal local efficiency 4 (nodalEloc) of node i is defined in the subgraph of the direct neighbors of i: where Gi The nodal global efficiency 4 (nodalEglob)of node i is computed as: where N is the number of nodes in the network graph G; and Nodal centrality. Degree k i was used to measure the centrality of a node. It is defined as the number of links connected to the node, and it is a simple measurement of connectivity of a node with the rest of nodes in a network. Hub regions often interact with many other regions in the network and thus have high centrality. Formally, in a network G with N nodes and K edges, the degree i k (nodalDeg) of node i is defined as 5 : where ij a is the i th row and j th column element of the adjacency matrix.
Supplement Tables  Table S1. The regions are listed in terms of a prior AAL atlas 6 . Odd and even numbers represent brain regions of left and right hemispheres, respectively.