This script is intended to calculate common graph features typically used with electrode-based neural data, such as EEG and MEG. It was originally created to function as a post-processing step for the functional connectivity matrix generated by the Brainstorm toolbox in MATLAB. It is meant to process weighted undirected matrices. Please note that this work has not undergone formal verification and should be used with caution. The features included are:
- Centrality (“eigenvector”, “pagerank”, “betweenness”, “closeness”, and “degree”). Centrality is found according the definitions in: https://www.mathworks.com/help/matlab/ref/graph.centrality.html
- Characteristic Path Length (CPL): the average shortest path length between all pairs of nodes in the network. The formula is obtained from: Latora, V., & Marchiori, M. (2003). Economic small-world behavior in weighted networks. The European Physical Journal B-Condensed Matter and Complex Systems, 32, 249-263.
- Global Efficiency (EGlob): the average of the inverse distances between all pairs of nodes in the network. The formula is obtained from: Ek, B., VerSchneider, C., & Narayan, D. A. (2015). Global efficiency of graphs. AKCE International Journal of Graphs and Combinatorics, 12(1), 1-13.
- Local Efficiency (Eloc): the global efficiency of the subgraph composed of the neighbors of a certain node. The formula is obtained from: Wang, J., Zuo, X., & He, Y. (2010). Graph-based network analysis of resting-state functional MRI. Frontiers in systems neuroscience, 4, 1419.
- Clustering Coefficient (CC): the number of edges of the subgraph composed of the neighbors of a certain node to the total number of possible edges. The formula is obtained from Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’networks. nature, 393(6684), 440-442.
- Network Density (ND): the total number of edges to the total number of possible edges. The formula is taken from: Fallani, F. D. V., Astolfi, L., Cincotti, F., Mattia, D., Tocci, A., Salinari, S., ... & Babiloni, F. (2008). Brain network analysis from high-resolution EEG recordings by the application of theoretical graph indexes. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 16(5), 442-452.
- Assortativity is taken from: https://github.com/jblocher/matlab-network-utilities/blob/master/BrainConnectivity/assortativity.m
- Modularity (Modu): A quantifiable measurement for the tendency of a graph to form modules. The formula is taken from: https://www.mathworks.com/matlabcentral/fileexchange/82018-modularity
- Degree Correlation (DC): the ratio of the degrees of the subgraph composed of the neighbors of a certain node to the squared node degree.*
- Transitivity (Trans): a ratio of number of triangles to the number of triples around a node.*
- Small Worldness (SW): the ratio of normalized CC to the normalized PL.*
- Resources to be added