Chunk #16 — Resting State Functional Connectivity MRI Signal, Brain Networks, and Common Analysis Techniques — Graph Theoretic Analyses of Region Matrices: Communities and Small-World Properties
In addition to providing the basis for dividing networks of nodes into communities, graph theory can be used to describe the properties of networks (Watts and Strogatz 1998). Network measures include the characteristic path length (the average number of connections it takes to travel from one node to another) and the average clustering coefficient (on average, how many of the nodes connected to a given node are also connected to one another). Until a decade ago, classic models of networks came in two predominant strains: random and regular networks. Random networks, in which edges are placed between nodes randomly, have short average path lengths but low clustering coefficients, affording them the ability to transfer information efficiently globally (though the whole graph) but not locally (to nearby nodes). Regular networks have nodes connected to nearby nodes in a regular, lattice-like pattern of edges. These networks have high clustering coefficients because each node is well-connected to nearby nodes, but they also have a long average path length. Thus regular networks have efficient local but not global information transfer. A critical discovery, made
