Chunk #17 — Resting State Functional Connectivity MRI Signal, Brain Networks, and Common Analysis Techniques — Graph Theoretic Analyses of Region Matrices: Communities and Small-World Properties
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 by Watts and Strogatz in 1998, is that a wide variety of real-world networks, which have been termed small world networks, enjoy the best of both worlds—a high clustering coefficient and a short path length, allowing for both globally and locally efficient information transfer (Watts and Strogatz 1998; Sporns and Honey 2006). These networks possess intermediate structures to the random and regular graphs, such that lattice-like portions of networks are connected by long-range shortcuts, facilitating both local and global efficiency. In other words, small world networks allow all nodes to share information with all other nodes, despite each node having only a small number of connections. Different networks are efficient to differing extents, and the small-world properties capture how well or poorly networks are suited to efficient processing. Note that here we are using efficiency to refer to the ease of information transfer (passing information from node to node); a mathematical definition of efficiency can be found in Latora and
