To reiterate, networks are collections of items that possess pairwise relationships. Graphs represent these items and relationships as nodes and edges. The structure of a graph is fully described as a list of nodes and the edges between nodes, and this structure can be conveniently organized as a matrix, called an adjacency matrix, in which each node has a column (and a row) of entries describing that node’s relationship to itself and to all other nodes (see Figure 3A). In fcMRI studies, nodes represent voxels or collections of voxels, and edges between nodes are typically similarity measures between node BOLD timecourses. Thus, a representative fcMRI graph might be a cross correlation matrix derived from the fcMRI timecourses of a collection of regions of interest (ROIs). Edges in such networks have values between −1 and 1, and the values of edges are called edge weights. Adjacency matrices fully describe the structure of a graph, and are the substrate for graph theoretic analyses, but it is difficult to comprehend the structure of a network by inspecting a matrix. We now describe a method of visualizing networks.
