Triad count statistics

It is shown how triad counts in multigraphs can be used in various kinds of statistical analyses of graphs and digraphs defined on a common vertex set.

Abstract

The triad counts of a graph G are the numbers of various distinct induced subgraphs of order 3. If G is an undirected graph, there are 4 triad counts, and if G is a digraph, there are 16 triad counts. A multigraph is a sequence G = (G1,..., Gr) of graphs and digraphs defined on a common vertex set. The concept of triad counts is generalized to multigraphs with colored vertices, edges, and arcs. It is shown how triad counts in multigraphs can be used in various kinds of statistical analyses of graph data. In particular, probability distributions are investigated of the triad counts in random multigraphs.