Triad count statistics (Q1121915)

The triad counts of a graph G are the numbers of various distinct induced subgraphs of order 3. A multigraph is a sequence \(G=(G_ 1,G_ 2,...,G_ r)\) of graphs and digraphs defined on a common vertex set. The concept of triad counts is generalized in this paper to multigraphs with coloured edges, vertices, and arcs. It is shown how triad counts in multigraphs can be used in various kinds of statistical analyses. Probability distributions of the triad counts of random multigraphs are investigated.