Establish the Expected Number of Injective Motifs on Unlabeled Graphs Through Analytical Models

Abstract

Network motifs have a central role in explaining the functionality of complex systems. Establishing motif significance requires the computation of the expected number of their occurrences according to a random graph model. Few models have been proposed to analytically derive the expected number of non-induced occurrences of a motif. In this paper we present an analytical model to compute the expected number of occurrences of induced motifs in unlabeled graphs. We will illustrate two different algorithms for computing the occurrence probability of induced motifs. We evaluate the performance of our algorithms for calculating the expected number of induced motifs with up to 10 nodes.