Efficient Counting of Network Motifs

Counting network motifs has an important role in studying a wide range of complex networks. However, when the network size is large, as in the case of Internet Topology and WWW graphs counting the number of motifs becomes prohibitive. Devising efficient motif counting algorithms thus becomes an important goal. In this paper, we present efficient counting algorithms for 4-nodemotifs. We show how to efficiently count the total number of each type of motif, and the number of motifs adjacent to a node. We further present a new algorithm for node position-aware motif counting, namely partitioning the motif count by the node position in the motif. Since our algorithm is based on motifs, which are non-induced we also show how to calculate the count of induced motifs given the non-induced motif count. Finally, we report on initial implementation performance result using evaluation on a large-scale graph.