Algorithmic Tools for Understanding the Motif Structure of Networks

Tianyi Chen, Brian Matejek, Michael Mitzenmacher, Charalampos E. Tsourakakis

Abstract: Motifs are small subgraph patterns that play a key role towards understanding the structure and the function of biological and social networks. The current de facto approach towards assessing the statistical significance of a motif \(\mathcal {M}\) relies on counting its occurrences across the network, and comparing that count to its expected count under some null generative model. This approach can be misleading due to combinatorial artifacts. That is, there may be a large count for a motif due to multiple copies sharing many vertices and edges connected to a subgraph, such as a clique, that completes the multiple copies of the motif.