Finding Network Motifs in Large Graphs using Compression as a Measure of Relevance

We introduce a new method for finding network motifs: interesting or informative subgraph patterns in a network. Current methods for finding motifs rely on the frequency of the motif: specifically, subgraphs are motifs when their frequency in the data is high compared to the expected frequency under a null model. To compute this expectation, the search for motifs is normally repeated on as many as 1000 random graphs sampled from the null model; a prohibitively expensive step. We use ideas from the Minimum Description Length (MDL) literature to define a new measure of motif relevance, and a new algorithm for detecting motifs. Our method allows motif analysis to scale to networks with billions of links, while still resulting in informative motifs.