Large-scale network motif analysis using compression

TL;DR

This paper presents a scalable method for network motif analysis that leverages compression principles to identify significant subgraph patterns without extensive sampling, enabling analysis of very large networks.

Contribution

The authors introduce a novel MDL-based relevance measure that eliminates the need for repeated motif counting on random graphs, significantly improving scalability.

Findings

Method scales to networks with billions of links.

Reduces computational cost compared to traditional motif analysis.

Successfully identifies meaningful motifs in large real-world networks.

Abstract

We introduce a new method for finding network motifs: interesting or informative subgraph patterns in a network. Subgraphs are motifs when their frequency in the data is high compared to the expected frequency under a null model. To compute this expectation, a full or approximate count of the occurrences of a motif 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. With our method, samples from the null model are not required. Instead we compute the probability of the data under the null model and compare this to the probability under a specially designed alternative model. With this new relevance test, we can search for motifs by random sampling, rather than requiring an accurate count of all instances of a motif. This allows motif analysis to scale to networks with billions of links.