DeMEtRIS: Counting (near)-Cliques by Crawling

TL;DR

DeMEtRIS is a scalable algorithm for estimating the number of cliques and near cliques in large graphs using limited vertex sampling via random walks, outperforming previous methods.

Contribution

The paper introduces DeMEtRIS, a novel method for approximate clique counting in the random walk model, with proven correctness and high accuracy from sub-linear vertex samples.

Findings

DeMEtRIS achieves high precision with sub-linear vertex sampling.

The method significantly outperforms previous approaches.

Theoretical analysis confirms the algorithm's correctness.

Abstract

We study the problem of approximately counting cliques and near cliques in a graph, where the access to the graph is only available through crawling its vertices; thus typically seeing only a small portion of it. This model, known as the random walk model or the neighborhood query model has been introduced recently and captures real-life scenarios in which the entire graph is too massive to be stored as a whole or be scanned entirely and sampling vertices independently is non-trivial in it. We introduce DeMEtRIS: Dense Motif Estimation through Random Incident Sampling. This method provides a scalable algorithm for clique and near clique counting in the random walk model. We prove the correctness of our algorithm through rigorous mathematical analysis and extensive experiments. Both our theoretical results and our experiments show that DeMEtRIS obtains a high precision estimation by only crawling a sub-linear portion on vertices, thus we demonstrate a significant improvement over previously known results.