Efficient and near-optimal algorithms for sampling small connected subgraphs

TL;DR

This paper introduces the first efficient, truly uniform, and sublinear-time algorithms for sampling small connected subgraphs (graphlets) in large graphs, with significant implications for graph analysis tasks.

Contribution

It presents a near-optimal mixing time bound, the first truly uniform sampling algorithm, and a sublinear-time method for graphlet sampling.

Findings

Established a near-optimal mixing time bound for a known random walk.

Developed the first efficient algorithm for uniform graphlet sampling.

Created the first sublinear-time algorithm for epsilon-uniform graphlet sampling.

Abstract

We study the following problem: given an integer $k \ge 3$ and a simple graph $G$, sample a connected induced $k$-node subgraph of $G$ uniformly at random. This is a fundamental graph mining primitive with applications in social network analysis, bioinformatics, and more. Surprisingly, no efficient algorithm is known for uniform sampling; the only somewhat efficient algorithms available yield samples that are only approximately uniform, with running times that are unclear or suboptimal. In this work we provide: (i) a near-optimal mixing time bound for a well-known random walk technique, (ii) the first efficient algorithm for truly uniform graphlet sampling, and (iii) the first sublinear-time algorithm for $\epsilon$-uniform graphlet sampling.