Efficient and Near-optimal Algorithms for Sampling Small Connected Subgraphs

We study the following problem: Given an integer k >= 3 and a simple graph G, sample a connected induced k-vertex subgraph ofG 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 e-uniform graphlet sampling.