We study the following problem: Given an integer k ≥ 3 and a simple graph G, sample a connected induced k-vertex 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 ε-uniform graphlet sampling.

我们研究以下问题：给定一个整数k ≥ 3 和一个简单图G ，均匀地随机采样G的连通诱导k顶点子图。这是一种基本的图挖掘原语，可应用于社交网络分析、生物信息学等领域。令人惊讶的是，目前还没有有效的均匀采样算法。唯一有效的算法产生的样本只是大致均匀，运行时间不明确或次优。在这项工作中，我们提供：（i）众所周知的随机游走技术的接近最佳混合时间界限，（ii）第一个真正均匀图基采样的有效算法，以及（iii）第一个亚线性时间算法ε-均匀图基采样。