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Local graph clustering methods aim to detect small clusters in very largegraphs without the need to process the whole graph. They are fundamental andscalable tools for a wide range of tasks such as local community detection,node ranking and node embedding. While prior work on local graph clusteringmainly focuses on graphs without node attributes, modern real-world graphdatasets typically come with node attributes that provide valuable additionalinformation. We present a simple local graph clustering algorithm for graphswith node attributes, based on the idea of diffusing mass locally in the graphwhile accounting for both structural and attribute proximities. Usinghigh-dimensional concentration results, we provide statistical guarantees onthe performance of the algorithm for the recovery of a target cluster with asingle seed node. We give conditions under which a target cluster generatedfrom a fairly general contextual random graph model, which includes both thestochastic block model and the planted cluster model as special cases, can befully recovered with bounded false positives. Empirically, we validate alltheoretical claims using synthetic data, and we show that incorporating nodeattributes leads to superior local clustering performances using real-worldgraph datasets.

Weighted Flow Diffusion for Local Graph Clustering with Node Attributes: an Algorithm and Statistical Guarantees