Local Algorithms for Finding Densely Connected Clusters
This work addresses the need for analyzing inter-cluster relationships in graph data, which is incremental to prior research on low-conductance clustering.
The paper tackles the problem of finding densely connected clusters in massive graphs by developing local algorithms that focus on inter-connections between clusters, and demonstrates successful recovery of such clusters in real-world datasets like the Interstate Disputes and US Migration Datasets.
Local graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most (local) graph clustering algorithms is to find a vertex set of low conductance, there has been a sequence of recent studies that highlight the importance of the inter-connection between clusters when analysing real-world datasets. Following this line of research, in this work we study local algorithms for finding a pair of vertex sets defined with respect to their inter-connection and their relationship with the rest of the graph. The key to our analysis is a new reduction technique that relates the structure of multiple sets to a single vertex set in the reduced graph. Among many potential applications, we show that our algorithms successfully recover densely connected clusters in the Interstate Disputes Dataset and the US Migration Dataset.