Mining Dense Subgraphs with Similar Edges

TL;DR

This paper introduces a novel method for mining dense subgraphs with similar edges by leveraging metadata-based similarity functions, formulated as an optimization problem solved via parametric MinCut, and validated on real datasets.

Contribution

It proposes a new optimization framework and algorithm for finding dense, similar-edge subgraphs using metadata-based similarity measures.

Findings

Effective in real-world datasets

Efficient algorithm with parametric MinCut

Demonstrates usefulness of metadata in subgraph mining

Abstract

When searching for interesting structures in graphs, it is often important to take into account not only the graph connectivity, but also the metadata available, such as node and edge labels, or temporal information. In this paper we are interested in settings where such metadata is used to define a similarity between edges. We consider the problem of finding subgraphs that are dense and whose edges are similar to each other with respect to a given similarity function. Depending on the application, this function can be, for example, the Jaccard similarity between the edge label sets, or the temporal correlation of the edge occurrences in a temporal graph. We formulate a Lagrangian relaxation-based optimization problem to search for dense subgraphs with high pairwise edge similarity. We design a novel algorithm to solve the problem through parametric MinCut, and provide an efficient search scheme to iterate through the values of the Lagrangian multipliers. Our study is complemented by an evaluation on real-world datasets, which demonstrates the usefulness and efficiency of the proposed approach.