Local triangle-densest subgraphs

Abstract

Finding dense subgraphs in large graphs is a key primitive in a variety of real-world application domains, encompassing social network analysis, event detection, problems arising in biology and many others. Several recent works have studied some variants of the classical densest subgraph problem, considering alternative quality measures such as the average number of triangles in the subgraphs and their compactness. Those are desirable properties when the task is to find communities or interesting events in social networks. In our work, we capitalize on previous works and study a variant of the problem where we aim at finding subgraphs which are both compact and contain a large number of triangles. We provide a formal definition for our problem, while developing efficient algorithms with strong theoretical guarantees. Our experimental evaluation on large real-world networks shows the effectiveness of our approach.