DMCS : Density Modularity based Community Search

TL;DR

This paper introduces a novel community search method based on a new graph modularity measure called Density Modularity, aiming to find high-quality communities containing specific query nodes with high internal density and low external connections.

Contribution

It pioneers the use of modularity for community search with query nodes, proposing a new density modularity function and efficient algorithms for the NP-hard problem.

Findings

Up to 8.5 times higher accuracy in NMI compared to baselines.

Algorithms run in log-linear time relative to graph size.

Effective in real-world and synthetic networks.

Abstract

Community Search, or finding a connected subgraph (known as a community) containing the given query nodes in a social network, is a fundamental problem. Most of the existing community search models only focus on the internal cohesiveness of a community. However, a high-quality community often has high modularity, which means dense connections inside communities and sparse connections to the nodes outside the community. In this paper, we conduct a pioneer study on searching a community with high modularity. We point out that while modularity has been popularly used in community detection (without query nodes), it has not been adopted for community search, surprisingly, and its application in community search (related to query nodes) brings in new challenges. We address these challenges by designing a new graph modularity function named Density Modularity. To the best of our knowledge, this is the first work on the community search problem using graph modularity. The community search based on the density modularity, termed as DMCS, is to find a community in a social network that contains all the query nodes and has high density-modularity. We prove that the DMCS problem is NP-hard. To efficiently address DMCS, we present new algorithms that run in log-linear time to the graph size. We conduct extensive experimental studies in real-world and synthetic networks, which offer insights into the efficiency and effectiveness of our algorithms. In particular, our algorithm achieves up to 8.5 times higher accuracy in terms of NMI than baseline algorithms.