Dense subgraphs induced by edge labels

TL;DR

This paper introduces methods for identifying dense subgraphs in edge-labeled networks, proposing heuristics for conjunctive and disjunctive label sets, with efficient algorithms and validation on synthetic and real data.

Contribution

It studies the problem of finding dense subgraphs induced by label sets, introduces greedy heuristics, and analyzes their efficiency and effectiveness.

Findings

Greedy heuristics effectively find ground truth in synthetic graphs.

Algorithms run efficiently with logarithmic time complexity.

Real-world networks yield interpretable dense subgraphs.

Abstract

Finding densely connected groups of nodes in networks is a widely used tool for analysis in graph mining. A popular choice for finding such groups is to find subgraphs with a high average degree. While useful, interpreting such subgraphs may be difficult. On the other hand, many real-world networks have additional information, and we are specifically interested in networks with labels on edges. In this paper, we study finding sets of labels that induce dense subgraphs. We consider two notions of density: average degree and the number of edges minus the number of nodes weighted by a parameter $\alpha$. There are many ways to induce a subgraph from a set of labels, and we study two cases: First, we study conjunctive-induced dense subgraphs, where the subgraph edges need to have all labels. Secondly, we study disjunctive-induced dense subgraphs, where the subgraph edges need to have at least one label. We show that both problems are NP-hard. Because of the hardness, we resort to greedy heuristics. We show that we can implement the greedy search efficiently: the respective running times for finding conjunctive-induced and disjunctive-induced dense subgraphs are in $O(p \log k)$ and $O(p \log^2 k)$, where $p$ is the number of edge-label pairs and $k$ is the number of labels. Our experimental evaluation demonstrates that we can find the ground truth in synthetic graphs and that we can find interpretable subgraphs from real-world networks.