Most Probable Densest Subgraphs

TL;DR

This paper introduces the novel problem of finding the most probable densest subgraph in uncertain graphs, extending traditional densest subgraph computations to probabilistic settings with applications in various network domains.

Contribution

It formulates the MPDS problem, proves its #P-hardness, and proposes sampling-based algorithms with accuracy guarantees, validated by extensive experiments and case studies.

Findings

Sampling algorithms effectively compute MPDS with accuracy guarantees.

MPDS discovery is computationally hard (#P-hard).

Experimental results demonstrate efficiency and practical usefulness.

Abstract

Computing the densest subgraph is a primitive graph operation with critical applications in detecting communities, events, and anomalies in biological, social, Web, and financial networks. In this paper, we study the novel problem of Most Probable Densest Subgraph (MPDS) discovery in uncertain graphs: Find the node set that is the most likely to induce a densest subgraph in an uncertain graph. We further extend our problem by considering various notions of density, e.g., clique and pattern densities, studying the top-k MPDSs, and finding the node set with the largest containment probability within densest subgraphs. We show that it is #P-hard to compute the probability of a node set inducing a densest subgraph. We then devise sampling-based efficient algorithms, with end-to-end accuracy guarantees, to compute the MPDS. Our thorough experimental results and real-world case studies on brain and social networks validate the effectiveness, efficiency, and usefulness of our solution.