Mining Maximal Cliques from an Uncertain Graph

TL;DR

This paper introduces a formal definition and an efficient algorithm for mining maximal cliques in uncertain graphs, providing theoretical bounds and demonstrating practical effectiveness.

Contribution

It defines {\

Findings

Established bounds on the number of {\

paper_type":"method"}}

Abstract

We consider mining dense substructures (maximal cliques) from an uncertain graph, which is a probability distribution on a set of deterministic graphs. For parameter 0 < {\alpha} < 1, we present a precise definition of an {\alpha}-maximal clique in an uncertain graph. We present matching upper and lower bounds on the number of {\alpha}-maximal cliques possible within an uncertain graph. We present an algorithm to enumerate {\alpha}-maximal cliques in an uncertain graph whose worst-case runtime is near-optimal, and an experimental evaluation showing the practical utility of the algorithm.