Fast maximal clique enumeration in weighted temporal networks

TL;DR

This paper presents a highly efficient algorithm for enumerating maximal cliques in weighted temporal networks, significantly improving speed and extending applicability compared to previous methods.

Contribution

It introduces a new algorithm that extends gamma constraints to weights, improves the initial phase to linear complexity, and enhances pruning in the second phase, outperforming existing methods.

Findings

Achieves several orders of magnitude speed-up on real-world datasets.

Outperforms state-of-the-art methods in temporal network clique enumeration.

Extends applicability to weighted networks.

Abstract

Cliques, groups of fully connected nodes in a network, are often used to study group dynamics of complex systems. In real-world settings, group dynamics often have a temporal component. For example, conference attendees moving from one group conversation to another. Recently, maximal clique enumeration methods have been introduced that add temporal (and frequency) constraints, to account for such phenomena. These methods enumerate so called (delta,gamma)-maximal cliques. In this work, we introduce an efficient (delta,gamma)-maximal clique enumeration algorithm, that extends gamma from a frequency constraint to a more versatile weighting constraint. Additionally, we introduce a definition of (delta,gamma)-cliques, that resolves a problem of existing definitions in the temporal domain. Our approach, which was inspired by a state-of-the-art two-phase approach, introduces a more efficient initial (stretching) phase. Specifically, we reduce the time complexity of this phase to be linear with respect to the number of temporal edges. Furthermore, we introduce a new approach to the second (bulking) phase, which allows us to efficiently prune search tree branches. Consequently, in experiments we observe speed-ups, often by several order of magnitude, on various (large) real-world datasets. Our algorithm vastly outperforms the existing state-of-the-art methods for temporal networks, while also extending applicability to weighted networks.