Spectral Algorithms for Temporal Graph Cuts

TL;DR

This paper introduces spectral algorithms for identifying meaningful cuts in dynamic, temporal graphs, extending traditional static graph cut concepts to capture temporal smoothness and dynamic community structures.

Contribution

It presents novel formulations and algorithms for temporal graph cuts using spectral methods, multiplex graphs, and low-rank approximations, addressing the dynamic nature of modern graphs.

Findings

Algorithms are accurate and scalable.

Effective in discovering dynamic communities.

Applicable to dynamic graph signal analysis.

Abstract

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of graph cuts include community detection and computer vision. However, cut problems were originally proposed for static graphs, an assumption that does not hold in many modern applications where graphs are highly dynamic. In this paper, we introduce the sparsest and normalized cut problems in temporal graphs, which generalize their standard definitions by enforcing the smoothness of cuts over time. We propose novel formulations and algorithms for computing temporal cuts using spectral graph theory, multiplex graphs, divide-and-conquer and low-rank matrix approximation. Furthermore, we extend our formulation to dynamic graph signals, where cuts also capture node values, as graph wavelets. Experiments show that our solutions are accurate and scalable, enabling the discovery of dynamic communities and the analysis of dynamic graph processes.