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arXiv · 2507.17541

Approximating temporal modularity on graphs of small underlying treewidth

Vilhelm Agdur·Jessica Enright·Laura Larios-Jones·Kitty Meeks·Fiona Skerman·Ella Yates
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Abstract

Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete timesteps; such graphs offer a more realistic model of many real-world networks in which connections between entities (for example, between individuals in a social network) evolve over time. Computing modularity is notoriously difficult: it is NP-hard even to approximate in general, and only admits efficient exact algorithms in very restricted special cases. Our main result is that a multiplicative approximation to temporal modularity can be computed efficiently when the underlying graph has small treewidth. This generalises a similar approximation algorithm for the static case, but requires some substantially new ideas to overcome technical challenges associated with the temporal nature of the problem.

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Vilhelm Agdur, Jessica Enright, Laura Larios-Jones, Kitty Meeks, Fiona Skerman, Ella Yates. 2025-07-23. Approximating temporal modularity on graphs of small underlying treewidth. https://arxiv.org/abs/2507.17541

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