Approximating temporal modularity on graphs of small underlying treewidth
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915406452621312 |
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| author | Agdur, Vilhelm Enright, Jessica Larios-Jones, Laura Meeks, Kitty Skerman, Fiona Yates, Ella |
| author_facet | Agdur, Vilhelm Enright, Jessica Larios-Jones, Laura Meeks, Kitty Skerman, Fiona Yates, Ella |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximating temporal modularity on graphs of small underlying treewidth Agdur, Vilhelm Enright, Jessica Larios-Jones, Laura Meeks, Kitty Skerman, Fiona Yates, Ella Combinatorics Discrete Mathematics 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. |
| title | Approximating temporal modularity on graphs of small underlying treewidth |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2507.17541 |