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arXiv · 2312.01378

The reachability homology of a directed graph

Richard Hepworth·Emily Roff
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Abstract

The last decade has seen the development of path homology and magnitude homology -- two homology theories of directed graphs, each satisfying classic properties such as Kunneth and Mayer-Vietoris theorems. Recent work of Asao has shown that magnitude homology and path homology are related, appearing in different pages of a certain spectral sequence. Here we study the target of that spectral sequence, which we call reachability homology. We prove that it satisfies appropriate homotopy invariance, Kunneth, excision, and Mayer-Vietoris theorems, these all being stronger than the corresponding properties for either magnitude or path homology.

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Richard Hepworth, Emily Roff. 2023-12-03. The reachability homology of a directed graph. https://arxiv.org/abs/2312.01378

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