# Categorifying the magnitude of a graph

@article{Hepworth2015CategorifyingTM,
title={Categorifying the magnitude of a graph},
author={Richard A. Hepworth and Simon Willerton},
journal={arXiv: Combinatorics},
year={2015}
}
• Published 15 May 2015
• Mathematics
• arXiv: Combinatorics
The magnitude of a graph can be thought of as an integer power series associated to a graph; Leinster introduced it using his idea of magnitude of a metric space. Here we introduce a bigraded homology theory for graphs which has the magnitude as its graded Euler characteristic. This is a categorification of the magnitude in the same spirit as Khovanov homology is a categorification of the Jones polynomial. We show how properties of magnitude proved by Leinster categorify to properties such as a…

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