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}
}
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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