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Curvature on a graph via its geometric spectrum
Paul Baird1
1 Laboratoire de Mathématiques de Bretagne Atlantique Université de Bretagne Occidentale 6 av. Victor Le Gorgeu – CS 93837 29238 BREST CEDEX FRANCE
Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 97-105.

We approach the problem of defining curvature on a graph by attempting to attach a ‘best-fit polytope’ to each vertex, or more precisely what we refer to as a configured star. How this should be done depends upon the global structure of the graph which is reflected in its geometric spectrum. Mean curvature is the most natural curvature that arises in this context and corresponds to local liftings of the graph into a suitable Euclidean space. We discuss some examples.

Published online:
DOI: 10.5802/acirm.59
Classification: 05C10, 52C99, 52B11, 39A14
Keywords: graph theory, curvature, geometric spectrum, shape recognition
Paul Baird 1

1 Laboratoire de Mathématiques de Bretagne Atlantique Université de Bretagne Occidentale 6 av. Victor Le Gorgeu – CS 93837 29238 BREST CEDEX FRANCE 
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Paul Baird. Curvature on a graph via its geometric spectrum. Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 97-105. doi : 10.5802/acirm.59. https://acirm.centre-mersenne.org/articles/10.5802/acirm.59/

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