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The Geometric Spectrum of a Graph and Associated Curvatures

  • Paul Baird
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2184)

Abstract

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. Various curvatures naturally arise from local liftings of the graph into a suitable Euclidean space.

Notes

Acknowledgements

The author would like to express his thanks to Pascal Romon and the referee whose insightful comments have helped to improve this work.

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© The Author(s) 2017

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de Bretagne AtlantiqueUniversité de Bretagne OccidentaleBrest CedexFrance

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