Modern Approaches to Discrete Curvature pp 211-258 | Cite as

# The Geometric Spectrum of a Graph and Associated Curvatures

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## 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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