# Curvature on a graph via its geometric spectrum

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

Actes des rencontres du CIRM (2013)

- Volume: 3, Issue: 1, page 97-105
- ISSN: 2105-0597

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top## How to cite

topBaird, Paul. "Curvature on a graph via its geometric spectrum." Actes des rencontres du CIRM 3.1 (2013): 97-105. <http://eudml.org/doc/275380>.

@article{Baird2013,

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. 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.},

affiliation = {Laboratoire de Mathématiques de Bretagne Atlantique Université de Bretagne Occidentale 6 av. Victor Le Gorgeu – CS 93837 29238 BREST CEDEX FRANCE},

author = {Baird, Paul},

journal = {Actes des rencontres du CIRM},

keywords = {graph theory; curvature; geometric spectrum; shape recognition},

language = {eng},

month = {11},

number = {1},

pages = {97-105},

publisher = {CIRM},

title = {Curvature on a graph via its geometric spectrum},

url = {http://eudml.org/doc/275380},

volume = {3},

year = {2013},

}

TY - JOUR

AU - Baird, Paul

TI - Curvature on a graph via its geometric spectrum

JO - Actes des rencontres du CIRM

DA - 2013/11//

PB - CIRM

VL - 3

IS - 1

SP - 97

EP - 105

AB - 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.

LA - eng

KW - graph theory; curvature; geometric spectrum; shape recognition

UR - http://eudml.org/doc/275380

ER -

## References

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- C. Delaunay, Sur la surface de révolution dont la courbure moyenne est constante, 6 ((1841)), 309-320
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