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Discrete curvature on graphs from the effective resistance

Abstract:

This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably, we find a relation to a number of well-established discrete curvatures (Ollivier, Forman, combinatorial curvature) and show evidence for convergence to continuous curvature in the case of Euclidean random graphs. Being both efficient to approximate and high...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1088/2632-072X/ac730d

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Somerville College
Role:
Author
ORCID:
0000-0002-0583-4595
Publisher:
IOP Publishing Publisher's website
Volume:
3
Issue:
2
Publication date:
2022-06-08
Acceptance date:
2022-05-24
DOI:
EISSN:
2632-072X
Language:
English
Keywords:
Pubs id:
1236250
Local pid:
pubs:1236250
Deposit date:
2022-05-13

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