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Algebraic Potential Theory on Graphs
Abstract
This paper encompasses a motley collection of ideas from several areas of mathematics, including, in no particular order, random walks, the Picard group, exchange rate networks, chip-firing games, cohomology, and the conductance of an electrical network. The linking threads are the discrete Laplacian on a graph and the solution of the associated Dirichlet problem. Thirty years ago, this subject was dismissed by many as a trivial specialisation of cohomology theory, but it has now been shown to have hidden depths. Plumbing these depths leads to new theoretical advances, many of which throw light on the diverse applications of the theory. 1991 Mathematics Subject Classification 05C50.
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Cited by
Random Walks for Image Segmentation
Grady, L. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.233 · Cited by 2,624
Synchronization and power sharing for droop-controlled inverters in islanded microgrids
Simpson-Porco, J. W., Dörfler, F., & Bullo, F. (2013) · Automatica · doi:10.1016/j.automatica.2013.05.018 · Cited by 832
Random walks and diffusion on networks
Masuda, N., Porter, M. A., & Lambiotte, R. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.07.007 · Cited by 657
Metadata
- Authors
- Biggs, N.
- Venue
- Bulletin of the London Mathematical Society
- Publisher
- Wiley
- Published
- 1997-11
- Volume
- 29
- Issue
- 6
- Pages
- 641-682
- ISSN
- 0024-6093 (ISSN-L)
- OpenAlex
- W2111293718
- Cited by
- 238
- References
- 0
- FWCI
- 3.55
- Type
- journal article
- Language
- en
- Open access
- closed
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- Biggs, N. (1997). Algebraic Potential Theory on Graphs. Bulletin of the London Mathematical Society. https://doi.org/10.1112/s0024609397003305
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
