https://github.com/jacksonwalters/graphs

Embeds the adjacency matrix of a graph into the finite field F_q
https://github.com/jacksonwalters/graphs

adjacency-matrix finite-fields graph-embedding graphs

Last synced: 6 months ago
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Embeds the adjacency matrix of a graph into the finite field F_q

• Host: GitHub
• URL: https://github.com/jacksonwalters/graphs
• Owner: jacksonwalters
• License: mit
• Created: 2024-07-09T20:21:29.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2025-01-16T22:21:12.000Z (about 1 year ago)
• Last Synced: 2025-01-16T23:19:28.833Z (about 1 year ago)
• Topics: adjacency-matrix, finite-fields, graph-embedding, graphs
• Language: Jupyter Notebook
• Homepage:
• Size: 461 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# embedding-graphs-finite-fields

- embeds the adjacency matrix of a graph into the finite field F_q by viewing edges as bits, writing the bitstring k as an integer, and using that as the exponent of a multiplicative generator

- factors an adjacency matrix U = AA^* using the Hermitian decomposition used for unitary rep'ns of the symmetric group over a finite field. note the adjacency matrix is symmetric and values are in {0,1}, which are in any field