Geometric multiplicity of unitary non-backtracking eigenvalues
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909979226669056 |
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| author | Torres, Leo |
| author_facet | Torres, Leo |
| contents | We completely characterize the conditions under which a complex unitary number is an eigenvalue of the non-backtracking matrix of an undirected graph. Further, we provide a closed formula to compute its geometric multiplicity and describe an algorithm to compute this multiplicity without making a single matrix computation. The algorithm has time complexity that is linear in the size of the graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_02004 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geometric multiplicity of unitary non-backtracking eigenvalues Torres, Leo Combinatorics 05C50, 05C82, 05C85, 15A18, 15B99 We completely characterize the conditions under which a complex unitary number is an eigenvalue of the non-backtracking matrix of an undirected graph. Further, we provide a closed formula to compute its geometric multiplicity and describe an algorithm to compute this multiplicity without making a single matrix computation. The algorithm has time complexity that is linear in the size of the graph. |
| title | Geometric multiplicity of unitary non-backtracking eigenvalues |
| topic | Combinatorics 05C50, 05C82, 05C85, 15A18, 15B99 |
| url | https://arxiv.org/abs/2205.02004 |