An algebraic-combinatorial framework for finding the average hitting times in graphs with high regularity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914557753032704 |
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| author | Abiad, Aida Nishimura, Yusaku |
| author_facet | Abiad, Aida Nishimura, Yusaku |
| contents | For any given vertices $u$ and $v$ in a graph, the hitting time of a random walk on a finite graph is the number of steps it takes for a random walk to reach vertex $v$ starting at vertex $u$. The expected value of the hitting time is the average hitting time. In this paper, we present an algebraic-combinatorial method for calculating the average hitting time between vertices of finite graphs exhibiting high regularity, along with its applications to multiple graph classes. Our approach exploits a novel connection between maximal-entropy random walks and weight-equitable partitions, providing a unifying framework that strengthens and extends several known results, including Rao's method [Statistics \& Probability Letters, 2013] for computing the hitting time from a vertex to a neighbor under certain symmetries of the starting vertex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11812 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An algebraic-combinatorial framework for finding the average hitting times in graphs with high regularity Abiad, Aida Nishimura, Yusaku Combinatorics For any given vertices $u$ and $v$ in a graph, the hitting time of a random walk on a finite graph is the number of steps it takes for a random walk to reach vertex $v$ starting at vertex $u$. The expected value of the hitting time is the average hitting time. In this paper, we present an algebraic-combinatorial method for calculating the average hitting time between vertices of finite graphs exhibiting high regularity, along with its applications to multiple graph classes. Our approach exploits a novel connection between maximal-entropy random walks and weight-equitable partitions, providing a unifying framework that strengthens and extends several known results, including Rao's method [Statistics \& Probability Letters, 2013] for computing the hitting time from a vertex to a neighbor under certain symmetries of the starting vertex. |
| title | An algebraic-combinatorial framework for finding the average hitting times in graphs with high regularity |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.11812 |