Publication details
Walk entropy and walk-regularity
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | Linear Algebra and its Applications |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.laa.2018.02.009 |
| Keywords | Graph entropy; Walk-regularity; Subgraph centrality; Matrix exponential |
| Description | A graph is said to be walk-regular if, for each l >= 1, every vertex is contained in the same number of closed walks of length l. We construct a 24-vertex graph H-4 that is not walk regular yet has maximized walk entropy, S-v (H-4, beta) = log 24, for some beta > 0. This graph is a counterexample to a conjecture of Benzi (2014) [1, Conjecture 3.1]. We also show that there exist infinitely many temperatures beta(0) > 0 so that S-V (G, beta(0)) = log n(G) if and only if a graph G is walk-regular. (C) 2018 Elsevier Inc. All rights reserved. |