---
tag: CEVS6RA6CM
kind: concept
name: Walk-regular graph
aliases: [0-walk-regular-graph, 1-walk-regular-graph]
sources:
  - wikipedia: en:54617362@r1330034833
    locator: Walk-regular graph
    note: adopted
    mention: wikipedia://en/54617362
    sections: [Summary]
same_as:
  wikidata: Q48996522
  wikipedia: Walk-regular graph
inventory: [Y7S249QFND]
---

## Summary

In graph theory, a **walk-regular graph** is a simple graph where the number of closed walks of any length $\ell$ from a vertex to itself does only depend on $\ell$ but not depend on the choice of vertex. Walk-regular graphs can be thought of as a spectral graph theory analogue of vertex-transitive graphs. While a walk-regular graph is not necessarily very symmetric, all its vertices still behave identically with respect to the graph's spectral properties.