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  "body": "\n## Summary\n\nIn 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.\n",
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