= Uniform connective constant of a bounded-degree graph
{title2=$\mu=\lim_n(\sup_v\sigma_n(v))^{1/n}$}
For an infinite connected <locally finite graph> with a uniform degree bound, let $\sigma_n(v)$ count its length-$n$ <self-avoiding walks> from $v$. The suprema satisfy $\sigma_{m+n}\leq\sigma_m\sigma_n$, so the <Fekete lemma> applied to their logarithms gives a finite <connective constant>. Unlike the usual rooted definition on a <vertex-transitive graph>, this definition explicitly takes the supremum over roots.
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