Let $G$ be a vertex-transitive locally finite graph and $c_n$ the number of self-avoiding walks in $G$ starting from some fixed vertex $v_0$. One can easily see that $c_{m+n} \leq c_m c_n$ and hence Fekete's subadditive lemma gives that there exists the limit $\mu := \lim_{n\to\infty} c_n^{1/n}$. This quantity is known in the literature as the **connective constant** of $G$.

My question is basically what is the source of this term? I.e. it seems to be a strange choice of words for this quantity, so is there some application where it plays a role in some kind of "connectedness" which would excuse the name?