  The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the
exponential growth rate of the number of self-avoiding walks from a given
origin. We prove a locality theorem for connective constants, namely, that the
connective constants of two graphs are close in value whenever the graphs agree
on a large ball around the origin (and a further condition is satisfied). The
proof exploits a generalized bridge decomposition of self-avoiding walks, which
is valid subject to the assumption that the underlying graph is
quasi-transitive and possesses a so-called unimodular graph height function.
