  The complexity of graph homomorphisms has been a subject of intense study
[11, 12, 4, 42, 21, 17, 6, 20]. The partition function $Z_{\mathbf A}(\cdot)$
of graph homomorphism is defined by a symmetric matrix $\mathbf A$ over
$\mathbb C$. We prove that the complexity dichotomy of [6] extends to bounded
degree graphs. More precisely, we prove that either $G \mapsto Z_{\mathbf
A}(G)$ is computable in polynomial-time for every $G$, or for some $\Delta > 0$
it is #P-hard over (simple) graphs $G$ with maximum degree $\Delta(G) \le
\Delta$. The tractability criterion on $\mathbf A$ for this dichotomy is
explicit, and can be decided in polynomial-time in the size of $\mathbf A$. We
also show that the dichotomy is effective in that either a P-time algorithm
for, or a reduction from #SAT to, $Z_{\mathbf A}(\cdot)$ can be constructed
from $\mathbf A$, in the respective cases.
