  We study the 4-d holomorphic Spin Foam amplitude on arbitrary connected
2-complexes and degrees of divergence. With recently developed tools and
truncation scheme, we derive a formula for a certain class of graphs, which
allows us to write down the value of bulk amplitudes simply based on graph
properties. We then generalize the result to arbitrary connected 2-complexes
and extract a simple expression for the degree of divergence only in terms of
combinatorial properties and topological invariants. The distinct behaviors of
the model in different regions of parameter space signal phase transitions. In
the regime which is of physical interest for recovering diffeomorphsim symmetry
in the continuum limit, the most divergent configurations are melonic graphs.
We end with a discussion of physical implications.
