  Inspired by connections described in a recent paper by Mark L. Lewis, between
the common divisor graph $\Ga(X)$ and the prime vertex graph $\Delta(X)$, for a
set $X$ of positive integers, we define the bipartite divisor graph $B(X)$, and
show that many of these connections flow naturally from properties of $B(X)$.
In particular we establish links between parameters of these three graphs, such
as number and diameter of components, and we characterise bipartite graphs that
can arise as $B(X)$ for some $X$. Also we obtain necessary and sufficient
conditions, in terms of subconfigurations of $B(X)$, for one $\Gamma(X)$ or
$\Delta(X)$ to contain a complete subgraph of size 3 or 4.
