  In this paper, we introduce the concept of the independence graph of a
directed 2-complex. We show that the class of diagram groups is closed under
graph products over independence graphs of rooted 2-trees. This allows us to
show that a diagram group containing all countable diagram groups is a
semi-direct product of a partially commutative group and R. Thompson's group
$F$. As a result, we prove that all diagram groups are totally orderable.
