  Graph construction, a fundamental operation in a data processing pipeline, is
typically done by multiplying the incidence array representations of a graph,
$\mathbf{E}_\mathrm{in}$ and $\mathbf{E}_\mathrm{out}$, to produce an adjacency
array of the graph, $\mathbf{A}$, that can be processed with a variety of
algorithms. This paper provides the mathematical criteria to determine if the
product $\mathbf{A} = \mathbf{E}^{\sf T}_\mathrm{out}\mathbf{E}_\mathrm{in}$
will have the required structure of the adjacency array of the graph. The
values in the resulting adjacency array are determined by the corresponding
addition $\oplus$ and multiplication $\otimes$ operations used to perform the
array multiplication. Illustrations of the various results possible from
different $\oplus$ and $\otimes$ operations are provided using a small
collection of popular music metadata.
