Constructing Adjacency Arrays from Incidence Arrays

Graph construction, a fundamental operation in a data processing pipeline, is typically done by multiplying the incidence array representations of a graph, E in and E out, to produce an adjacency array of the graph, A, that can be processed with a variety of algorithms. This paper provides the mathematical criteria to determine if the product A = E T\out E 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 ⊕ and multiplication ⊗ operations used to perform the array multiplication. Illustrations of the various results possible from different ⊕ and ⊗ operations are provided using a small collection of popular music metadata.