An efficient counting method for the colored triad census
Jeffrey Lienert, Laura Koehly, Felix Reed-Tsochas, Christopher Steven, Marcum

TL;DR
This paper introduces an efficient algorithm for the colored triad census in network analysis, enabling faster computation and statistical testing of relational configurations with node attributes.
Contribution
The paper presents a novel, computationally efficient algorithm for the colored triad census, extending existing methods for the classic triad census.
Findings
Algorithm reduces computational time significantly.
Demonstrates utility with empirical and simulated data.
Enables statistical testing of triad configurations.
Abstract
The triad census is an important approach to understand local structure in network science, providing comprehensive assessments of the observed relational configurations between triples of actors in a network. However, researchers are often interested in combinations of relational and categorical nodal attributes. In this case, it is desirable to account for the label, or color, of the nodes in the triad census. In this paper, we describe an efficient algorithm for constructing the colored triad census, based, in part, on existing methods for the classic triad census. We evaluate the performance of the algorithm using empirical and simulated data for both undirected and directed graphs. The results of the simulation demonstrate that the proposed algorithm reduces computational time many-fold over the naive approach. We also apply the colored triad census to the Zachary karate club…
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