An Efficient Counting Method for the Colored Triad Census

Social Networks, 58, 136 - 142, July 2019.

26 Pages Posted: 12 Feb 2018 Last revised: 22 Jun 2020

See all articles by Jeffrey Lienert

Jeffrey Lienert

National Institutes of Health (NIH) - National Human Genome Research Institute; University of Oxford - CABDyN Complexity Centre

Laura Koehly

National Institutes of Health (NIH) - National Human Genome Research Institute

Felix Reed-Tsochas

University of Oxford - Said Business School

Christopher Steven Marcum

National Institutes of Health (NIH) - National Human Genome Research Institute

Date Written: February 6, 2018

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 by approximately 17,400% over the naive approach. We also apply the colored triad census to the Zachary karate club network dataset. We simultaneously show the efficiency of the algorithm, and a way to conduct a statistical test on the census by forming a null distribution from 1,000 realizations of a mixing-matrix conditioned graph and comparing the observed colored triad counts to the expected. From this, we demonstrate the method's utility in our discussion of results about homophily, heterophily, and bridging, simultaneously gained via the colored triad census. In sum, the proposed algorithm for the colored triad census brings novel utility to social network analysis in an efficient package.

Keywords: triad census, labeled graphs, simulation

Suggested Citation

Lienert, Jeffrey and Koehly, Laura and Reed-Tsochas, Felix and Marcum, Christopher Steven, An Efficient Counting Method for the Colored Triad Census (February 6, 2018). Social Networks, 58, 136 - 142, July 2019., Available at SSRN: https://ssrn.com/abstract=3119068 or http://dx.doi.org/10.2139/ssrn.3119068

Jeffrey Lienert (Contact Author)

National Institutes of Health (NIH) - National Human Genome Research Institute ( email )

Building 29, Room $a56
49 Convent Dr, MSC 4472
Bethesda, MD 20892
United States

University of Oxford - CABDyN Complexity Centre ( email )

Park End Street
Oxford, OX1 1HP
United Kingdom

Laura Koehly

National Institutes of Health (NIH) - National Human Genome Research Institute ( email )

Building 29, Room $a56
49 Convent Dr, MSC 4472
Bethesda, MD 20892
United States

Felix Reed-Tsochas

University of Oxford - Said Business School ( email )

Park End Street
Oxford, OX1 1HP
Great Britain

HOME PAGE: http://www.sbs.ox.ac.uk/community/people/felix-reed-tsochas

Christopher Steven Marcum

National Institutes of Health (NIH) - National Human Genome Research Institute ( email )

Building 29, Room $a56
49 Convent Dr, MSC 4472
Bethesda, MD 20892
United States

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