bitriad: 'bitriad': Triadic analysis of affiliation networks

Description Details Triad censuses Measures of triad closure Author(s) References


Calculate triad censuses and triad closure statistics designed for affiliation networks.


The package contains two principal tools for the triadic analysis of affiliation networks: triad censuses and measures of triad closure. Assorted additional functions, including a measure of dynamic triad closure, are also included.

Triad censuses

Three triad censuses are implemented for affiliation networks:

Each of these censuses can be projected from the previous using the function project_census. A fourth census, called the uniformity triad census and implemented as unif_triad_census, is deprecated. Three-actor triad affiliation networks can be constructed and plotted using the triad functions.

The default method for the two affiliation network–specific triad censuses is adapted from the algorithm of Batagelj and Mrvar (2001) for calculating the classical triad census for a directed graph.

Measures of triad closure

Each measure of triad closure is defined as the proportion of wedges that are closed, where a wedge is the image of a specified two-event triad W under a specified subcategory of graph maps C subject to a specified congruence relation ~, and where a wedge is closed if it is the image of such a map that factors through a canonical inclusion of W to a specified self-dual three-event triad X.

The alcove, wedge, maps, and congruence can be specified by numerical codes as follows (no plans exist to implement more measures than these):

Some specifications correspond to statistics of especial interest:

See Brunson (2015) for a general definition and the aforecited references for discussions of each statistic.


Jason Cory Brunson


Kreher, D.L., & Stinson, D.R. (1999). Combinatorial algorithms: generation, enumeration, and search. SIGACT News, 30(1), 33–35.

Batagelj, V., & Mrvar, A. (2001). A subquadratic triad census algorithm for large sparse networks with small maximum degree. Social Networks, 23(3), 237–243.

Brunson, J.C. (2015). Triadic analysis of affiliation networks. Network Science, 3(4), 480–508.

Watts, D.J., & Strogatz, S.H. (1998). Collective dynamics of "small-world" networks. Nature, 393(6684), 440–442.

Opsahl, T. (2013). Triadic closure in two-mode networks: Redefining the global and local clustering coefficients. Social Networks, 35(2), 159–167. Special Issue on Advances in Two-mode Social Networks.

Liebig, J., & Rao, A. (2014). Identifying influential nodes in bipartite networks using the clustering coefficient. Pages 323–330 of: Proceedings of the tenth international conference on signal-image technology and internet-based systems.

Brunson, J.C. (2015). Triadic analysis of affiliation networks. Network Science, 3(4), 480–508.

corybrunson/bitriad documentation built on May 13, 2019, 10:51 p.m.