An Omnibus Test for Social Structure Using Triads

Abstract

A general or omnibus test of structure in social network data is proposed. The test exploits all of the information contained in the triad census. Analogous to the classical F-test for contrasts among means, the proposed test involves finding a weighting vector which maximizes a test statistic, τ 2 ( max), in the context ofan empirical data matrix and then determining whether this quantity is statistically significant by reference to a table of the chi-square distribution. An insignificant value of τ2 ( max) implies that the structure of the network data matrix is ran dom, and, therefore, that the search for recognizable or substantively meaning ful pattern in the data may be subject to artifactual discoveries. Empirical results are presented which indicate that, of the networks commonly studied by social researchers, some have random structure, others have nonrandom structure and exhibit strong indications of transitivity and still others, with strong indications of nonrandom structure, do not exhibit strong indications of transitivity.