Considering clustering measures: Third ties, means, and triplets

Measures that estimate the clustering coefficients of ego and overall social networks are important to social network studies. Existing measures differ in how they define and estimate triplet clustering with implications for how network theoretic properties are reflected. In this paper, we propose a novel definition of triplet clustering for weighted and undirected social networks that explicitly considers the relative strength of the tie connecting the two alters of the ego in the triplet. We argue that our proposed definition better reflects theorized effects of the important third tie in the social network literature. We also develop new methods for estimating triplet, local and global clustering. Three different types of mathematical means, i.e. arithmetic, geometric, and quadratic, are used to reflect alternative theoretical assumptions concerning the marginal effect of tie substitution.

► A new definition of triplet clustering for weighted social networks is proposed.
► The proposed definition reflects theorized effects of the important third tie.
► New methods for estimating triplet, local and global clustering are developed.
► Different types of mathematical means reflect marginal effect of tie substitution.
► Network theoretic properties/considerations dictate choice of clustering measure.