Edge weight variance: population genetic metrics for social network analysis

We present novel metrics for analysis of weighted social networks that focus explicitly on the distribution of edge weights at hierarchical scales from node to egonet to community and to the network as a whole. The formulae are adapted from existing measures, originally developed in the context of population genetics to analyse variance in gene frequencies at different levels of organization. Our metrics, including 'effective degree' (by analogy to effective number of alleles), 'concentration' (by analogy to the inbreeding coefficient), 'observed' and 'expected edge weight diversity' (by analogy to observed and expected gene diversity) and F statistics allow one to partition the variance in edge weights among hierarchical levels of organization within networks. They provide a quantitative method for addressing issues as diverse as disease transmission, social complexity, the spread of learned behaviours and the evolution of cooperation. We illustrate the utility of these new metrics by applying them to three empirical social networks: long-tailed manakins, Chiroxiphia linearis, monk parakeets, Myiopsitta monachus, and mountain goats, Oreamnos americanus.