Network measures for dyadic interactions: stability and reliability.

Social network analysis (SNA) is a general heading for a collection of statistical tools that aim to describe social interactions and social structure by representing individuals and their interactions as graph objects. It was originally developed for the social sciences, but more recently it was also adopted by behavioral ecologists. However, although SNA offers a full range of exciting possibilities for the study of animal societies, some authors have raised concerns about the correct application and interpretation of network measures. In this article, we investigate how reliable and how stable network measures are (i.e. how much variation they show under re-sampling and how much they are influenced by erroneous observations). For this purpose, we took a data set of 44 nonhuman primate grooming networks and studied the effects of re-sampling at lower re-sampling rates than the originally observed ones and the inclusion of two types of errors, "mis-identification" and "mis-classification," on six different network metrics, i.e. density, degree variance, vertex strength variance, edge weight disparity, clustering coefficient, and closeness centrality. Although some measures were tolerant toward reduced sample sizes, others were sensitive and even slightly reduced samples could yield drastically different results. How strongly a metric is affected seems to depend on both the sample size and the structure of the specific network. The same general effects were found for the inclusion of sampling errors. We, therefore, emphasize the importance of calculating valid confidence intervals for network measures and, finally, we suggest a rough research plan for network studies.