Methods for Analysing Dynamics of Social Networks

Abstract

Social networks can be defined as the patterns of ties between social actors. They are usually represented by graphs and digraphs. The crucial issue for statistical modelling of social network data is how to deal with the stochastic dependencies between the variables indicating the existence of different ties. Such dependencies could express, e.g., tendencies toward reciprocation in directed networks, and tendencies toward transitivity. In this presentation attention will be given to Stochastic Actor-oriented Dynamic Graph Models, a flexible class of continuous-time Markov chain models which can be used for longitudinal observations on social networks. These models can incorporate so-called structural effects – where the transition probabilities depend on the current network structure reflecting, e.g., tendencies toward reciprocity and transitivity – as well as covariate effects. In the social sciences it is common to collect longitudinal network data in a panel design. This leads to complications in the analysis because it is plausible to assume that changes in the network take place in continuous time, unobserved between observation moments.