Accounting for degree distributions in empirical analysis of network dynamics. Pp

Degrees (the number of links attached to a given node) play a particular and important role in empirical network analysis because of their obvious importance for expressing the position of nodes. It is argued here that there is no general straightforward relation between the degree distribution on one hand and structural aspects on the other hand, as this relation depends on further characteristics of the presumed model for the network. Therefore empirical inference from observed network characteristics to the processes that could be responsible for network genesis and dynamics cannot be based only, or mainly, on the observed degree distribution. As an elaboration and practical implementation of this point, a statistical model for the dynamics of networks, expressed as digraphs with a fixed vertex set, is proposed in which the outdegree distribution is governed by parameters that are not connected to the parameters for the structural dynamics. The use of such an approach in statistical modeling minimizes the influence of the observed degrees on the conclusions about the structural aspects of the network dynamics. The model is a stochastic actor-oriented model, and deals with the de-grees in a manner resembling Tversky’s Elimination by Aspects approach. A statistical procedure for parameter estimation in this model is proposed, and an example is given