Random graph models for temporal processes in social networks

Abstract

We generalize the graphical modeling approach of p* social influence models to develop discrete time models for the temporal evolution of social networks. Plausible general processes pertaining to network evolution are broadly discussed as a basis for across‐time dependence assumptions. Systematic temporal processes are construed as effects that are homogeneous across the network, and that reflect dynamics inherent in a particular social relation. Any one actor cannot control these dynamics, especially given that non‐dyadic configurations may be implicated, for instance, tendencies for various triadic configurations to be constructed or to collapse of over time. Non‐systematic processes, on the other hand, may pertain to the changing nature of a particular dyadic tie, or to change involving a particular sociotemporal neighborhood of the network. Non‐systematic processes are inhomogeneous across time and across the network, and are modeled as random. In constructing p* dependence graphs, systematic temporal processes may be represented, in part, by the perfect dependence assumption, whereby network across‐time dependencies “mirror” within‐time dependencies. We develop temporal perfect dependence models appropriate for Markov random graphs. To disentangle non‐systematic from systematic temporal processes is not straightforward, but the use of the constant tie assumption ‐ whereby ephemeral ties are assumed not to have influence across time ‐is one possible approach. We illustrate these models with three empirical examples: first, with an analysis of the Freeman EIES data; and then with data from a newly formed small training group involving two networks, trust and friendship.