A dynamic model for social networks†

This report is part of a continuing research series and describes work that is collaborative in every respect. The order of authorship is alphabetical. We are grateful to Stanley Wasserman for assistance in conducting the reported research. Support was provided by NSF Grant SOC 73–05489 to Carnegie‐Mellon University.

A continuous‐time binary‐matrix‐valued Markov chain is used to model the process by which social structure effects individual behavior. The model is developed in the context of sociometric networks of interpersonal affect. By viewing the network as a time‐dependent stochastic process it is possible to construct transition intensity equations for the probability that choices between group members will change. These equations can contain parameters for structural effects. Empirical estimates of the parameters can be interpreted as measures of structural tendencies. Some elementary processes are described and the application of the model to cross‐sectional data is explained in terms of the steady state solution to the process.

Notes

This report is part of a continuing research series and describes work that is collaborative in every respect. The order of authorship is alphabetical. We are grateful to Stanley Wasserman for assistance in conducting the reported research. Support was provided by NSF Grant SOC 73–05489 to Carnegie‐Mellon University.