Models for network dynamics: A Markovian framework*

I am indebted to Tom Snijders, Frans Stokman, and Stanley Wasserman for their comments on an earlier draft of this paper and for making comments on previous work. I thank Marjolein Achterkamp for programming assistance. This project is subsidized by The Netherlands Organization for Scientific Research (NWO, 500–278–401).

A question not very often addressed in social network analysis relates to network dynamics and focuses on how networks arise and change. It alludes to the idea that ties do not arise or vanish randomly, but (partly) as a consequence of human behavior and preferences. Statistical models for modeling changes in the structure of social networks are rare and often strongly restricted substantively. The common approach is to focus on conditional transition probabilities using loglinear modeling. In the present article it is argued that it is more natural to model transition rates instead of probabilities. A model for explaining transition rates is presented using continuous time Markov theory. It is shown that a Markovian approach yields a very flexible model that can handle a wide variety of parameters that may be structural, non‐structural or a combination. A range of possible models is discussed and applied to data on friendship formation in a classroom.

Key words:

• Markov
• friendship
• network dynamics
• transition rates

Notes

I am indebted to Tom Snijders, Frans Stokman, and Stanley Wasserman for their comments on an earlier draft of this paper and for making comments on previous work. I thank Marjolein Achterkamp for programming assistance. This project is subsidized by The Netherlands Organization for Scientific Research (NWO, 500–278–401).