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I could only give you some examples of theories of network stability from
the point of view a certain theoretical concepualizations of dynamically
changing social structure (which perhaps fall outside of what you're

Network exchange theory is a first possibility (although I cannot think of
a single general reference which is explicitly treating stability). But in
the more specific context of E-states model, I could recommend:

Skvoretz, J., Faust, K, & Fararo, T.J. (1997). Social structure, networks,
and E-state structuralism models. In P. Doreian & F.N. Stokman (eds.),
"Evolution of Social Networks", pp. 73-92. Amsterdam: Gordon & Breach.

Of course, this is just an example of Skvoretz work: he and his coworkers
have written much more. For example, some recent work has been done by T.

Burkett, T. (1997). Cencorship in the United States Senate: A network
analysis of senate communication and leadership, 1973-1990. Unpublished
Ph.D. thesis. University of South Carolina.

Burkett, T., & Skvoretz, J. (2001). Political support networks among US
senators: Stability and change from 1973 to 1990.

The other suggestions I can make are related to game theory and economic
reasoning of social networks. The basic definition of stochastic stability
is explained analytically in the book:

Young, H.P. (1998). Individual Strategy and Social Structure. An
Evolutionary Theory of Institutions. Princeton, NJ: Princeton University

Some works related to such game-theoretic notions of network stability

Bala, V., & Goyal, S. (2000). A nooncooperative model of network
formation. Econometrica, vol. 68, no. 5, pp. 1181-1229.

Skyrms, B., & Pemantle, R. (2000). A dynamic model of social network
formation. Proceedings of the National Academy of Sciences, vol. 97,
no. 16, pp. 9340-9346.

Pemantle, R., & Skyrms, B. (2004). Network formation by reinforcement
learning: The long and medium run. Mathematical Social Sciences, vol.
48, pp. 315-327.

Jackson, M.O., & Watts, A. (2002). On the formation of interaction
networks in social coordination games. Games & Economic Behavior, vol.
41, pp. 265-291.

Finally, although not explicitly related to stability, I would mention the
following works too (which are in the context of interacting particle

Bonacich, P. , & Liggett, T.M. (2003). Asymptotics of a matrix valued
Markov chain arising in sociology. Stochastic Processes & their
Applications, vol. 104, no. 1, pp. 155-171.

Liggett, T.M., & Rolles, S.W.W. (2004). An infinite stochastic model
of social network formation. Stochastic Processes & their
Applications, vol. 113, pp. 65-80.

I understand that I might not have been too much helpful in terms of what
exactly you're looking for but I've tried to quote relevant theoretical
work from which an insight to more practical issues might be drawn.



  M.A. Boudourides
  Associate Professor

  Department of Mathematics
  University of Patras
  265 00 Rio-Patras

  Tel.: +30-2610-996318
  Fax:  +30-2610-996318, +30-2610-992965

On Thu, 17 Feb 2005, Corey Phelps wrote:

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> I am looking for studies that have examined how the stability of
> networks influence the behavior of their members. I am particularly
> interested in research that has looked at the aggregate durability of
> ego's ties on ego's behavior and performance. For example, it strikes me
> that the structural holes and network closure arguments of social
> capital make implicit assumptions regarding the length of time the ties
> in ego's network have existed. Will the ties in a newly formed (ego)
> network have the same information diffusion properties of a
> long-existing network and thus give rise to the same degree of
> deterrence-based trust? How might the addition of a new dyad (or triad)
> to a network alter the dynamics of the whole network? These are the
> sorts of questions for which I am looking for answers. I would
> appreciate any suggestions on potentially relevant studies. I will post
> a summary of responses for the list. Thanks in advance.
> Corey Phelps
> Asst. Professor, Management & Organization
> University of Washington Business School
> Box 353200
> Seattle, WA 98195
> ph. 206-543-6579
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