Stability in flux: Community structure in dynamic networks
Bryden, John, Funk, Sebastian, Geard, Nicholas, Bullock, Seth and Jansen, Vincent (2010) Stability in flux: Community structure in dynamic networks. Journal of The Royal Society Interface, 8, (60), 1031-1040. (doi:10.1098/rsif.2010.0524).
- Published Version
The structure of many biological, social and technological systems can usefully be described in terms of complex networks. Although often portrayed as fixed in time, such networks are inherently dynamic, as the edges that join nodes are cut and rewired, and nodes themselves update their states. Understanding the structure of these networks requires us to understand the dynamic processes that create, maintain and modify them. Here, we build upon existing models of coevolving networks to characterize how dynamic behaviour at the level of individual nodes generates stable aggregate behaviours. We focus particularly on the dynamics of groups of nodes formed endogenously by nodes that share similar properties (represented as node state) and demonstrate that, under certain conditions, network modularity based on state compares well with network modularity based on topology. We show that if nodes rewire their edges based on fixed node states, the network modularity reaches a stable equilibrium which we quantify analytically. Furthermore, if node state is not fixed, but can be adopted from neighbouring nodes, the distribution of group sizes reaches a dynamic equilibrium, which remains stable even as the composition and identity of the groups change. These results show that dynamic networks can maintain the stable community structure that has been observed in many social and biological systems.
|Subjects:||Q Science > QA Mathematics > QA75 Electronic computers. Computer science|
|Divisions:||Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Agents, Interactions & Complexity
|Date Deposited:||15 Sep 2010 20:25|
|Last Modified:||29 Mar 2014 13:10|
Amorphous computation, random graphs and complex biological networks
Funded by: EPSRC (EP/D00232X/1)
1 January 2006 to 30 September 2010
|Further Information:||Google Scholar|
|ISI Citation Count:||7|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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