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Stability in flux: Community structure in dynamic networks

Stability in flux: Community structure in dynamic networks
Stability in flux: Community structure in dynamic networks
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.
1031-1040
Bryden, John
3656afbb-69a4-40d1-bc3b-53453ba40118
Funk, Sebastian
99328474-b245-47ab-8bc1-d2854032a577
Geard, Nicholas
e9933f78-10b8-4454-8c8d-c2c75e040346
Bullock, Seth
2ad576e4-56b8-4f31-84e0-51bd0b7a1cd3
Jansen, Vincent
690054ce-506e-4773-b026-8163abff5cb9
Bryden, John
3656afbb-69a4-40d1-bc3b-53453ba40118
Funk, Sebastian
99328474-b245-47ab-8bc1-d2854032a577
Geard, Nicholas
e9933f78-10b8-4454-8c8d-c2c75e040346
Bullock, Seth
2ad576e4-56b8-4f31-84e0-51bd0b7a1cd3
Jansen, Vincent
690054ce-506e-4773-b026-8163abff5cb9

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).

Record type: Article

Abstract

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.

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Published date: 2010
Organisations: Agents, Interactions & Complexity

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Local EPrints ID: 271552
URI: https://eprints.soton.ac.uk/id/eprint/271552
PURE UUID: 3637521c-880b-425c-bd54-3b9ff81261d2

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Date deposited: 15 Sep 2010 20:25
Last modified: 06 Nov 2017 17:31

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