Regensburg 2010 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 26: Networks: From Topology to Dynamics IV (joint session of BP, DY, SOE)
DY 26.2: Vortrag
Donnerstag, 25. März 2010, 14:15–14:30, H44
Evolution based on centrality: Bistability between hierarchical and destructured networks — •Claudio J. Tessone1, Matteo Marsili2, and Michael König1 — 1Chair of Systems Design, D-MTEC ETH Zürich — 2International Centre for Theoretical Physics Abdus Salam
We study a model of network evolution in which agents attempt to become the most central ones in a network. Considering purely strategic interactions, when agents try to maximise their centrality in the network, the best strategy for them is to create links with the most central agent among those they are not still connected to. Conversely, for link removal, the most efficient strategy is to remove a link to the least central node, among the neighbours. This condition leads to a self-reinforcing mechanism signalled by the emergence of highly centralised networks. These networks have the property of nestedness: for any two agents i and j, if the degree of agent i is lower than that of j, the neighbourhood of i is contained within the neighbourhood of j. Moreover, this mechanism simplifies the computational effort needed by the agents to identify their best strategy.
Interestingly, such structures only can appear if all the agents have been developing it. If disturbances, –such as decay of edges, introduced by finite of link life-time– are in place, we show that ergodicity in the system disappears. Under these conditions two equilibrium states can coexist for a given set of parameters: one where such hierarchical structure emerges; another where a completely random network prevails.