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Dynamics of link states in complex networks: The case of a majority rule

AuthorsFernández-Gracia, Juan ; Castelló, Xavier ; Eguíluz, Víctor M. ; San Miguel, Maxi
Issue Date17-Dec-2012
PublisherAmerican Physical Society
CitationPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics 86: 066113 (2012)
AbstractMotivated by the idea that some characteristics are specific to the relations between individuals and not to the individuals themselves, we study a prototype model for the dynamics of the states of the links in a fixed network of interacting units. Each link in the network can be in one of two equivalent states. A majority link-dynamics rule is implemented, so that in each dynamical step the state of a randomly chosen link is updated to the state of the majority of neighboring links. Nodes can be characterized by a link heterogeneity index, giving a measure of the likelihood of a node to have a link in one of the two states. We consider this link-dynamics model in fully connected networks, square lattices, and Erd¨os-Renyi random networks. In each case we find and characterize a number of nontrivial asymptotic configurations, as well as some of the mechanisms leading to them and the time evolution of the link heterogeneity index distribution. For a fully connected network and random networks there is a broad distribution of possible asymptotic configurations. Most asymptotic configurations that result from link dynamics have no counterpart under traditional node dynamics in the same topologies.. © 2012 American Physical Society.
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevE.86.066113
Identifiersdoi: 10.1103/PhysRevE.86.066113
issn: 1539-3755
e-issn: 1550-2376
Appears in Collections:(IFISC) Artículos
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