Dynamics of link states in complex networks: the case of a majority rule.
Motivated 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 Erdös-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.
IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain. juanf@ifisc.uib-csic.es
J
J
Fernández-Gracia
X
X
Castelló
V M
VM
Eguíluz
M
M
San Miguel
D000465:Algorithms; D001519:Behavior; D001703:Biophysics / Q000379:methods*; D003142:Communication; D006801:Humans; D007802:Language; D008962:Models, Theoretical; D011336:Probability; D012944:Social Support; D013997:Time Factors