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

摘要

Motivated by the idea that some characteristics are specific to the relationsbetween individuals and not of the individuals themselves, we study a prototypemodel for the dynamics of the states of the links in a fixed network ofinteracting units. Each link in the network can be in one of two equivalentstates. A majority link-dynamics rule is implemented, so that in each dynamicalstep the state of a randomly chosen link is updated to the state of themajority of neighboring links. Nodes can be characterized by a linkheterogeneity index, giving a measure of the likelihood of a node to have alink in one of the two states. We consider this link-dynamics model on fullyconnected networks, square lattices and Erd \"os-Renyi random networks. In eachcase 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 thelink heterogeneity index distribution. For a fully connected network and randomnetworks there is a broad distribution of possible asymptotic configurations.Most asymptotic configurations that result from link-dynamics have nocounterpart under traditional node dynamics in the same topologies.