Um modelo de ligação preferencial com fitness

Abstract

The preferential attachment network with fitness, introduced in [2], is adynamic random graph model. New vertices are introduced consecutivelyand each new vertex is attached to an existing vertex with probability proportional to the degree multiplied by a random fitness. We concentrate on the typical behaviour of the graph by calculating the fitness distributionof a vertex chosen proportional to its degree. For a particular variant of the model, this analysis was first carried out by Borgs, Chayes, Daskalakisand Roch. However, we present a method, found in [7], which is robust inthe sense that it does not depend on the exact specification of the attachment law. In particular, we show that a peculiar phenomenon, analog to the Bose-Einstein condensation, can be observed in a more general model than the one presented by [5]. Finally, we calculate the asymptotic degree distribution of the vertices of the model.