A stochastic model for the evolution of the web allowing link deletion

Abstract

Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. We present a generalisation of the basic model by allowing deletion of individual links and show that it also gives rise to a power-law distribution. We derive the mean-field equations for this stochastic model and show that by examining a snapshot of the distribution at the steady state of the model, we are able to tell whether any link deletion has taken place and estimate the link deletion probability. Our model enables us to gain some insight into the distribution of inlinks in the web graph, in particular it suggests a power-law exponent of approximately 2.15 rather than the widely published exponent of 2.1