World Wide Web scaling exponent from Simon’s 1955 model

Abstract

The statistical properties of the World Wide Web have attracted considerable attention recently since self-similar regimes were first observed in the scaling of its link structure. One characteristic quantity is the number of (in-)links k that point to a particular web page. Its probability distribution $P\left(k\right)\mathrm{}$ shows a pronounced power-law scaling $P\left(k\right)\mathrm{}\sim k^{-\gamma }$ that is not readily explained by standard random graph theory. Here, we recall a simple and elegant model for scaling phenomena in general copy- and growth-processes as proposed by Simon in 1955. When combined with an experimental measurement of network growth in the World Wide Web, this classical model is able to model the in-link dynamics and predicts the scaling exponent $\gamma =2.1\mathrm{}$ in accordance with observation.