World Wide Web scaling exponent from Simon’s 1955 model

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(k) shows a pronounced power-law scaling P(k) approximately 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 in accordance with observation.