World Wide Web scaling exponent from Simon's 1955 model - art. no. 035104

The statistical properties of the World Wide Web have attracted considerabl e attention recently since selfsimilar regimes were first observed in the s caling of its link structure. One characteristic quantity is the number of (in-)links k that point to a particular web page. Its probability distribut ion P (k) shows a pronounced power-law scaling P (k) similar to k-gamma tha t is not readily explained by standard random graph theory. Here, we recall a simple and elegant model for scaling phenomena in general copy- and grow th-processes as proposed by Simon in 1955. When combined with an experiment al measurement of network growth in the World Wide Web, this classical mode l is able to model the in-link dynamics and predicts the scaling exponent g amma =2.1 in accordance with observation.