Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the “rich get richer ” phenomenon. However, these models fail to explain several distributions arising from empirical results, due to the fact that the exponent they predict is not consistent with the data. To address this problem we extend the evolutionary model of the Web graph by including a non-preferential component and viewing the stochastic process in terms of an urn transfer model. By making this extension we can now explain a wider variety of empirically discovered power-law distributions provided the exponent is greater than two. These include: the distribution of incoming links, the distribution of outgoing links, the distribution of pages in a Web site and the distribution of visitors to a Web site.
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