We propose a model for the World Wide Web graph that couples the topological growth with the traffic's dynamical evolution. The model is based on a simple traffic-driven dynamics and generates weighted directed graphs exhibiting the statistical properties observed in the Web. In particular, the model yields a non-trivial time evolution of vertices and heavy-tail distributions for the topological and traffic properties. The generated graphs exhibit a complex architecture with a hierarchy of cohesiveness levels similar to those observed in the analysis of real data.
A very interesting class of models that considers the main features of the WWW growth has been introduced by @cite_11 in order to produce a mechanism which does not assume the knowledge of the degree of the existing vertices. Each newly introduced vertex @math selects at random an already existing vertex @math ; for each out-neighbour @math of @math , @math connects to @math with a certain probability @math ; with probability @math it connects instead to another randomly chosen node. This model describes the growth process of the WWW as a copy mechanism in which newly arriving web-pages tends to reproduce the hyperlinks of similar web-pages; i.e. the first to which they connect. Interestingly, this model effectively recovers a preferential attachment mechanism without explicitely introducing it.
@cite_11
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The Web may be viewed as a directed graph each of whose vertices is a static HTML Web page, and each of whose edges corresponds to a hyperlink from one Web page to another. We propose and analyze random graph models inspired by a series of empirical observations on the Web. Our graph models differ from the traditional G sub n,p models in two ways: 1. Independently chosen edges do not result in the statistics (degree distributions, clique multitudes) observed on the Web. Thus, edges in our model are statistically dependent on each other. 2. Our model introduces new vertices in the graph as time evolves. This captures the fact that the Web is changing with time. Our results are two fold: we show that graphs generated using our model exhibit the statistics observed on the Web graph, and additionally, that natural graph models proposed earlier do not exhibit them. This remains true even when these earlier models are generalized to account for the arrival of vertices over time. In particular, the sparse random graphs in our models exhibit properties that do not arise in far denser random graphs generated by Erdos-Renyi models.