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Growing protean graphs. (English) Zbl 1167.05047

Summary: The web may be viewed as a graph each of whose vertices corresponds to a static HTML web page and each of whose edges corresponds to a hyperlink from one web page to another. Recently, there has been considerable interest in using random graphs to model complex real-world networks to gain an insight into their properties. In this paper we propose an extended version of a new random model of the web graph in which the degree of a vertex depends on its age. We use the differential equation method to obtain basic results on the probability of edges being present. From this we are able to characterize the degree sequence of the model and study its behaviour near the connectivity threshold.

MSC:

05C80 Random graphs (graph-theoretic aspects)
68R10 Graph theory (including graph drawing) in computer science
05C07 Vertex degrees
34F05 Ordinary differential equations and systems with randomness
68M10 Network design and communication in computer systems
05C40 Connectivity
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