Connectivity threshold and recovery time in rank-based models for complex networks

The World Wide 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 study a generalized version of the protean graph (a random model of the ‘web graph’) in which the degree of a vertex depends on its age as well as its rank. Classic protean graphs can be seen as a special case of the rank-based approach where vertices are ranked according to age. Here, we investigate graph generation models based on other ranking schemes that also lead to graphs with a power law degree distribution. The main aim of this paper is to study the behaviour of the protean process near the connectivity threshold.

• Type: Journal
• Year: 2011
• Where: DM
• Authors: Pawel Pralat
• Keywords: Classic Protean Graphs, DM 2011, Education, Protean Graphs, Web Page