Component Evolution in General Random Intersection Graphs

Details Component Evolution in General Random Intersection Graphs Component Evolution in General Random Intersection Graphs

2010-05-29

arxiv.org/abs/1005.5475v1

Computer Science

Discrete Mathematics

Scientific paper

Random intersection graphs (RIGs) are an important random structure with applications in social networks, epidemic networks, blog readership, and wireless sensor networks. RIGs can be interpreted as a model for large randomly formed non-metric data sets. We analyze the component evolution in general RIGs, and give conditions on existence and uniqueness of the giant component. Our techniques generalize existing methods for analysis of component evolution: we analyze survival and extinction properties of a dependent, inhomogeneous Galton-Watson branching process on general RIGs. Our analysis relies on bounding the branching processes and inherits the fundamental concepts of the study of component evolution in Erd\H{o}s-R\'enyi graphs. The major challenge comes from the underlying structure of RIGs, which involves its both the set of nodes and the set of attributes, as well as the set of different probabilities among the nodes and attributes.

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