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http://worldcat.org/entity/work/id/328200994

Probabilistic inductive classes of graphs

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  • "A unifying framework-probabilistic inductive classes of graphs (PICGs)-is defined by imposing a probability space on the rules and their left elements from the standard notion of inductive class of graphs. The rules can model theprocesses creating real-world social networks, such as spread of knowledge,dynamics of acquaintanceships or sexual contacts, and emergence of clusters. We demonstrate the characteristics of PICGs by casting some well-known models of growing networks in this framework. Results regarding expected size and order are derived. For PICG models of connected and 2-connected graphs order, size and asymptotic degree distribution are presented. The approaches used represent analytic alternative to computer simulation, which is mostly used to obtain the properties of evolving graphs."

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  • "Probabilistic inductive classes of graphs"