Probabilistic inductive classes of graphs
Nataša Kejžar, Zoran Nikoloski and Vladimir Batagelj
Journal of mathematical sociology Volume 32, Number 2, pp. 85-109, 2008. ISSN 0022-250X

Abstract

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 the processes 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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