PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:5391
Deposited By:Vladimir Batagelj
Deposited On:31 March 2009