Network Transitivity and Matrix Models

Abstract

This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix model, where matrices are random, but their elements take values 0 and 1 only. Confusion present in some papers where earlier attempts to incorporate transitivity in a similar framework have been made is hopefully dissipated. Inspired by more conventional matrix models, new analytic techniques to develop a static model with non-trivial clustering are introduced. Computer simulations complete the analytic discussion.

arXiv comment11 pages, 7 eps figures, 2-column revtex format, print bug corrected

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• Statistical mechanics of complex networks
• The structure and function of complex networks
• Evolution of networks
• Properties of highly clustered networks
• Class of correlated random networks with hidden variables
• Statistical ensemble of scale-free random graphs
• Correlated random networks
• Random incidence matrices: moments of the spectral density
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