Network Transitivity and Matrix Models

Details Network Transitivity and Matrix Models Network Transitivity and Matrix Models

2003-10-10

arxiv.org/abs/cond-mat/0310234v2

Phys. Rev. E69 (2004) 026106

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevE.69.026106

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.

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