Network transitivity and matrix models.
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, analytic techniques to develop a static model with nontrivial clustering are introduced. Computer simulations complete the analytic discussion.
M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Krakow, Poland.
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Burda
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Jurkiewicz
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Krzywicki
D016000:Cluster Analysis; D003198:Computer Simulation; D015233:Models, Statistical; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D010825:Physics / Q000379:methods*