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Gossip in random networks 
Krzysztof Malarz ^{1}, Zsuzsanna Szvetelszky ^{2}, Balazs Szekfu ^{3}, Krzysztof Kułakowski ^{1} 
1. AGH University of Science and Technology, Faculty of Physics and Applied Computer Science (AGH), Mickiewicza 30, Kraków 30059, Poland 
Abstract 
We consider the average probability X of being informed on a gossip in a given social network. The network is modeled within the random graph theory of Erdös and Rényi. In this theory, a network is characterized by two parameters: the size N and the link probability p. Our experimental data suggest three levels of social inclusion of friendship. The critical value p_{c}, for which half of agents are informed, scales with the system size as N^{γ} with γ=0.68. Computer simulations show that the probability X varies with p as a sigmoidal curve. Influence of correlations between neighbors is also evaluated: with increasing the clustering coefficient C, X decreases.
[1] arXiv preprint: physics/0601158 
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Presentation: Oral at 2 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", Sociophysics, by Krzysztof Malarz Submitted: 20051116 13:13 Revised: 20090607 00:44 