Gossip in random networks

Faculty of Physics and Applied Computer Science, AGH University of Scienceand Technology, al. Mickiewicza 30, PL-30059 Cracow, PolandWe consider the average probability X of being informed on a gossip ina given social network. The network is modeled within the random graphtheory of Erdo˝s and R´enyi. In this theory, a network is characterized bytwo parameters: the size N and the link probability p. Our experimentaldata suggest three levels of social inclusion of friendship. The critical valuep