Mathematical Model of Diffusion in Social Networks

Network of interacting agents whose actions are influenced by the actions of their neighbors according to the simple diffusion rule is considered. The paper examines some special types of the diffusion function for which the conditions of the network equilibrium are derived. Network equilibrium supposes that the network dynamics is in the stationary state, i.e. relative density of active agents is not changed. The numerical experiment for social network “vkontakte.ru” was made. Some statistical hypotheses about the type of connectivity distribution were checked.