Network of social groups or Let's have a party

Abstract

We present a simple model for growing up and depletion of parties due to the permanent communication between the participants of the events. Because of the rapid exchange of information, everybody is able to evaluate its own and and all other parties by means of the list of its friends. Therefore the number of participants at different parties can be changed incessantly. Depending on the deepness of the social contacts, which will be characterized by a parameter $α$, a stable distribution of party members emerges. At a critical $α_c$ an abrupt depletion of almost all parties is observed and as the consequence all the peoples are assembled at a single party. The model is based on a hierarchical social network. The probability that a certain person is contacted to another one depends on the social distance introduced within the network and homophily parameter $α$.