Although a number of models have been developed to investigate the emergence of culture and evolutionary phases in social systems, one important aspect has not yet been sufficiently emphasized. This is the structure of the underlaying network of soci
al relations serving as channels in transmitting cultural traits, which is expected to play a crucial role in the evolutionary processes in social systems. In this paper we contribute to the understanding of the role of the network structure by developing a layered ego-centric network structure based model, inspired by the social brain hypothesis, to study transmission of cultural traits and their evolution in social network. For this model we first find analytical results in the spirit of mean-field approximation and then to validate the results we compare them with the results of extensive numerical simulations.
Mobile phone communication as digital service generates ever-increasing datasets of human communication actions, which in turn allow us to investigate the structure and evolution of social interactions and their networks. These datasets can be used t
o study the structuring of such egocentric networks with respect to the strength of the relationships by assuming direct dependence of the communication intensity on the strength of the social tie. Recently we have discovered that there are significant differences between the first and further best friends from the point of view of age and gender preferences. Here we introduce a control parameter $p_{rm max}$ based on the statistics of communication with the first and second best friend and use it to filter the data. We find that when $p_{rm max}$ is decreased the identification of the best friend becomes less ambiguous and the earlier observed effects get stronger, thus corroborating them.
