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.
In complex network research clique percolation, introduced by Palla et al., is a deterministic community detection method, which allows for overlapping communities and is purely based on local topological properties of a network. Here we present a se
quential clique percolation algorithm (SCP) to do fast community detection in weighted and unweighted networks, for cliques of a chosen size. This method is based on sequentially inserting the constituent links to the network and simultaneously keeping track of the emerging community structure. Unlike existing algorithms, the SCP method allows for detecting k-clique communities at multiple weight thresholds in a single run, and can simultaneously produce a dendrogram representation of hierarchical community structure. In sparse weighted networks, the SCP algorithm can also be used for implementing the weighted clique percolation method recently introduced by Farkas et al. The computational time of the SCP algorithm scales linearly with the number of k-cliques in the network. As an example, the method is applied to a product association network, revealing its nested community structure.
