In the 90s Robert Axelrod have proposed the canonical model of social interactions [1] explaining one of possible and important mechanisms of dissemination of culture. He have found that depending on initial conditions the system can end up in one of two states: ordered with global culture or disordered with many small subcultures. The dynamics of this model captured complexities of real interactions between people, but the square lattice which was considered is far from satisfying reflection of real-world social networks. Others have studied Axelrod's model deeper on complex networks and it turned out that structure can have fundamental influence on the  behaviour of a system. Maxi San Miguel et. al. [2] made the next step by exploring the model of social interactions on coevolving random networks and finding two phase transitions with interesting properties. Unfortunately social networks are as far from randomness as from regularity. In our work we present mechanisms, which can be applied to model [2], leading to important features of social networks, i. e. high clustering and power tails in degree distribution.

References

[1] R. Axelrod, The dissemination of culture, J. Conflict Res. 41, 203 (1997)
[2] F. Vazquez, J. C. Gonzalez-Avella, V. M. Eguíluz, M. San Miguel, Time-scale competition leading to fragmetation and recombination transitions in the coevolution of network and states, Phys. Rev. E 76, 046120 (2007)

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