  We analyze Axelrod's model of social interactions on coevolving complex
networks. We introduce four extensions with different mechanisms of edge
rewiring. The models are intended to catch two kinds of interactions -
preferential attachment, which can be observed in scientists or actors
collaborations, and local rewiring, which can be observed in friendship
formation in everyday relations. Numerical simulations show that proposed
dynamics can lead to the power-law distribution of nodes' degree and high value
of the clustering coefficient, while still retaining the small-world effect in
three models. All models are characterized by two phase transitions of a
different nature. In case of local rewiring we obtain order-disorder
discontinuous phase transition even in the thermodynamic limit, while in case
of long-distance switching discontinuity disappears in the thermodynamic limit,
leaving one continuous phase transition. In addition, we discover a new and
universal characteristic of the second transition point - an abrupt increase of
the clustering coefficient, due to formation of many small complete subgraphs
inside the network.

Physics and Society;Social and Information Networks