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Changing correlations in networks: Assortativity and dissortativity

Abstract:

To analyze the role of correlations in networks, in particular, assortativity and dissortativity, we introduce two algorithms which respectively produce assortative and dissortative mixing to a desired degree. In both procedures this degree is governed by a single parameter p. Varying this parameter, one can change correlations in networks without modifying their degree distribution to produce new versions ranging from fully random (p = 0) to totally assortative or dissortative (p = 1), depending on the algorithm used. We discuss the properties of networks emerging when applying our algorithms to a Barabási-Albert scale-free construction. In spite of having exactly the same degree distribution, different correlated networks exhibit different geometrical and transport properties. Thus, the average path length and clustering coefficient, as well as the shell structure and percolation properties change significantly when modifying correlations.