Towards correlated random networks

Abstract

A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be arbitrarily chosen. Two different methods for the creation of such networks are presented: one of them is a generalization of a well-known algorithm by Maslov and Sneppen. The percolation threshold for the model is calculated and the result is tested using analytically solvable examples and simulations. In the end the principal importance of correlations and clustering for the topology of networks is discussed. Using a straight-forward extension of the network model by Barabasi and Albert, it is shown how a clustering-coefficient independent of the network size can originate in growing networks.