Clustering of random scale-free networks

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007

Physical Review E, 2003

European Physical Journal B, 2006

We calculate the mean neighboring degree function \(\bar k_{\rm{nn}}(k)\) and the mean clustering function C(k) of vertices with degree k as a function of k in finite scale-free random networks through the static model. While both are independent of k when the degree exponent γ≥3, they show the crossover behavior for 2

Physical Review E, 2005

2006

Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

The statistical property of a growing scale-free network is studied based on an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett. 86, 5401 (2001)], with the additional constraints of forbidding self-connection and multiple links of the same direction between any two nodes. Scaling exponents in the range of 1-2 are obtained through Monte Carlo simulations and various clustering coefficients are calculated, one of which, C(out), is of the order of 10(-1), indicating that the network resembles a small world. The out-degree distribution has an exponential cutoff for large out degree.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2006

In this paper we study the impact of degree correlations in the subgraph statistics of scale-free networks. In particular we consider loops, simple cases of network subgraphs which encode the redundancy of the paths passing through every two nodes of the network. We provide an understanding of the scaling of the clustering coefficient in modular networks in terms of the maximal eigenvector of the average adjacency matrix of the ensemble. Furthermore we show that correlations affect in a relevant way the average number of Hamiltonian paths in a three-core of real world networks. We prove our results in the two-vertex correlated hidden variable ensemble and we check the results with exact counting of small loops in real graphs.

Lecture Notes in Physics, 2003