Scaling of nearest neighbors' connectivity distribution for scale-free networks
1 Department of Modern Physics, University of Science and Technology of China - Hefei 230026, China
2 Department of Satellite Measurement and Control on Sea of China - Jiangyin 214400, China
Received: 7 March 2015
Accepted: 8 September 2015
Most of real-world networks are called scale-free networks, since the degree distribution follows a power law. However, observing from a node, its nearest neighbors' degree distribution expressed by conditional probability lacks definite studies and conclusions. Here, we provide a systematic study combined with theoretical and empirical demonstrations, which reveal the inherent connectivity profile of real-world networks. We show that in the regime and can be approximated by different power laws. One is strongly determined by the degree correlation, and the other depends on both degree distribution and correlation. Based on this result, we propose a degree correlation spectra approach beyond the widely used Pearson correlation coefficient, finding that some networks exhibit sophisticated hybrid correlation patterns. Our results represent a step forward in understanding the structure of complex networks.
PACS: 89.75.Fb – Structures and organization in complex systems / 89.75.Da – Systems obeying scaling laws / 89.75.Hc – Networks and genealogical trees
© EPLA, 2015