Asymptotic behavior of the node degrees in the ensemble average of adjacency matrix

Abstract

Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by the beforehand averaged adjacency matrix over samples of growing networks as a new general framework for investigating the characteristic quantities. It is applied to some network models, and shows a good approximation of degree distribution asymptotically. In particular, our approach will be applicable through the numerical calculations instead of intractable theoretical analysises, when the time-course of degree is a monotone increasing function like power-law or logarithm.

13 paghes, 7 figures

References in corpus (3)

• Mitigation of Malicious Attacks on Networks
• Onion structure and network robustness
• Growing Self-organized Design of Efficient and Robust Complex Networks

Cited by in corpus (1)

• A new design principle of robust onion-like networks self-organized in growth