Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-10-28
Journal of Statistical Mechanics: Theory and Experiment, 2009, P10022
Physics
Condensed Matter
Statistical Mechanics
Definitive version published in Journal of Statistical Mechanics
Scientific paper
10.1088/1742-5468/2009/10/P10022
Various real systems simultaneously exhibit scale-free and hierarchical structure. In this paper, we study analytically average distance in a deterministic scale-free network with hierarchical organization. Using a recursive method based on the network construction, we determine explicitly the average distance, obtaining an exact expression for it, which is confirmed by extensive numerical calculations. The obtained rigorous solution shows that the average distance grows logarithmically with the network order (number of nodes in the network). We exhibit the similarity and dissimilarity in average distance between the network under consideration and some previously studied networks, including random networks and other deterministic networks. On the basis of the comparison, we argue that the logarithmic scaling of average distance with network order could be a generic feature of deterministic scale-free networks.
Gao Shuyang
Guan Jihong
Lin Yuan
Zhang Zhongzhi
Zhou Shuigeng
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