Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-08-02
EPL (Europhysics Letters), 2010, 90:68002
Physics
Condensed Matter
Statistical Mechanics
Definitive version accepted for publication in EPL (Europhysics Letters)
Scientific paper
10.1209/0295-5075/90/68002
Spanning trees are an important quantity characterizing the reliability of a network, however, explicitly determining the number of spanning trees in networks is a theoretical challenge. In this paper, we study the number of spanning trees in a small-world scale-free network and obtain the exact expressions. We find that the entropy of spanning trees in the studied network is less than 1, which is in sharp contrast to previous result for the regular lattice with the same average degree, the entropy of which is higher than 1. Thus, the number of spanning trees in the scale-free network is much less than that of the corresponding regular lattice. We present that this difference lies in disparate structure of the two networks. Since scale-free networks are more robust than regular networks under random attack, our result can lead to the counterintuitive conclusion that a network with more spanning trees may be relatively unreliable.
Liu Hongxiao
Wu Bin
Zhang Zhongzhi
Zhou Shuigeng
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