InterJournal Complex Systems, 1626
Status: Accepted
Manuscript Number: [1626]
Submission Date: 2006
A new measure of heterogeneity of complex networks based on degree sequence
Author(s): Jun Wu , Yue-jin TAN ,Hong-zhong DENG , Da-zhi ZHU

Subject(s): CX.18

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Abstract:

Many unique properties of complex networks are due to the heterogeneity. The measure and analysis of heterogeneity is important and desirable to research the behaviours and functions of complex networks. In this paper,entropy of degree sequence (EDS) as a new measure of the heterogeneity of complex networks is proposed and normalized entropy of degree sequence (NEDS) is defined. EDS is agreement with the normal meaning of heterogeneity within the context of complex networks compared with conventional measures. The heterogeneity of scale-free networks is studied using EDS. The analytical expression of EDS of scale-free networks is presented by introducing degree-rank function. It is demonstrated that scale-free networks become more heterogeneous as scaling exponent decreases. It is also demonstrated that NEDS of scale-free networks is independent of the size of networks which indicates that NEDS is a suitable and effective measure of heterogeneity.

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