A new measure of heterogeneity of complex networks based on degree sequence

Jun Wu
College of Information Systems and Management, National Univ

Yue-jin TAN
College of Information Systems and Management, National University of Defense Technology

Hong-zhong DENG
College of Information Systems and Management, National University of Defense Technology

Da-zhi ZHU
College of Information Systems and Management, National University of Defense Technology

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     Last modified: August 9, 2006

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.