Unified index to quantifying heterogeneity of complex networks

Hai-Bo Hu and Xiao-Fan Wang

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 14, 3769-3780

Abstract: Although recent studies have revealed that degree heterogeneity of a complex network has significant impact on the network performance and function, a unified definition of the heterogeneity of a network with any degree distribution is absent. In this paper, we define a heterogeneity index 0≤H<1 to quantify the degree heterogeneity of any given network. We analytically show the existence of an upper bound of H=0.5 for exponential networks, thus explain why exponential networks are homogeneous. On the other hand, we also analytically show that the heterogeneity index of an infinite power law network is between 1 and 0.5 if and only if its degree exponent is between 2 and 2.5. We further show that for any power law network with a degree exponent greater than 2.5, there always exists an exponential network such that both networks have the same heterogeneity index. This may help to explain why 2.5 is a critical degree exponent for some dynamic behaviors on power law networks.

Keywords: Heterogeneity; Complex networks; Power law networks; Exponential networks (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (26)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:14:p:3769-3780

DOI: 10.1016/j.physa.2008.01.113

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