Unified index to quantifying heterogeneity of complex networks |
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Authors: | Hai-Bo Hu |
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Institution: | Complex Networks and Control Lab, Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China |
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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. |
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Keywords: | 89 75 -k 89 75 Hc 89 75 Fb |
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