Heterogeneity of Scale-free Networks

The heterogeneity of scale-free networks is studied using the network structure entropy (NSE). The NSE of scale-free networks is presented analytically by introducing the degree-rank function. It is shown that the normalized NSE of scale-free networks is only dependent on the scaling exponent and is independent of the size or the minimum degree of networks when scaling exponent is greater than 2. Given the size and the minimum degree of scale-free networks, it is shown that the NSE reached a minimum value when scaling exponent is about 1.7 and then the scale-free networks become more homogeneous as scaling exponent increases after the minimum value.