Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

Significance It is hard to decide if a real-world complex network is scale free, as it has never reached an agreement on how to confirm whether the network exhibits statistically favored power-law distributions. Here, we define a fundamental property—the degree–degree distance—possessed by each link, the distribution of which usually exhibits a stronger power law than the degree distribution of a finite-size network as indicated by empirical and statistical studies. A bidirectional preferential selection model is introduced to explain and reproduce this finding, which implies that being scale free as a property should not be defined by apparent statistics but determined by the underlying mechanism. We conclude that power-law degree–degree distance distribution better represents the scale-free property.