Measuring mixing patterns in complex networks by Spearman rank correlation coefficient

•A novel measure of assortative mixing based on the Spearman correlation coefficient is proposed.•The modified Spearman rank satisfies a linearity condition.•The linear relation is an important factor for inferring other parameters of networks.•The simple exponent model can generate networks with certain coefficient directly.

In this paper, we utilize Spearman rank correlation coefficient to measure mixing patterns in complex networks. Compared with the widely used Pearson coefficient, Spearman coefficient is rank-based, nonparametric, and size-independent. Thus it is more effective to assess linking patterns of diverse networks, especially for large-size networks. We demonstrate this point by testing a variety of empirical and artificial networks. Moreover, we show that normalized Spearman ranks of stubs are subject to an interesting linear rule where the correlation coefficient is just the Spearman coefficient. This compelling linear relationship allows us to directly produce networks with any prescribed Spearman coefficient. Our method apparently has an edge over the well known uncorrelated configuration model.