Degree-degree correlations in directed networks with scale-free degrees

The dependency between the degrees on both sides of a randomly sampled edge in a network, called degree-degree correlation or degree assortativity, is an important characteristic of the topology of the network, influencing many processes on it, like information spread and percolation. In this talk I will discuss these dependencies on directed networks and how to measure them. I will explain the shortcomings of the most widely used measure, based on Pearson’s correlation coefficient, and introduce different measures based on rank statistics. I will show that these are statistically consistent estimators for degree-degree correlations, for a broad class of networks. Finally, I will describe how degree-degree correlations behave in the directed configuration model. I will show that when the degree distribution has infinite variance we encounter negative correlations, generated by finite size effects, and I will discuss some scaling results for these, in terms of the size of the network.