Degree-degree correlations are a structural feature of networks that describe the dependencies between the degrees of neighboring nodes. Another term that is often used is network assortativity. These correlations are an important topological feature which can have a strong impact on how processes behave on the network.
One key difficulty with analyzing degree-degree correlation in complex networks is that many networks have degree distributions with heavy-tails (infinite second moment). This feature makes the majority of standard correlation measures, such as Pearson's correlation coefficient, dependent on the size of the network, becoming smaller as the network grows.
To overcome this problem I developed measures for degree-degree correlations in networks which are consistent when the degree distributions have heavy tails. The behavior of these measures in several models has been analyzed to better understand their performance and develop null models.
Current projects:
Construction of Inhomogeneous Random Graphs with given degree-degree correlations.
Limit behavior of degree-degree correlation measures in Spatial Inhomogeneous Random Graphs.
Future projects:
Limit theorems for degree-degree correlations measures in the erased configuration model
Relevant papers:
Convergence of rank based degree-degree correlations in random directed networks
Degree-degree correlations in directed networks with heavy-tailed degrees
Phase transitions for scaling of structural correlations in directed networks
Generating maximally disassortative graphs with given degree distribution
Limit theorems for assortativity and clustering in the configuration model with scale-free degrees