The correlations between the degrees of connected nodes in a network are an important characteristic of the global structure. The influence the behavior of diffusion processes on the networks, such as the spreading of infections or information, and play a role in the robustness of the network when attacked.
The main research questions for me are:
- What is the structure of large assortative graphs with scale-free degree distributions?
- How are degree-degree correlations and clustering related?
- What do limit theorems for rank-correlations measures such as Spearman’s rho look like?
Related papers:
- Limit theorems for assortativity and clustering in the configuration model with scale-free degrees [arxiv]
- Generating maximally disassortative graphs with given degree distribution [pdf] [arxiv]
- Average nearest neighbor degrees in scale-free networks [pdf] [arxiv]
- Phase transitions for scaling of structural correlations in directed networks [pdf] [arxiv]
- Degree-degree correlations in directed networks with heavy-tailed degrees [pdf] [arxiv]
- Convergence of rank based degree-degree correlations in random directed networks [pdf] [arxiv]