## Stochastic analysis for average nearest neighbor degree

Yao Dong, UT-EWI-SOR

## Abstract:

Average nearest neighbor degree (ANND) is a measure for the degree-degree correlation for complex network. This talk is concerned with the probabilistic properties of ANND in random complex network generated by IID Algorithm. We prove if the variable *X* generating the IID Algorithm has moment of order higher than 2, then the ANND will converge to certain number in probability. In particular, in the configuration model, we prove that the limit is exactly μ_{2}/μ_{1} , where μ_{2} is the second moment of *X*, and μ_{1} is the first moment. For the case that *X* has infinite variance, we show the scaling of ANND. Finally we consider an alternative measure for ANND. We also use numerical experiments to show these results.

This work is a summer internship at University of Twente, SOR group, supervised by Prof. Nelly Litvak (University of Twente) and PhD student Pim van de Hoorn (University of Twente).