Average Nearest Neighbor Degree and Its Distribution in Social Networks

The paper is focused on the analysis of average nearest neighbor degree (ANND) in complex social networks. The ANND of nodes with degree k is defined as the average degree of their neighbors over all nodes with degree k. ANND is one of the well-established tools for the analysis of degree-degree correlation and assortativity in complex networks. In this paper, we analytically examine the properties of ANND in undirected networks generated by the Barabasi-Albert model. First, we prove that for every node, the average degree of its neighbors is increasing logarithmically over time. Then we show that the ANND distribution at each iteration is uniform, i.e. the values of ANND are the same for every k, and therefore, Barabasi-Albert networks are uncorrelated. Moreover, we compare the ANND distributions in simulated graphs (derived by the Barabasi-Albert model) with distributions in real-world social networks (Twitter, Facebook, GitHub and Flickr).