Quantitative Study on the Friendship Paradox in Networks with Power-Law Degree Distribution

For a node of a complex network, the friendship index is obtained as the average degree of neighbors divided by its own degree. This index is broadly used in social network analysis. It is known that for the vast majority of real complex networks, their degree distributions follow a power-law with some exponent \(\gamma \) . In this paper, we establish a quantitative relationship between the parameter \(\gamma \) and the proportion of network nodes for which the values of their friendship index is greater than 1. We will explore scale-free networks with degree-degree neutral mixing and compare our findings with the empirical behavior for several real networks.