How people compare their own characteristics to those of their neighbors: A mathematical approach

What is it about?

The generalized friendship paradox (GFP) states that on average your friends have not only more friends than you do, but also better characteristics, like happiness or achievement, than yours. This has been one of the intriguing topics in network science for many years. Yet an analytical, rigorous understanding of it was hampered partly due to the lack of mathematical tools for modeling the complex correlation structure of individual characteristics embedded in complex networks. This paper successfully derived a mathematical solution for the networks abundant of triangles by employing a vine-copula method that is increasingly utilized in many disciplines.

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Photo by Duy Pham on Unsplash

Photo by Duy Pham on Unsplash

Why is it important?

The GFP is fundamentally related to how people perceive their neighborhood, more precisely, how people compare their own characteristics to those of their neighbors. In that sense, the mathematical solution obtained in this paper sheds light on the role of triangles around an individual on the individual’s perception of their neighbors’ characteristics.