Mixing properties of growing networks and Simpson’s paradox

This work proves that networks previously classified as disassortative reveal instead assortative behavior to a careful analysis, by analytical calculations and simulations on three classes of growing networks based on preferential attachment and fitness, where the disassorting behavior observed is a spurious effect.

Abstract

The mixing properties of networks are usually inferred by comparing the degree of a node with the average degree of its neighbors. This kind of analysis often leads to incorrect conclusions: Assortative patterns may appear reversed by a mechanism known as Simpson's paradox. We prove this fact by analytical calculations and simulations on three classes of growing networks based on preferential attachment and fitness, where the disassortative behavior observed is a spurious effect. Our results give a crucial contribution to the debate about the origin of disassortative mixing, since networks previously classified as disassortative reveal instead assortative behavior to a careful analysis.