Mixing properties of growing networks and the Simpson's paradox

TL;DR

This paper investigates how the apparent disassortative mixing in growing networks can be misleading due to Simpson's paradox, revealing true positive correlations when considering link directions through analytical and simulation methods.

Contribution

It demonstrates that the observed disassortativity in directed networks can be a spurious effect, providing analytical and numerical evidence for genuine positive correlations.

Findings

Disassortative patterns are often spurious in directed networks.

Considering link directions reveals true positive correlations.

Implications for network resilience, spreading, and synchronization.

Abstract

We analyze the mixing properties of growing networks and find that, in some cases, the assortativity patterns are reversed once links' direction is considered: the disassortative behavior observed in such networks is a spurious effect, and a careful analysis reveals genuine positive correlations. We prove our claim by analytical calculations and numerical simulations for two classes of models based on preferential attachment and fitness. Such counterintuitive phenomenon is a manifestation of the well known Simpson's paradox. Results concerning mixing patterns may have important consequences, since they reflect on structural properties as resilience, epidemic spreading and synchronization. Our findings suggest that a more detailed analysis of real directed networks, such as the World Wide Web, is needed.