# Rich-Club Ordering and the Dyadic Effect: Two Interrelated Phenomena

## TL;DR

This paper explores the relationship between rich-club ordering and the dyadic effect in complex networks, introducing new measures and demonstrating their usefulness through computational experiments on real-world networks.

## Contribution

It presents a novel formulation linking rich-club measures with the dyadic effect and introduces new metrics for analyzing these phenomena in complex networks.

## Key findings

- New measures effectively confirm rich-club presence in networks
- Formulation links rich-club ordering with the dyadic effect
- Computational experiments validate the usefulness of the measures

## Abstract

Rich-club ordering and the dyadic effect are two phenomena observed in complex networks that are based on the presence of certain substructures composed of specific nodes. Rich-club ordering represents the tendency of highly connected and important elements to form tight communities with other central elements. The dyadic effect denotes the tendency of nodes that share a common property to be much more interconnected than expected. In this study, we consider the interrelation between these two phenomena, which until now have always been studied separately. We contribute with a new formulation of the rich-club measures in terms of the dyadic effect. Moreover, we introduce certain measures related to the analysis of the dyadic effect, which are useful in confirming the presence and relevance of rich-clubs in complex networks. In addition, certain computational experiences show the usefulness of the introduced quantities with regard to different classes of real networks.