# Quantifying Triadic Closure in Multi-Edge Social Networks

## TL;DR

This paper introduces a new measure for triadic closure in multi-edge social networks, effectively capturing closure in networks with repeated interactions, which traditional methods fail to do.

## Contribution

The authors propose a novel shared partner statistic for measuring triadic closure in multi-edge networks, enabling more accurate analysis of complex social interactions.

## Key findings

- The new measure detects meaningful triadic closure in synthetic networks.
- It successfully identifies closure in empirical social networks.
- Traditional methods fail to capture closure in multi-edge contexts.

## Abstract

Multi-edge networks capture repeated interactions between individuals. In social networks, such edges often form closed triangles, or triads. Standard approaches to measure this triadic closure, however, fail for multi-edge networks, because they do not consider that triads can be formed by edges of different multiplicity. We propose a novel measure of triadic closure for multi-edge networks of social interactions based on a shared partner statistic. We demonstrate that our operalization is able to detect meaningful closure in synthetic and empirical multi-edge networks, where common approaches fail. This is a cornerstone in driving inferential network analyses from the analysis of binary networks towards the analyses of multi-edge and weighted networks, which offer a more realistic representation of social interactions and relations.