# Directed clustering in weighted networks: a new perspective

## TL;DR

This paper introduces a novel local clustering coefficient for weighted directed networks, capturing diverse link patterns and demonstrating its effectiveness through empirical analysis on real-world networks.

## Contribution

It proposes a new clustering coefficient for weighted directed networks, including four components to analyze different triangle configurations, advancing network analysis methods.

## Key findings

- The new coefficient outperforms existing measures in empirical tests.
- It effectively captures complex link patterns in real networks.
- The approach provides a nuanced understanding of local clustering in directed weighted networks.

## Abstract

In this paper, we consider the problem of assessing local clustering in complex networks. Various definitions for this measure have been proposed for the cases of networks having weighted edges, but less attention has been paid to both weighted and directed networks. We provide a new local clustering coefficient for this kind of networks, starting from those existing in the literature for the weighted and undirected case. Furthermore, we extract from our coefficient four specific components, in order to separately consider different link patterns of triangles. Empirical applications on several real networks from different frameworks and with different order are provided. The performance of our coefficient is also compared with that of existing coefficients in the literature.