# Corrected overlap weight and clustering coefficient

## TL;DR

This paper identifies limitations in the traditional overlap weight and clustering coefficient measures for network analysis and proposes corrected definitions that better identify important network elements, demonstrated on the US Airports network.

## Contribution

The authors introduce corrected versions of the overlap weight and clustering coefficient measures to improve their usefulness in data analysis tasks.

## Key findings

- Corrected measures provide more meaningful identification of important nodes and links.
- Application on US Airports network demonstrates the effectiveness of the corrected measures.
- Traditional measures tend to highlight small maximal subgraphs, which can be misleading.

## Abstract

We discuss two well known network measures: the overlap weight of an edge and the clustering coefficient of a node. For both of them it turns out that they are not very useful for data analytic task to identify important elements (nodes or links) of a given network. The reason for this is that they attain their largest values on maximal subgraphs of relatively small size that are more probable to appear in a network than that of larger size. We show how the definitions of these measures can be corrected in such a way that they give the expected results. We illustrate the proposed corrected measures by applying them on the US Airports network using the program Pajek.