# Stratified communities in complex business networks

## TL;DR

This paper introduces a new way to analyze community structures in networks by considering stratification levels, extending clustering coefficients, and applying the method to business and air traffic networks for validation.

## Contribution

It proposes a novel local $l$-adjacency clustering coefficient that accounts for community stratification, enhancing community detection insights.

## Key findings

- Validated on air traffic networks, demonstrating practical usefulness.
- Extended clustering coefficient provides deeper community structure insights.
- Empirical analysis supports the theoretical framework.

## Abstract

This paper presents a new definition of the community structure of a network, which takes also into account how communities are stratified. In particular, we extend the standard concept of clustering coefficient and provide the local $l$-adjacency clustering coefficient of a node $i$. We define it as an opportunely weighted mean of the clustering coefficients of nodes which are at distance $l$ from $i$. The stratus of the community associated to node $i$ is identified by the distance $l$ from $i$, so that the standard clustering coefficient is a peculiar local $l$-adjacency clustering coefficient at stratus $l=0$. As the distance $l$ varies, the local $l$-adjacency clustering coefficient is then used to infer insights on the community structure of the entire network. Empirical experiments on special business networks are carried out. In particular, the analysis of air traffic networks validate the theoretical proposal and provide supporting arguments on its usefulness.