Close Communities in Social Networks: Boroughs and 2-Clubs

TL;DR

This paper analyzes the structure of close communication communities in social networks using maximal diameter-2 subgraphs called 2-clubs, introducing the concept of boroughs to understand their organization.

Contribution

It introduces the concept of boroughs as unions of 2-clubs, providing a new framework to understand close communities in social networks.

Findings

Boroughs are chained unions of 2-clubs that contain the network's close communities.

Each 2-club belongs to exactly one borough, structuring the network's communication.

Applications demonstrate the framework on real-world network data.

Abstract

The structure of close communication, contacts and association in social networks is studied in the form of maximal subgraphs of diameter 2 (2-clubs), corresponding to three types of close communities: hamlets, social circles and coteries. The concept of borough of a graph is defined and introduced. Each borough is a chained union of 2-clubs of the network and any 2-club of the network belongs to one borough. Thus the set of boroughs of a network, together with the 2-clubs held by them, are shown to contain the structure of close communication in a network. Applications are given with examples from real world network data.