Coteries, Social Circles and Hamlets Close Communities: A Study of Acquaintance Networks

TL;DR

This paper investigates the structure of close-knit social communities, defined by mutual or shared acquaintances, using graph theory to classify them into distinct types based on their network properties.

Contribution

It introduces a formal definition of close communities in social networks and provides a typology based on graph characteristics like diameter, spanning trees, and girth.

Findings

Typology of close communities with three or six types

Characterization of community structure via graph properties

Insights into the stability and connectivity of social circles

Abstract

In the analysis of social networks many relatively loose and heuristic definitions of 'community' abound. In this paper the concept of closely knit communities is studied as defined by the property that every pair of its members are neighbors or has at least one common neighbor, where the neighboring relationship is based on some more or less durable and stable acquaintance or contact relation. In this paper these are studied in the form of graphs or networks of diameter two (2-clubs). Their structure can be characterized by investigating shortest spanning trees and girth leading to a typology containing just three or, in combination, six types of close communities.