Social cohesion, structural holes, and a tale of two measures

TL;DR

This paper explores the relationship between two social capital measures, clustering and effective size, revealing they are mathematically related, and proposes a new measure called Simmelian brokerage to better capture brokerage opportunities.

Contribution

It demonstrates the mathematical equivalence of clustering and effective size and introduces Simmelian brokerage as a novel measure for social capital analysis.

Findings

Clustering and effective size are mathematically related.

Simmelian brokerage captures brokerage opportunities between cohesive groups.

Implications for social capital research and network analysis.

Abstract

In the social sciences, the debate over the structural foundations of social capital has long vacillated between two positions on the relative benefits associated with two types of social structures: closed structures, rich in third-party relationships, and open structures, rich in structural holes and brokerage opportunities. In this paper, we engage with this debate by focusing on the measures typically used for formalising the two conceptions of social capital: clustering and effective size. We show that these two measures are simply two sides of the same coin, as they can be expressed one in terms of the other through a simple functional relation. Building on this relation, we then attempt to reconcile closed and open structures by proposing a new measure, Simmelian brokerage, that captures opportunities of brokerage between otherwise disconnected cohesive groups of contacts. Implications of our findings for research on social capital and complex networks are discussed.