A note on (matricial and fast) ways to compute Burt's structural holes

TL;DR

This paper presents simple matrix-based formulas to compute Burt's structural holes measures, facilitating interpretation and enabling naive algorithms for their calculation using adjacency matrices.

Contribution

It introduces straightforward formulas for calculating Burt's structural holes measures directly from adjacency matrices, simplifying their interpretation and computation.

Findings

Formulas for effective size, redundancy, local constraint, and constraint derived from adjacency matrices.

Provides matrix operation-based algorithms for structural holes measures.

Enhances understanding and computation of network structural holes.

Abstract

In this note I derive simple formulas based on the adjacency matrix of a network to compute measures associated with Ronald S. Burt's structural holes (effective size, redundancy, local constraint and constraint). This can help to interpret these measures and also to define naive algorithms for their computation based on matrix operations.