A note on matricial ways to compute Burt's structural holes

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), together with the measure called improved structural holes introduced in 2017. This can help to see these measures within a unified computation framework because they can all be expressed in matricial form. These formulas can also be used to define naïve algorithms based on matrix operations for their computation. Such naïve algorithms can be used for small- and medium-sized networks, where exploiting the sparsity of the matrices and efficient triangle listing techniques are not necessary.