A note on (matricial and fast) 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 Burt's structural holes (effective size, local constraint and constraint). This not only can help to interpret these measures, but also the computational advantage is enormous when analyzing real-world networks, often characterized by large and sparse adjacency matrices: instead of looping over nodes, one can rely on very efficient and fast matrix operations (e.g., multiplication).