The blessing of transitivity in sparse and stochastic networks

Understand

The interaction between transitivity and sparsity, two common features in empirical networks, implies that there are local regions of large sparse networks that are dense.

• We call this the blessing of transitivity and it has consequences for both modeling and inference.
• Extant research suggests that statistical inference for the Stochastic Blockmodel is more difficult when the edges are sparse.
• However, this conclusion is confounded by the fact that the asymptotic limit in all of the previous studies is not merely sparse, but also non-transitive.