  When facing complex mesoscale network structures, it is generally believed
that (null) models encoding the modular organization of nodes must be employed.
The present paper focuses on two block structures that characterize the
mesoscale organization of many real-world networks, i.e. the bow-tie and the
core-periphery ones. Our analysis shows that constraining the network degree
sequence is often enough to reproduce such structures, as confirmed by model
selection criteria as AIC or BIC. As a byproduct, our paper enriches the
toolbox for the analysis of bipartite networks - still far from being complete.
The aforementioned structures, in fact, partition the networks into asymmetric
blocks characterized by binary, directed connections, thus calling for the
extension of a recently-proposed method to randomize undirected, bipartite
networks to the directed case.
