  Stochastic block models (SBMs) are often used to find assortative community
structures in networks, such that the probability of connections within
communities is higher than in between communities. However, classic SBMs are
not limited to assortative structures. In this study, we discuss the
implications of this model-inherent indifference towards assortativity or
disassortativity, and show that this characteristic can lead to undesirable
outcomes for networks which are presupposedy assortative but which contain a
reduced amount of information. To circumvent this issue, we introduce a
constrained SBM that imposes strong assortativity constraints, along with
efficient algorithmic approaches to solve it. These constraints significantly
boost community recovery capabilities in regimes that are close to the
information-theoretic threshold. They also permit to identify
structurally-different communities in networks representing cerebral-cortex
activity regions.
