Assortative-Constrained Stochastic Block Models
This work addresses a specific issue in network analysis for researchers dealing with assortative networks, offering an incremental improvement over existing SBMs.
The authors tackled the problem that classic stochastic block models (SBMs) can produce undesirable outcomes for assortative networks with limited information by introducing a constrained SBM with strong assortativity constraints. This approach significantly boosts community recovery capabilities near the information-theoretic threshold and identifies structurally-different communities in cerebral-cortex activity networks.
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.