The stochastic block model (aka. planted partition model) is a popular model for representing networks with communities. Elchanan Mossel, Joe Neeman, and Allan Sly have been investigating algorithms and fundamental limits for detecting and recovering these communities. They established sharp transitions for the problem of extracting non-trivial information and the problem of exactly recovering communities. They also gave a new algorithm that obtains provably optimal accuracy for the problem of detecting communities in “Consistency thresholds for the planted bisection model” and “Belief propagation, robust reconstruction, and optimal recovery of block models“.
Avhishek Chatterjee, François Baccelli and Sriram Vishwanath proposed a stochastic extension of the bounded confidence model where opinions take their values in the Euclidean space and where friendship and interactions are dynamically defined through time varying and random neighborhoods. Two basic sub-models are defined: the influencing model where each agent is an attractor to the opinions of its neighbors and the listening model where each agent gathers information from others to update its own opinions. The general model contains a rich set of variants for which they proposed a classification. They analyzed the stability of its dynamics. The analysis highlights the need of certain leaders with heavy tailed neighborhoods for stability to hold.