Inference in the Stochastic Block Model with a Markovian assignment of the communities

We tackle the community detection problem in the Stochastic Block Model (SBM) when the communities of the nodes of the graph are assigned with a Markovian dynamic. To recover the partition of the nodes, we adapt the relaxed K-means SDP program presented in [11]. We identify the relevant signal-to-noise ratio (SNR) in our framework and we prove that the misclassification error decays exponentially fast with respect to this SNR. We provide infinity norm consistent estimation of the parameters of our model and we discuss our results through the prism of classical degree regimes of the SBMs' literature. MSC 2010 subject classifications: Primary 68Q32; secondary 68R10, 90C35.