Modeling sequences and temporal networks with dynamic community structures

Community-detection methods that describe large-scale patterns in the dynamics on and of networks suffer from effects of limited memory and arbitrary time binning. We develop a variable-order Markov chain model that generalizes the stochastic block model for discrete time-series as well as temporal networks. The temporal model does not use time binning but takes full advantage of the time-ordering of the tokens or edges. When the edge ordering is random, we recover the traditional static block model as a special case. Based on statistical evidence and without overfitting, we show how a Bayesian formulation of the model allows us to select the most appropriate Markov order and number of communities.