We propose a method to simplify textual Twitter data into understandable networks of terms that can signify important events and their possible changes over time. The method allows for common characteristics of the networks across time periods and each period can comprise multiple unknown sub-networks. The networks are described by Gaussian graphical models and their parameter values are estimated through a Bayesian approach with a fused lasso-type prior on the precision matrices of the underlying mixtures of the sub-models. A flexible data allocation scheme is at the heart of an MCMC algorithm to recover mean and covariance parameters of the mixture components. Several implementations of the outlined estimation procedure are studied and compared based on simulated data. The procedure with the highest predictive power is used for mining tweets regarding the 2009 Iranian presidential election.