This paper proposes a mixture model of low pass filtered graph signals. Our aim is to jointly estimate the eigen-centrality vectors for the underlying graphs and identify the graph signal samples with their corresponding graphs, without knowing the graph topology a-priori. The problem is challenging as the observed graph signals lack any obvious identity with their associated graphs. We leverage a low-rank plus sparse structure of the unknown parameters to de-rive a customized expectation-maximization (EM) algorithm for the joint problem. Our algorithm assumes general excitation and does not require prior knowledge of the graph topology. Numerical experiments show the efficacy of our customized EM algorithm.