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Statistical physics has provided concepts and techniquesuseful for describing and analyzing social phenomenology. In particular complexity within the sociological interpretation has resulted in different relevant  situations. In a recent work, intriguing non-monotonous properties were observed in the 2-Dim Sznajd model. Here we introduce a unified complexity-entropy framework that provides a deeper understanding of those system features. By performing numerical simulations, the system track probabilistic dependence quantified in terms of Shannon entropy. By means of a complexity – entropy map we observe a non monotonous behavior in the relation between entropy and complexity. We also show a maximum complexity in a region that is associated with a phase transition indicating, on one hand, social mobility and on the other hand a structural rearrangement of the network.