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In the outline of works on structural balance, a new graph (the “families graph”) is proposed to complete the analysis of the classic graph (the “graph of relations”). Two new constructs have been introduced in the formal theory: the constructs of interval and disjoint. These constructs fulfil two functions. At the formal level, they symbolize families of balanced or unbalanced triads which are not only relations between two elements. At the psychological level they represent two processes working in beliefs systems construction : assimilation and differentiation of the objects of cognitive universes. An empirical longitudinal study of political believes systems shows the specificity of these two constructs faced with constructs at work in balance theories.