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The theory presented is applicable to any system with discrete interactions, i.e., one that lacks long-range crystal-like translational symmetry but is such that any of its structural elements interacts directly with only a finite (in most cases small) number of other elements, i.e., for materials such as cross-linked polymers, superpolymers (ferrofluids, wormlike micelles, colloidal necklaces), ceramics and glasses obtained by sol-gel processes, as well as for biophysical systems such as membrane receptors, cellular aggregates, neuronal branching patterns.The theory systematizes the information one needs to represent the system by a hypergraph, which then makes possible application of the so-called difference a posteriori (DAPOST) algorithm to calculate structural characteristics of the system and structure–property relationships. It is based on probabilistic and topological considerations; thus, it is applicable to systems far from thermodynamic equilibrium and to the analysis of spatiotemporal patterns.

The scheme of calculations, which subsequently will be called the difference a posteriori algorithm (or just DAPOST), is formulated in a general and rigorous manner to make its application to different systems with discrete interactions (SDI) possible. The DAPOST enables one to calculate important probabilistic characteristics of SDI while having only general information about its composition and interactions between system elements. The DAPOST is easily adaptable to very different physicochemical and biophysical systems, especially to the problems of element aggregation and binding. When applied together with a hypergraph representation of the SDI under consideration the DAPOST allows construction of equivalent probabilistic representations of the hypergraph modelling the SDI, in this way often considerably simplifying calculations of the structure–property relationships of the SDI.