Journal of Computing
A relation on a set which is reflexive and symmetric is called a Compatibility Relation (CR). It is difficult to trace since when the profound mathematics of compatibility relation came into existence. In this paper, some new properties of compatibility classes of a finite set endowed with a suitable compatibility relation are described. An algorithm to compute maximal compatibility classes is constructed and an application of maximal compatibles to network segmentation and decentralization is demonstrated. Moreover, vector representation of compatibility classes is presented.