Study on social relations between individuals based on graph theory

A formulated framework of tolerance relation in the applications of social activities is presented. The formulation can not only describe the activity degree of entities in a society, but also the average cost and the maximum cost at which one completes a task through various social relations. The algorithms for computing the maximum tolerance classes, the activity degree, the average cost and the maximum cost are given. Examples show the algorithms are effective. This is a very preliminary formulation, which need further study.