Quasi-Networks in Social Relational Systems.

摘要

In social sciences it is more or less generally acknowledged that (social) networks seem to be the natural tool in the organization of social activity. The paper focuses on the development of a possible mathematical formulation of the properties of a social network within the setting of an economic trade system. In order to capture asymmetric features of economic agents it proposes to alter the fundamental notion of a social system by introducing a binary relation on the set of agents. The relation is describing the incomplete (asymmetric) possibilities of communication between the individual agents in the social system. Mathematically it introduces the notion of a social relational system consisting of a collection of agents, represented by their individual attributes within a topological attribute space and a binary relation on the set of agents. It shows that generically there exist minimal subsystems, which are nearly complete in the sense that within the hyperspace endowed with the topology of closed convergence it is the limit of a sequence of complete subsystems. It refers to such a minimal and nearly complete social relational subsystem as a quasi-network. It argues that the notion of a quasi-network is giving a proper description of a crudely efficient organization that is able to handle all communication within a social relational system.