Topology, computational models, and social-cognitive complexity

Abstract

The topology or topological structure S, respectively, of a complex system can be defined in a graph theoretical way, i.e., S ⊆ ((V × V), E), V being a set of vertices and E a set of edges. Therefore, a topological structure in this sense can be represented as a directed graph. A relation e(v1, v2), e ∈ E, v1, v2 ∈ V may represent, e.g., a social relation in a social group between group members, a cognitive (semantical or logical) relation between concepts or an economical relation between economical actors. By defining a certain topology and by adding certain rules of interaction between elements vi and vj ∈ V, one obtains a literally universal modeling schema for arbitrarily complex problems (6). This modeling schema will be applied in this article to several different problems, i.e., predictions of social group dynamical processes, the diagnosis of certain diseases via a medical diagnosis system constructed this way, and the solving of a murder case in a detective story. The schema will in some cases be extended to two levels, i.e., one element of a first level will consist of different elements itself. © 2006 Wiley Periodicals, Inc. Complexity 11:43–55, 2006