Edges, chains, shadows, neighbors and subgraphs in the intrinsic order graph

Abstract

Many different scientific, technical or social phenomena can be modeled by a complex system depending on a large number n of random Boolean variables. Such systems are called complex stochastic Boolean systems (CSBSs). The most useful representation of a CSBS is the intrinsic order graph. This is a symmetric digraph on 2 n nodes, with a characteristic fractal structure. In this paper, different properties of the intrinsic order graph are studied, namely those dealing with its edges; chains; shadows, neighbors and degrees of its vertices; and some relevant subgraphs, as well as the natural isomorphisms between them.