Coverage, invariability and orbits by structural functions

Abstract

Purpose

Based on some of the results and definitions provided in the paper “system linkage: structural functions and hierarchies” and adding new definitions that are in keeping with the spirit of the same paper, new results have been obtained that explore the utility of the structural input‐output function.

Design/methodology/approach

Our approach is based principally on the application of graph theory to the study of relationships between variables using specific set theory concepts.

Findings

A result such as the fact that A covers B, for example, can be interpreted in terms of the latter set being formed of direct influences from elements in the former set in relation to one or more than one relationships. Analogously, the invariant set concept may be interpreted as the set maintaining its structure and status, remaining constant with respect to any possible relationships.

Originality/value

From a practical point of view, in the context of the study of networks within an ecosystem, authors (such as Patten et al. and Patten) have demonstrated that indirect effects between the variables of an ecosystem outweigh direct effects. This is the notion that the present authors have borne in mind in order to extend previous results to indirect influences from a discrete perspective.

Citation

Francesc Esteve‐Calvo, P. and Lloret‐Climent, M. (2006), "Coverage, invariability and orbits by structural functions", Kybernetes, Vol. 35 No. 7/8, pp. 1236-1240. https://doi.org/10.1108/03684920610675210