St. BEER writes: "… the most useful scientific language for discussing… networks… is really the theory of graphs… "
"… the graph as a logical entity, consisting of an arborescence of binary relations (is) to be treated by Boolean functions. Now, the modern mathematical statement of graphs is achieved with the help of the theory of sets, and it looks like subsuming all the other descriptions in one. (The vertices of a graph are regarded as elements of a set which is mapped into itself, of which set the whole graph is then a multi-valued function)" (1968, p.218).
Three different, but related, graph descriptions of a network can be thought of:
- The static "vertical" arborescence representing a supposedly invariable hierarchy (Example: the structural representation of an organization);
- A dynamic "horizontal" arborescence, representing the flow lines of the interconnected variables of the system in time (Example: Critical paths graphs);
- A closed cyclical graph, also allowing for the representation of the dynamics of feedbacks between elements. (Example: M. EIGEN's Hypercycles graphs).
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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