Demiarcs, creaons and genons

Abstract

Useful insights into the representation of natural systems can be gained by decomposing directed graphs (digraphs) into elementary components. Arcs of digraphs can be split into male demiarcs (outarcs) which leave vertices and female demiarcs (inarcs) which enter demiarcs. Likewise, a vertex can be split into an input perceiving side called the creaon and an output generating side called the genon. Digraphs can be regarded as being hierarchically organized because each vertex in a level-1 digraph can be expanded into a level-2 digraph. In general, each vertex of a level-i digraph can be expanded into a level-(i+1) digraph. Arcs of a level-i digraph can be regarded as bundles of level-(i + 1) arcs which are split at the vertex boundary. These elementary graphical components are shown to be useful for depicting input-output systems such as organisms, ecosystems and societies.