Automatic display of a given system structure is a useful tool in the analysis of large scale systems.
This paper presents a method for drawing a graph representing the system structure, which is basically an extensive application of Tutte's method to a system consisting of components strongly connected with each other.
Steps are, firstly to extract a strongly connected graph from a given system, secondly to condense the graph and extract a proper planer graph, thirdly to locate its vertices on the two-dimensional space so as to construct a graph without any crossing of edges, and finally to complete the entire figure by adding both the condensed vertices and the deleted edges.
Application to a few system models such as a model of climatic effects of carbon dioxide and a social event map in Japan demonstrates usefulness of this method. The graphs envisaged by this method have the following characteristics.
1) A system can be expressed as a graph with straight edges in which the number of edge crossings are almost minimized.
2) A system can be easily disaggregated into sub-blocks, as the graph is drawn on the principle that the closer related vertices are, the nearer they are located to each other.
3) The process is flexible enough to allow some important cycles in the system to be located in the center of the system graph, which may help realize the entire system structure, especially in the case of closely connected social systems.
View full abstract