Using Tube Graphs to Model Architectural Designs of Software Systems

A tube graph is a mathematical entity that can be used for modelling architectural designs of software systems. It consists of a tree (representing containment) with a set of edges called tubes (representing dependencies) between the tree's vertices (representing components). Tubes, for example, can model the import relation at the module level and the use dependency relation at the subsystem level. Well-formedness constraints are imposed on tube edges to deene restricted tube graphs that model particular styles of architectural designs. In this paper, the well-formedness constraints deene tube graphs that model SIL language architectural designs. Diierent mathematical formulations of these well-formed tube graphs are given and proven to be equivalent. Algorithms for manipulating tube graphs, for possible use in a software development environment, are also given and their complexities are shown to be modest in most cases.