An Efficient Program for Cycle Basis Selection and Bandwidth Optimization

The applicability of graph theory for optimizing the sparsity and the bandwidth of cycleadjacency matrices of graphs is shown. Fundamental and subminimal cycle basis selectionalgorithms are presented in an algorithmic way. It is shown how the pattern of the cycleadjacency matrix changes during different phases of cycle selection and in particular whencycles are ordered. At each stage small pieces of code are presented to illustrate thesimplicity of the implementation of the graph theoretical approaches using a computerlanguage such as C++. The use of other languages should not cause much difficulty,although many aspects of an object oriented language such as C++ have been employedextensively throughout. This is intended to demonstrate the efficiency of graph theoretical methods combined with advanced techniques of computer programming