Ranking components of scientific software using spectral methods

In this thesis we explore the centrality rankings of functions in call graphs of scientific software using spectral method. Dependency Structure Matrix (DSM) is used as a modeling tool to represent and examine pattern of inter-dependencies among functions. We compute the hubs and authorities in directed networks using functions of matrices. The non-symmetry nature of the dependency relations is addressed by bipartization, i.e., by defining a symmetric matrix B using the original matrix and its transpose as shown below: B =[O A] [AT O] We use the matrix exponential method for computing hubs and authorities. We show that the hub and authority ranking provided by the diagonal entries of the matrix exponential may vary from the ranking provided using HITS algorithm. These two methods have been applied on both non-weighted and weighted call graphs of three scientific software and the results have been analyzed.