Authors:
Iaakov Exman
and
Rawi Sakhnini
Affiliation:
The Jerusalem College of Engineering – JCE-Azrieli, Israel
Keyword(s):
Linear Software Models, Modularity Matrix, Laplacian Matrix, Connected Components, Eigenvectors, Zero-valued Eigenvalues, Bipartite Graph, Software Redesign, Coupling Resolution, Outliers.
Related
Ontology
Subjects/Areas/Topics:
Model Analysis and Checking
;
Model Composition
;
Model Tools
;
Models
;
Paradigm Trends
;
Software Engineering
Abstract:
We have recently shown that one can obtain the number and sizes of modules of a software system from the eigenvectors of the Modularity Matrix weighted by an affinity matrix. However such a weighting still demands a suitable definition of an affinity. This paper obtains the same results by means of a Laplacian Matrix, directly based upon the Modularity Matrix without the need of weighting. These formalizations are different alternatives leading to the same outcomes based upon a central idea: modules are connected components. The important point is that, independently of specific advantages of given techniques, there is just one single unified algebraic theory of software composition – the Linear Software Models – behind the different approaches. The specifics of the Laplacian Matrix technique, after its formal enunciation, are illustrated by calculations made for case studies.