title: Spectral Characterization of Hierarchical Modularity in Product Architectures.
abstract: Despite the importance of the architectural modularity of products and systems, existing modularity metrics or algorithms do not account for overlapping and hierarchically embedded modules. This paper presents a graph theoretic spectral approach to characterize the degree of modular hierarchical-overlapping organization in the architecture of products and complex engineered systems. It is shown that the eigenvalues of the adjacency matrix of a product architecture graph can reveal layers of hidden modular or hierarchical modular organization that are not immediately visible in the predefined architectural description. We use the approach to analyze and discuss several design, management, and system resilience implications for complex engineered systems.
authors.affiliation: Design Lab, Faculty of Architecture, Design, and Planning, University of Sydney , Sydney NSW 2006 , Australia e-mail:  somwrita.sarkar@sydney.edu.au.
authors.forename: Somwrita
authors.initials: S
authors.lastname: Sarkar
authors.affiliation: Faculty of Engineering and Information Technologies, University of Sydney , Sydney NSW 2006 , Australia e-mail:  andy.dong@sydney.edu.au.
authors.forename: Andy
authors.initials: A
authors.lastname: Dong
authors.affiliation: Complex Systems Group, School of Physics, University of Sydney , Sydney NSW 2006 , Australia e-mail:  henderso@physics.usyd.edu.au.
authors.forename: James A
authors.initials: JA
authors.lastname: Henderson
authors.affiliation: Complex Systems Group, School of Physics, University of Sydney , Sydney NSW 2006 , Australia.
authors.forename: P A
authors.initials: PA
authors.lastname: Robinson