Developing Spectral Structural Complexity Metrics

Abstract

There are various approaches to measure the complexity of engineered systems. The structural approach to the measurement of system complexity is only one of the possible routes that are currently under consideration. This approach considers the complexity of the internal structure of the system and the organization of its components, as a snapshot frozen in time.The most common approach to the definition of structural complexity metrics is through the concepts of entropy, algorithmic information content, and logical depth. Another approach looks at the set of the eigenvalues–the spectrum–of a graph representation of the system of interest. The most popular spectral structural complexity metrics are graph energy and natural connectivity. The authors in this article present a set of metrics that are created based on the existing metrics. The metrics assume that the graphs representing the system of interest are weighted with values representing the complexity of components and interfaces. The metrics are then explored through two sets of random graphs, representing the architecture of an engineered system.