Due to their many advantages, modular structures commonly exist in artificial and natural systems, and the concept of modular product design has recently received extensive attention from the engineering research community. Although some work has been done on modularity, most of it is qualitative and exploratory in nature, and little is quantitative. One reason for this gap is the lack of a cle...

This paper introduces a conceptual, yet quantifiable, architecture framework by extending the notion of system modularity in its broadest sense. Acknowledging that modularity is not a binary feature and comes in various types and levels, the proposed framework introduces higher levels of modularity that naturally incorporate decentralized architecture on the one hand and autonomy in agents and ...

Research on ‘‘modularity’’ has made an important contribution to the study of technical change and economic institutions. It demonstrates that progress in the division of labor in design (technical modularity) has created new opportunities for the organization of firms beyond vertical integration, by fostering vertical specialization in both manufacturing and innovation. However, a small, but g...

We use the network science concept of modularity to measure polarization in the United States Congress. As a measure of the relationship between intra-community and extra-community ties, modularity provides a conceptually-clear measure of polarization that directly reveals both the number of relevant groups and the strength of their divisions. Moreover, unlike measures based on spatial models, ...

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Modularity is a popular measure for the quality of a cluster partition. Primarily, its popularity originates from its suitability for community identification through maximization. A lot of algorithms to maximize modularity have been proposed in recent years. Especially agglomerative hierarchical algorithms showed to be fast and find clusterings with high modularity. In this paper we present se...

Informally, a community within a graph is a subgraph whose vertices are more connected to one another than to the vertices outside the community. One of the most popular community detection methods is the Newman’s spectral modularity maximization algorithm, which divides a graph into two communities based on the signs of the principal eigenvector of its modularity matrix in the case that the mo...

Modularity of ontologies is currently an active research field, and many different notions of a module have been proposed. In this paper, we review the fundamental principles of modularity and identify formal properties that a robust notion of modularity should satisfy. We explore these properties in detail in the contexts of description logic and classical predicate logic and put them into the...

To identify communities in directed networks, we propose a generalized form of modularity in directed networks by presenting the quantity LinkRank, which can be considered as the PageRank of links. This generalization is consistent with the original modularity in undirected networks and the modularity optimization methods developed for undirected networks can be directly applied to directed net...

Many architectures of mind assume some form of modularity, but what is meant by the term ‘module’? This chapter creates a framework for understanding current modularity research in three subdisciplines of cognitive science — psychology, artificial intelligence and neuroscience. This framework starts from the distinction between horizontal modules which support all expressed behaviors vs. vertic...