Expressions and bounds for Newman's modularity are presented. These results reveal conditions for or properties of the maximum modularity of a network. The influence of the spectrum of the modularity matrix on the maximum modularity is discussed. The second part of the paper investigates how the maximum modularity, the number of clusters, and the hop count of the shortest paths vary when the as...

Some temporal networks, most notably citation networks, are naturally represented as directed acyclic graphs (DAGs). To detect communities in DAGs, we propose a modularity for DAGs by defining an appropriate null model (i.e., randomized network) respecting the order of nodes. We implement a spectral method to approximately maximize the proposed modularity measure and test the method on citation...

We study how modularity of the human brain changes as children develop into adults. Theory suggests that modularity can enhance the response function of a networked system subject to changing external stimuli. Thus, greater cognitive performance might be achieved for more modular neural activity, and modularity might likely increase as children develop. The value of modularity calculated from f...

Despite the major role that modularity occupies in computer science all the known results on modular analysis only treat particular problems and there is no general unifying theory In this paper we provide such a general theory of modularity First we study the space of the criteria for modularity the so called modularity space and give results on its complexity Then we introduce the notion of v...

The concept of modularity is a main concern for the generation of artificially intelligent systems. Modularity is an ubiquitous organization principle found everywhere in natural and artificial complex systems (Callebaut, 2005). Evidences from biological and philosophical points of view (Caelli and Wen, 1999) (Fodor, 1983), indicate that modularity is a requisite for complex intelligent behavio...

Modularity is the fundamental aspect of modern software engineering, however many advanced modularity techniques requires prospective technologies as part of development and operation process. In this paper, we present Refinable Function, an object-oriented approach to advanced languagebased, symmetric modularity technique for the procedure. We conceptually compare Refinable Function to existin...

Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the modularity of two kinds of graphs. For r-regular graphs with a given number of vertices, we investigate the minimum possible modularity, the typical modulari...

Against a background of recent progress in developmental neuroscience, some of which has been taken as challenging to the modularity hypothesis of Fodor (1983), this article contrasts two competing conceptions of modularity: sui generis modularity, according to which modules are treated as independent neurocognitive entities that owe nothing to one another, and descent-with-modiWcation modulari...

Against a background of recent progress in developmental neuroscience, some of which has been taken as challenging to the modularity hypothesis of , this article contrasts two competing conceptions of modularity: sui generis modularity, according to which modules are treated as independent neurocognitive entities that owe nothing to one another, and descent-with-modification modularity, accordi...