In [1] a interconnected system consisted of two sub-systems is studied, which leads to a generalized small-gain theorem, which gives the express of the gain of the output of the interconnected system w.r.t external input signals. However, sometimes we are interested in the gain from the input to the output of each sub-system. Such a result will offer more flexibility in control synthesis. For t...

The present paper aims to investigate the effects of modularity and the layout of subsystems and parts of a complex system on its maintainability. For this purpose, four objective functions have been considered simultaneously: I) maximizing the level of accordance between system design and optimum modularity design,II) maximizing the level of accessibility and the maintenance space required,III...

The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational comp...

Online social media such as delicious and digg are represented as tripartite networks whose vertices are users, tags, and resources. Detecting communities from such tripartite networks is practically important. Newman-Girvan modularity is often used as the criteria for evaluating the goodness of network divisions into communities. Murata has extended Newman-Girvan modularity in order to evaluat...

While much has changed in product modularity research in the 18 years since the independence axiom, some basic questions remain unanswered. Perhaps the most fundamental of those questions is whether increasing modularity actually saves money. The goal of the research behind this paper was to clearly define the fundamental relationship between product modularity and product cost. Our previous wo...

The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). Community detection in graphs is now often conducted through modularity maximization: given an undirected graph G = (V,E), we are asked to find a partition C of V that maximizes the modularity. Although numerous algorithms have been developed to date, most of them have no theoretical a...

Newman and Girvan [12] recently proposed an objective function for graph clustering called the Modularity function which allows automatic selection of the number of clusters. Empirically, higher values of the Modularity function have been shown to correlate well with good graph clustering. In this paper we propose an extended Modularity measure for categorical data clustering; first, we establi...

Modularity has been introduced as a quality measure for graph partitioning. It has received considerable attention in several disciplines, especially complex systems. In order to better understand this measure from a graph theoretical point of view, we study the modularity of a variety of graph classes. We first consider simple graph classes such as tori and hypercubes. We show that these regul...

The recent boom of large-scale online social networks (OSNs) both enables and necessitates the use of parallelizable and scalable computational techniques for their analysis. We examine the problem of real-time community detection and a recently proposed linear time- O(m) on a network with m edges-label propagation, or "epidemic" community detection algorithm. We identify characteristics and dr...