Related papers: Generalized modularity matrices
Modularity, since its introduction, has remained one of the most widely used metrics to assess the quality of community structure in a complex network. However the resolution limit problem associated with modularity limits its applicability…
A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a…
We consider the problem of finding communities or modules in directed networks. The most common approach to this problem in the previous literature has been simply to ignore edge direction and apply methods developed for community discovery…
We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric…
In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and…
The study of the sub-structure of complex networks is of major importance to relate topology and functionality. Many efforts have been devoted to the analysis of the modular structure of networks using the quality function known as…
Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more.…
This paper introduces the notion of co-modularity, to co-cluster observations of bipartite networks into co-communities. The task of co-clustering is to group together nodes of one type with nodes of another type, according to the…
For data represented by networks, the community structure of the underlying graph is of great interest. A classical clustering problem is to uncover the overall ``best'' partition of nodes in communities. Here, a more elaborate description…
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
In the last few years many real-world networks have been found to show a so-called community structure organization. Much effort has been devoted in the literature to develop methods and algorithms that can efficiently highlight this hidden…
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…
Modularity maximization is the most popular technique for the detection of community structure in graphs. The resolution limit of the method is supposedly solvable with the introduction of modified versions of the measure, with tunable…
Much effort has gone into understanding the modular nature of complex networks. Communities, also known as clusters or modules, are typically considered to be densely interconnected groups of nodes that are only sparsely connected to other…
Community structure is a key feature omnipresent in real-world network data. Plethora of methods have been proposed to reveal subsets of densely interconnected nodes using criteria such as the modularity index. These approaches have been…
A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that…
In a graph or complex network, communities and anti-communities are node sets whose modularity attains extremely large values, positive and negative, respectively. We consider the simultaneous detection of communities and anti-communities,…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Proximity measures on graphs have a variety of applications in network analysis, including community detection. Previously they have been mainly studied in the context of networks without attributes. If node attributes are taken into…
We consider Gallai's graph Modular Decomposition theory for network analytics. On the one hand, by arguing that this is a choice tool for understanding structural and functional similarities among nodes in a network. On the other, by…