Networks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community structure in single (i.e., monoplex) networks. However, with the advent of relational data with multiple modalities, multiplex networks, i.e., networks composed of multiple layers representing different aspects of relations, have emerged. Consequently, community detection in multiplex network, i.e., detecting clusters of nodes shared by all layers, has become a new challenge. In this paper, we propose Network Fusion for Composite Community Extraction (NF-CCE), a new class of algorithms, based on four different non-negative matrix factorization models, capable of extracting composite communities in multiplex networks. Each algorithm works in two steps: first, it finds a non-negative, low-dimensional feature representation of each network layer; then, it fuses the feature representation of layers into a common non-negative, low-dimensional feature representation via collective factorization. The composite clusters are extracted from the common feature representation. We demonstrate the superior performance of our algorithms over the state-of-the-art methods on various types of multiplex networks, including biological, social, economic, citation, phone communication, and brain multiplex networks.
In the goal is to reveal network communities and their hierarchical structure based on a similarity (usually topological) measure computed between pairs of nodes @cite_32 . algorithms are among the most popular ones. Modularity was designed to measure the strength of partition of a network into communities. It is defined as a fraction of the edges that fall within the community minus the expected fraction when these edges are randomly distributed @cite_44 @cite_6 . Various algorithms have been proposed for modularity optimization, including greedy techniques, simulated annealing, spectral optimization, etc. @cite_16 .
@cite_44 @cite_16 @cite_32 @cite_6
2015953751 2040858714 2094934391 2131681506
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks. Modularity is widely used to effectively measure the strength of the disjoint community structure found by community detection algorithms. Although several overlapping extensions of modularity were proposed to measure the quality of overlapping community structure, there is lack of systematic comparison of different extensions. To fill this gap, we overview overlapping extensions of modularity to select the best. In addition, we extend the Modularity Density metric to enable its usage for overlapping communities. The experimental results on four real networks using overlapping extensions of modularity, overlapping modularity density, and six other community quality metrics show that the best results are obtained when the product of the belonging coefficients of two nodes is used as the belonging function. Moreover, our experiments indicate that overlapping modularity density is a better measure of the quality of overlapping community structure than other metrics considered. Many networks, indifferent of their function and scope, converge to a scale-free architecture in which the degree distribution approximately follows a power law. Meanwhile, many of those scale-free networks are found to be naturally divided into communities of densely connected nodes, known as community structure. Finding this community structure is a fundamental but challenging topic in network science. Since Newman's suggestion of using modularity as a measure to qualify the strength of community structure, many efficient methods that find community structure based on maximizing modularity have been proposed. However, there is a lack of approximation algorithms that provide provable quality bounds for the problem. In this paper, we propose polynomial-time approximation algorithms for the modularity maximization problem together with their theoretical justifications in the context of scale-free networks. We prove that the solutions of the proposed algorithms, even in the worst-case, are optimal up to a constant factor for scale-free networks with either bidirectional or unidirectional links. Even though our focus in this work is not on designing another empirically good algorithms to detect community structure, experiments on real-world networks suggest that the proposed algorithm is competitive with the state-of-the-art modularity maximization algorithm. We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks.