Related papers: Spectral tripartitioning of networks
One of the most widely used methods for community detection in networks is the maximization of the quality function known as modularity. Of the many maximization techniques that have been used in this context, some of the most conceptually…
We consider three distinct and well studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems…
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…
Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem.…
We investigate combinatorial properties of certain configurations of a graph partition which are related to the minimality of a cut. We show that such configurations are related to the third eigenvector of the Laplacian matrix. It is well…
With invaluable theoretical and practical benefits, the problem of partitioning networks for community structures has attracted significant research attention in scientific and engineering disciplines. In literature, Newman's modularity…
Community detection is a fundamental problem in the domain of complex-network analysis. It has received great attention, and many community detection methods have been proposed in the last decade. In this paper, we propose a divisive…
We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is…
A fundamental problem in mathematics and network analysis is to find conditions under which a graph can be partitioned into smaller pieces. The most important tool for this partitioning is the Fiedler vector or discrete Cheeger inequality.…
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…
Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to identify important nodes in a network and to uncover…
We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…
We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…
The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to…
Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with…
This paper presents the applications of Eigenvalues and Eigenvectors (as part of spectral decomposition) to analyze the bipartivity index of graphs as well as to predict the set of vertices that will constitute the two partitions of graphs…
Using methods from random matrix theory researchers have recently calculated the full spectra of random networks with arbitrary degrees and with community structure. Both reveal interesting spectral features, including deviations from the…
We will present improvements to famous algorithms for community detection, namely Newman's spectral method algorithm and the Louvain algorithm. The Newman algorithm begins by treating the original graph as a single cluster, then repeats the…
Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this…