English
Related papers

Related papers: Generalized modularity matrices

200 papers

We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…

Data Structures and Algorithms · Computer Science 2017-02-07 Charalampos Tsourakakis , Jakub Pachocki , Michael Mitzenmacher

Complex networks topologies present interesting and surprising properties, such as community structures, which can be exploited to optimize communication, to find new efficient and context-aware routing algorithms or simply to understand…

Data Analysis, Statistics and Probability · Physics 2009-03-24 V. Nicosia , G. Mangioni , V. Carchiolo , M. Malgeri

In signal processing, exploring complex systems through network representations has become an area of growing interest. This study introduces the modularity graph, a new graph-based feature, to highlight the relationship across the graph…

Neurons and Cognition · Quantitative Biology 2024-10-23 Tiziana Cattai , Camilla Caporali , Marie-Constance Corsi , Stefania Colonnese

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

Statistical Mechanics · Physics 2009-02-26 Alicia Miralles , Lichao Chen , Zhongzhi Zhang , Francesc Comellas

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…

Physics and Society · Physics 2015-11-24 Xiao Zhang , M. E. J. Newman

Spectral analysis has been successfully applied at the detection of community structure of networks, respectively being based on the adjacency matrix, the standard Laplacian matrix, the normalized Laplacian matrix, the modularity matrix,…

Physics and Society · Physics 2010-10-21 Hua-Wei Shen , Xue-Qi Cheng

We focus on the detection of communities in multi-scale networks, namely networks made of different levels of organization and in which modules exist at different scales. It is first shown that methods based on modularity are not…

Physics and Society · Physics 2010-09-14 Renaud Lambiotte

Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights in the structure-functionality Modular structure is ubiquitous in real-world complex networks, and its detection is…

Data Analysis, Statistics and Probability · Physics 2008-05-29 Alex Arenas , Alberto Fernandez , Sergio Gomez

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…

Combinatorics · Mathematics 2022-12-22 Colin McDiarmid , Fiona Skerman

We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…

Statistical Mechanics · Physics 2009-11-11 L. Angelini , D. Marinazzo , M. Pellicoro , S. Stramaglia

Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs…

Statistics Theory · Mathematics 2018-01-29 Can M. Le , Elizaveta Levina , Roman Vershynin

This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…

Methodology · Statistics 2024-02-26 Anirban Mitra , Konasale Prasad , Joshua Cape

There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the…

Machine Learning · Statistics 2020-01-01 Clement Lee , Darren J Wilkinson

Complex networks represent interactions between entities. They appear in various contexts such as sociology, biology, etc., and they generally contain highly connected subgroups called communities. Community detection is a well-studied…

Social and Information Networks · Computer Science 2014-06-11 Romain Campigotto , Patricia Conde Céspedes , Jean-Loup Guillaume

Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret…

Machine Learning · Statistics 2017-10-05 Chihiro Watanabe , Kaoru Hiramatsu , Kunio Kashino

Study of the cluster- or community structure of complex networks makes an important contribution to the understanding of networks at a functional level. Despite the many efforts, no definition of community has been agreed on and important…

Disordered Systems and Neural Networks · Physics 2008-12-11 Joerg Reichardt , Stefan Bornholdt

Time series of graphs are increasingly prevalent in modern data and pose unique challenges to visual exploration and pattern extraction. This paper describes the development and application of matrix factorizations for exploration and…

Social and Information Networks · Computer Science 2015-06-16 Shawn Mankad , George Michailidis

Complex networks play a crucial role in understanding physical, biological, social and technological systems. One of the most relevant features of graphs representing real systems is community structure. In this paper, for a specific…

Probability · Mathematics 2024-04-18 Yu Miao , Qing Yin

Community detection is a critical challenge in analysing real graphs, including social, transportation, citation, cybersecurity, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this…

Social and Information Networks · Computer Science 2023-05-25 Łukasz Brzozowski , Grzegorz Siudem , Marek Gagolewski

Modularity, first proposed by [Newman and Girvan, 2004], is one of the most popular ways to quantify the significance of community structure in complex networks. It can serve as both a standard benchmark to compare different community…

Social and Information Networks · Computer Science 2022-02-14 Qian Wang , Yongkang Guo , Zhihuan Huang , Yuqing Kong