Community Detection in Networks via Nonlinear Modularity Eigenvectors

DOI10.1137/17M1144143zbMath1397.90089arXiv1708.05569MaRDI QIDQ4683908

Francesco Tudisco, Matthias Hein, Pedro Mercado

Publication date: 26 September 2018

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05569

zbMATH Keywords

nonlinear eigenvaluescommunity detectiongraph modularityCheeger inequalityspectral partitioning

Mathematics Subject Classification ID

Deterministic network models in operations research (90B10) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (6)

Generalized K-Core Percolation in Networks with Community Structure ⋮ Total Variation Based Community Detection Using a Nonlinear Optimization Approach ⋮ Phase transitions in normalized cut of social networks ⋮ Stochastic block models are a discrete surface tension ⋮ Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix-Vector Products ⋮ A Nonlinear Spectral Method for Core--Periphery Detection in Networks

Uses Software

• SNAP
• SparseMatrix
• MNIST
• GenLouvain

Cites Work

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• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Generalized modularity matrices
• Graph clustering
• On the generalization of the Courant nodal domain theorem
• A nodal domain theorem and a higher-order Cheeger inequality for the graph \(p\)-Laplacian
• An algorithm for drawing general undirected graphs
• A first-order primal-dual algorithm for convex problems with applications to imaging
• An Algebraic Analysis of the Graph Modularity
• Predicting Triadic Closure in Networks Using Communicability Distance Functions
• The university of Florida sparse matrix collection
• Spectrum of the 1-Laplacian and Cheeger's Constant on Graphs
• On Finding Graph Clusterings with Maximum Modularity
• Communities in Networks
• An Efficient Heuristic Procedure for Partitioning Graphs
• First-principles multiway spectral partitioning of graphs
• Fast unfolding of communities in large networks
• Modularity bounds for clusters located by leading eigenvectors of the normalized modularity matrix
• Learning with Submodular Functions: A Convex Optimization Perspective
• A Method Based on Total Variation for Network Modularity Optimization Using the MBO Scheme
• Networks

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