Magnetic eigenmaps for community detection in directed networks

Abstract

Communities in directed networks have often been characterized as regions with a high density of links, or as sets of nodes with certain patterns of connection. Our approach for community detection combines the optimization of a quality function and a spectral clustering of a deformation of the combinatorial Laplacian, the so-called magnetic Laplacian. The eigenfunctions of the magnetic Laplacian, that we call magnetic eigenmaps, incorporate structural information. Hence, using the magnetic eigenmaps, dense communities including directed cycles can be revealed as well as "role" communities in networks with a running flow, usually discovered thanks to mixture models. Furthermore, in the spirit of the Markov stability method, an approach for studying communities at different energy levels in the network is put forward, based on a quantum mechanical system at finite temperature.

15 pages

References in corpus (31)

• Fast unfolding of communities in large networks
• Finding and evaluating community structure in networks
• Modularity and community structure in networks
• Community detection in graphs
• Finding community structure in networks using the eigenvectors of matrices
• Maps of random walks on complex networks reveal community structure
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• Statistical Mechanics of Community Detection
• Community structure in directed networks
• Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities
• Nonoptimal Component Placement, but Short Processing Paths, due to Long-Distance Projections in Neural Systems
• Clustering and Community Detection in Directed Networks: A Survey
• Mixture models and exploratory analysis in networks
• Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks
• Laplacian Dynamics and Multiscale Modular Structure in Networks
• Memory in network flows and its effects on spreading dynamics and community detection
• Narrow scope for resolution-limit-free community detection
• Size reduction of complex networks preserving modularity
• LinkRank: Finding communities in directed networks
• Diffusion on networked systems is a question of time or structure
• Spanning forests and the vector bundle Laplacian
• Tensor Spectral Clustering for Partitioning Higher-order Network Structures
• Neural development features: Spatio-temporal development of the Caenorhabditis elegans neuronal network
• Interest communities and flow roles in directed networks: the Twitter network of the UK riots
• Using Triangles to Improve Community Detection in Directed Networks
• Detecting communities of triangles in complex networks using spectral optimization
• Nodal count of graph eigenfunctions via magnetic perturbation
• Magnetic interpretation of the nodal defect on graphs
• Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians
• Role-based similarity in directed networks
• Dressed Fermions, Modular Transformations and Bosonization in the Compactified Schwinger Model

Cited by in corpus (11)

• Complex Networks from Classical to Quantum
• A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning
• MagNet: A Neural Network for Directed Graphs
• Complex Quantum Networks: a Topical Review
• Spacing ratio characterization of the spectra of directed random networks
• Characterization and comparison of large directed graphs through the spectra of the magnetic Laplacian
• Higher-order Connection Laplacians for Directed Simplicial Complexes
• Geometric Scattering on Measure Spaces
• The Geometry of Synchronization Problems and Learning Group Actions
• Characterization and space embedding of directed graphs and social networks through magnetic Laplacians
• Directed Network Laplacians and Random Graph Models