Eigenvector localization as a tool to study small communities in online social networks

Abstract

We present and discuss a mathematical procedure for identification of small "communities" or segments within large bipartite networks. The procedure is based on spectral analysis of the matrix encoding network structure. The principal tool here is localization of eigenvectors of the matrix, by means of which the relevant network segments become visible. We exemplified our approach by analyzing the data related to product reviewing on Amazon.com. We found several segments, a kind of hybrid communities of densely interlinked reviewers and products, which we were able to meaningfully interpret in terms of the type and thematic categorization of reviewed items. The method provides a complementary approach to other ways of community detection, typically aiming at identification of large network modules.

References in corpus (43)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Finding and evaluating community structure in networks
• Community detection in graphs
• Uncovering the overlapping community structure of complex networks in nature and society
• Finding community structure in networks using the eigenvectors of matrices
• Functional cartography of complex metabolic networks
• Evolution of networks
• Defining and identifying communities in networks
• Detecting the overlapping and hierarchical community structure of complex networks
• Noise Dressing of Financial Correlation Matrices
• How to project a bipartite network?
• Universal and non-universal properties of cross-correlations in financial time series
• A Random Matrix Approach to Cross-Correlations in Financial Data
• Modularity and community detection in bipartite networks
• Detecting fuzzy community structures in complex networks with a Potts model
• Pseudofractal Scale-free Web
• Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
• Detecting communities in large networks
• A Method to Find Community Structures Based on Information Centrality
• Spectra of complex networks
• Spectra and eigenvectors of scale-free networks
• Modularity and Extreme Edges of the Internet
• Random walks on graphs: ideas, techniques and results
• Sparse random matrices: the eigenvalue spectrum revisited
• Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
• Systematic analysis of group identification in stock markets
• Uncovering collective listening habits and music genres in bipartite networks
• Spectra of Sparse Random Matrices
• Rational Decisions, Random Matrices and Spin Glasses
• Mixing patterns and community structure in networks
• Identification of clusters of companies in stock indices via Potts super-paramagnetic transitions
• Networks in life: Scaling properties and eigenvalue spectra
• Clusters or networks of economies? A macroeconomy study through GDP fluctuation correlations
• Diffusion on Complex Networks : A way to probe their large scale topological structures
• Random matrix analysis of localization properties of Gene co-expression network
• Spectral Analysis of Protein-Protein Interactions in Drosophila melanogaster
• Scaling Invariance in Spectra of Complex Networks: A Diffusion Factorial Moment Approach
• Spectral Density of Sparse Sample Covariance Matrices
• Spectral Density of Complex Networks with a Finite Mean Degree
• Spectral methods and cluster structure in correlation-based networks
• Spectrum, Intensity and Coherence in Weighted Networks of a Financial Market
• Netons: Vibrations of Complex Networks

Cited by in corpus (5)

• Localization of eigenvectors in random graphs
• Localization in random bipartite graphs: numerical and empirical study
• Eigenvalue ratio statistics of complex networks: Disorder vs. Randomness
• Eigenvector localization in hypergraphs: pair-wise vs higher-order links
• Complex temporal structure of activity in on-line electronic auctions