scholarly journals Distinct types of eigenvector localization in networks

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Romualdo Pastor-Satorras ◽  
Claudio Castellano
Keyword(s):  
Eigenvector Localization

Comments on “absence of decay and eigenvector localization in a soluble one-dimensional system”

1972 ◽  
Vol 42 (3) ◽  
pp. 251-252
Author(s):  
J.C. Wang ◽  
K.S. Dy
Keyword(s):  
Dimensional System ◽  
One Dimensional ◽  
Eigenvector Localization

scholarly journals EIGENVECTOR LOCALIZATION AS A TOOL TO STUDY SMALL COMMUNITIES IN ONLINE SOCIAL NETWORKS

2010 ◽  
Vol 13 (06) ◽  
pp. 699-723 ◽  
Author(s):  
FRANTIŠEK SLANINA ◽  
ZDENĚK KONOPÁSEK
Keyword(s):  
Online Social Networks ◽  
Large Network ◽  
Bipartite Networks ◽  
Small Communities ◽  
Complementary Approach ◽  
Matrix Encoding ◽  
The Matrix ◽  
Network Modules ◽  
Principal Tool ◽  
Eigenvector Localization

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.

scholarly journals Eigenvector Localization in Real Networks and Its Implications for Epidemic Spreading

2018 ◽  
Vol 173 (3-4) ◽  
pp. 1110-1123 ◽  
Author(s):  
Romualdo Pastor-Satorras ◽  
Claudio Castellano
Keyword(s):  
Epidemic Spreading ◽  
Eigenvector Localization

Eigenvector localization on data-dependent graphs

2015 ◽  
Author(s):  
Alexander Cloninger ◽  
Wojciech Czaja
Keyword(s):  
Eigenvector Localization

scholarly journals Eigenvector Localization for Random Band Matrices with Power Law Band Width

2009 ◽  
Vol 290 (3) ◽  
pp. 1065-1097 ◽  
Author(s):  
Jeffrey Schenker
Keyword(s):  
Power Law ◽  
Band Width ◽  
Band Matrices ◽  
Eigenvector Localization ◽  
Random Band

scholarly journals Quasi-universality in single-cell sequencing data

2018 ◽  
Author(s):  
Luis Aparicio ◽  
Mykola Bordyuh ◽  
Andrew J. Blumberg ◽  
Raul Rabadan
Keyword(s):  
Single Cell ◽  
Matrix Theory ◽  
Biological Information ◽  
Sequencing Data ◽  
Data Set ◽  
Single Cell Sequencing ◽  
Marked Cell ◽  
Eigenvector Localization ◽  
Cell Data ◽  
Epigenetic Processes

ABSTRACTThe development of single-cell technologies provides the opportunity to identify new cellular states and reconstruct novel cell-to-cell relationships. Applications range from understanding the transcriptional and epigenetic processes involved in metazoan development to characterizing distinct cells types in heterogeneous populations like cancers or immune cells. However, analysis of the data is impeded by its unknown intrinsic biological and technical variability together with its sparseness; these factors complicate the identification of true biological signals amidst artifact and noise. Here we show that, across technologies, roughly 95% of the eigenvalues derived from each single-cell data set can be described by universal distributions predicted by Random Matrix Theory. Interestingly, 5% of the spectrum shows deviations from these distributions and present a phenomenon known as eigenvector localization, where information tightly concentrates in groups of cells. Some of the localized eigenvectors reflect underlying biological signal, and some are simply a consequence of the sparsity of single cell data; roughly 3% is artifactual. Based on the universal distributions and a technique for detecting sparsity induced localization, we present a strategy to identify the residual 2% of directions that encode biological information and thereby denoise single-cell data. We demonstrate the effectiveness of this approach by comparing with standard single-cell data analysis techniques in a variety of examples with marked cell populations.

scholarly journals Optimized evolution of networks for principal eigenvector localization

2017 ◽  
Vol 96 (2) ◽  
Author(s):  
Priodyuti Pradhan ◽  
Alok Yadav ◽  
Sanjiv K. Dwivedi ◽  
Sarika Jalan
Keyword(s):  
Principal Eigenvector ◽  
Eigenvector Localization

scholarly journals Susceptible-infected-susceptible model on networks with eigenvector localization

2020 ◽  
Vol 101 (4) ◽  
Author(s):  
Zong-Wen Wei ◽  
Bing-Hong Wang
Keyword(s):  
Eigenvector Localization

Absence of decay and eigenvector localization in a soluble one-dimensional system

1972 ◽  
Vol 39 (5) ◽  
pp. 393-394 ◽  
Author(s):  
G.C. Stey ◽  
G. Gusman
Keyword(s):  
Dimensional System ◽  
One Dimensional ◽  
Eigenvector Localization
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