scholarly journals Principal eigenvector localization and centrality in networks: Revisited

2020 ◽  
Vol 554 ◽  
pp. 124169 ◽  
Author(s):  
Priodyuti Pradhan ◽  
Angeliya C.U. ◽  
Sarika Jalan
Keyword(s):  
Principal Eigenvector ◽  
Eigenvector Localization

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 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 PROBING COMPLEX NETWORKS FROM MEASURED TIME SERIES

2012 ◽  
Vol 22 (10) ◽  
pp. 1250236 ◽  
Author(s):  
LIANG HUANG ◽  
YING-CHENG LAI ◽  
MARY ANN F. HARRISON
Keyword(s):  
Time Series ◽  
Complex Networks ◽  
Network Topology ◽  
Efficient Method ◽  
Relative Importance ◽  
Computationally Efficient ◽  
Heuristic Argument ◽  
Principal Eigenvector ◽  
Measured Time ◽  
Potential Applications

We propose a method to detect nodes of relative importance, e.g. hubs, in an unknown network based on a set of measured time series. The idea is to construct a matrix characterizing the synchronization probabilities between various pairs of time series and examine the components of the principal eigenvector. We provide a heuristic argument indicating the existence of an approximate one-to-one correspondence between the components and the degrees of the nodes from which measurements are obtained. The striking finding is that such a correspondence appears to be quite robust, which holds regardless of the detailed node dynamics and of the network topology. Our computationally efficient method thus provides a general means to address the important problem of network detection, with potential applications in a number of fields.

A Novel Heuristic PageRank Algorithm in Web Search

2011 ◽  
Vol 216 ◽  
pp. 747-751
Author(s):  
Yan Li He
Keyword(s):  
Probability Distribution ◽  
Web Search ◽  
The Internet ◽  
Power Method ◽  
Web Page ◽  
Principal Eigenvector ◽  
Pagerank Algorithm ◽  
Empirical Distributions ◽  
The Matrix ◽  
The Web

With the booming development of the Internet, web search engines have become the most important Internet tools for retrieving information. PageRank computes the principal eigenvector of the matrix describing the hyperlinks in the web using the famous power method. Based on empirical distributions of Web page degrees, we derived analytically the probability distribution for the PageRank metric. We found out that it follows the familiar inverse polynomial law reported for Web page degrees.

Diffusion tensor parameters and principal eigenvector coherence: Relation to b-value intervals and field strength

2013 ◽  
Vol 31 (5) ◽  
pp. 742-747 ◽  
Author(s):  
Ai Wern Chung ◽  
David L. Thomas ◽  
Roger J. Ordidge ◽  
Chris A. Clark
Keyword(s):  
Field Strength ◽  
Diffusion Tensor ◽  
B Value ◽  
Principal Eigenvector ◽  
Coherence Relation

Effects of diffusion weighting schemes on the reproducibility of DTI-derived fractional anisotropy, mean diffusivity, and principal eigenvector measurements at 1.5T

NeuroImage ◽  
2007 ◽  
Vol 36 (4) ◽  
pp. 1123-1138 ◽  
Author(s):  
Bennett A. Landman ◽  
Jonathan A.D. Farrell ◽  
Craig K. Jones ◽  
Seth A. Smith ◽  
Jerry L. Prince ◽  
...  
Keyword(s):  
Fractional Anisotropy ◽  
Mean Diffusivity ◽  
Principal Eigenvector ◽  
Weighting Schemes ◽  
Diffusion Weighting
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