Results 1  10
of
14
Spectral Ranking
, 2009
"... This note tries to attempt a sketch of the history of spectral ranking—a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather some kind of relationship between e ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
This note tries to attempt a sketch of the history of spectral ranking—a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather some kind of relationship between entities. Albeit recently made famous by the ample press coverage of Google’s PageRank algorithm, spectral ranking was devised more than fifty years ago, almost exactly in the same terms, and has been studied in psychology and social sciences. I will try to describe it in precise and modern mathematical terms, highlighting along the way the contributions given by previous scholars. Disclaimer This is is a work in progress with no claim of completeness. I have tried to collect evidence of spectral techniques in ranking from a number of sources, providing a unified mathematical framework that should make it possible to understand in a precise way the relationship between contributions. Reports of inaccuracies and missing references are more than welcome. 1
Network centrality in the human functional connectome
 Cereb. Cortex
, 2012
"... The network architecture of functional connectivity within the human brain connectome is poorly understood at the voxel level. Here, using resting state functional magnetic resonance imaging data from 1003 healthy adults, we investigate a broad array of network centrality measures to provide novel i ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
The network architecture of functional connectivity within the human brain connectome is poorly understood at the voxel level. Here, using resting state functional magnetic resonance imaging data from 1003 healthy adults, we investigate a broad array of network centrality measures to provide novel insights into connectivity within the wholebrain functional network (i.e., the functional connectome). We first assemble and visualize the voxelwise (4 mm) functional connectome as a functional network. We then demonstrate that each centrality measure captures different aspects of connectivity, highlighting the importance of considering both global and local connectivity properties of the functional connectome. Beyond ‘‘detecting functional hubs,’ ’ we treat centrality as measures of functional connectivity within the brain connectome and demonstrate their reliability and phenotypic correlates (i.e., age and sex). Specifically, our analyses reveal agerelated decreases in degree
BioMed Central
, 2009
"... Subjective versus objective risk in genetic counseling for hereditary breast and/or ovarian cancers ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
(Show Context)
Subjective versus objective risk in genetic counseling for hereditary breast and/or ovarian cancers
Robustness of Social Networks: Comparative Results Based on Distance Distributions
"... Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which noderemoval order has the greatest impact on the network structure? We approach this wellknown problem for the first time in a setting that combines both web graphs and social netwo ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which noderemoval order has the greatest impact on the network structure? We approach this wellknown problem for the first time in a setting that combines both web graphs and social networks, using datasets that are orders of magnitude larger than those appearing in the previous literature, thanks to some recently developed algorithms and software tools that make it possible to approximate accurately the number of reachable pairs and the distribution of distances in a graph. Our experiments highlight deep differences in the structure of social networks and web graphs, show significant limitations of previous experimental results, and at the same time reveal clustering by label propagation as a new and very effective way of locating nodes that are important from a structural viewpoint. 1
On the limiting behavior of parameterdependent network centrality measures
 SIAM J. Matrix Anal. Appl
"... Abstract. We consider a broad class of walkbased, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various wellknown centrality indices, including Katz and subgraph centralities. We show that the ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We consider a broad class of walkbased, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various wellknown centrality indices, including Katz and subgraph centralities. We show that the parameter can be “tuned ” to interpolate between degree and eigenvector centralities, which appear as limiting cases. Our analysis helps explain certain correlations often observed between the rankings obtained using different centrality measures and provides some guidance for the tuning of parameters. We also highlight the roles played by the spectral gap of the adjacency matrix and by the number of triangles in the network. Our analysis covers both undirected and directed networks, including weighted ones. A brief discussion of PageRank is also given.
A MATRIX ANALYSIS OF DIFFERENT CENTRALITY MEASURES
"... matrix analysis of different centrality measures by ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
matrix analysis of different centrality measures by
Viscous Democracy for Social Networks
, 2009
"... This is the author’s version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
This is the author’s version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in
Next, we modify the second column of H in order to have a columnstochastic matrix:
"... Abstract. This document contains details of numerical experiments performed to illustrate the theoretical results presented in our accompanying paper. 1. Limiting behavior of PageRank for small α. In this section we want to illustrate the behavior of the PageRank vector in the limit of small values ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. This document contains details of numerical experiments performed to illustrate the theoretical results presented in our accompanying paper. 1. Limiting behavior of PageRank for small α. In this section we want to illustrate the behavior of the PageRank vector in the limit of small values of the parameter α. We take the following example from [8, pp. 32–33]. Consider the simple digraph G with n = 6 nodes described in Fig. 1.1. 3