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Detection of core–periphery structure in networks using spectral methods and geodesic paths

Published online by Cambridge University Press:  03 August 2016

MIHAI CUCURINGU ,
PUCK ROMBACH ,
SANG HOON LEE  and
MASON A. PORTER
MIHAI CUCURINGU
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA, USA emails: mihai@math.ucla.edu, rombach@math.ucla.edu
PUCK ROMBACH
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA, USA emails: mihai@math.ucla.edu, rombach@math.ucla.edu
SANG HOON LEE
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford, UK email: porterm@maths.ox.ac.uk School of Physics, Korea Institute for Advanced Study, Seoul, Korea email: lshlj82@kias.re.kr
MASON A. PORTER
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford, UK email: porterm@maths.ox.ac.uk CABDyN Complexity Centre, University of Oxford, Oxford, UK
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Abstract

We introduce several novel and computationally efficient methods for detecting “core–periphery structure” in networks. Core–periphery structure is a type of mesoscale structure that consists of densely connected core vertices and sparsely connected peripheral vertices. Core vertices tend to be well-connected both among themselves and to peripheral vertices, which tend not to be well-connected to other vertices. Our first method, which is based on transportation in networks, aggregates information from many geodesic paths in a network and yields a score for each vertex that reflects the likelihood that that vertex is a core vertex. Our second method is based on a low-rank approximation of a network's adjacency matrix, which we express as a perturbation of a tensor-product matrix. Our third approach uses the bottom eigenvector of the random-walk Laplacian to infer a coreness score and a classification into core and peripheral vertices. We also design an objective function to (1) help classify vertices into core or peripheral vertices and (2) provide a goodness-of-fit criterion for classifications into core versus peripheral vertices. To examine the performance of our methods, we apply our algorithms to both synthetically generated networks and a variety of networks constructed from real-world data sets.

Keywords

Networkscore–periphery structureshortest-path algorithmslow-rank matrix approximationsgraph Laplacians

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Special Issue 6: Network Analysis and Modelling , December 2016 , pp. 846 - 887
Copyright
Copyright © Cambridge University Press 2016 

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