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

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-...

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Bibliographic Details
Published in:European journal of applied mathematics Vol. 27; no. 6; pp. 846 - 887
Main Authors: CUCURINGU, MIHAI, ROMBACH, PUCK, LEE, SANG HOON, PORTER, MASON A.
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.12.2016
Subjects:
Algorithms
Applied mathematics
Graphs
Matrix
Networks
low-rank matrix approximations
core–periphery structure
shortest-path algorithms
graph Laplacians
ISSN:0956-7925, 1469-4425
Online Access:Get full text
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Summary: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.
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ISSN:0956-7925
1469-4425
DOI:10.1017/S095679251600022X