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Detection of Core-Periphery Structure in Networks Using Spectral Methods and Geodesic Paths
- Source :
- European Journal of Applied Mathematics, Volume 27, Issue 6 (Network Analysis and Modelling) December 2016, pp. 846-887
- Publication Year :
- 2014
-
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 includes 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 a vertex is a core vertex. Our second method is based on a low-rank approximation of a network's adjacency matrix, which can often be expressed as 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.<br />Comment: This article is part of EJAM's December 2016 special issue on "Network Analysis and Modelling" (available at https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/issue/journal-ejm-volume-27-issue-6/D245C89CABF55DBF573BB412F7651ADB)
Details
- Database :
- arXiv
- Journal :
- European Journal of Applied Mathematics, Volume 27, Issue 6 (Network Analysis and Modelling) December 2016, pp. 846-887
- Publication Type :
- Report
- Accession number :
- edsarx.1410.6572
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1017/S095679251600022X