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NetworksAn Introduction$
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Mark Newman

Print publication date: 2010

Print ISBN-13: 9780199206650

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199206650.001.0001

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Matrix algorithms and graph partitioning

Matrix algorithms and graph partitioning

A discussion of network algorithms that use matrix and linear algebra methods, including algorithms for partitioning network nodes into groups

(p.345) Chapter 11 Matrix algorithms and graph partitioning

M. E. J. Newman

Oxford University Press

The preceding chapter discussed a variety of computer algorithms for calculating quantities of interest on networks, including degrees, centralities, shortest paths, and connectivity. This chapter continues the study of network algorithms with algorithms based on matrix calculations and methods of linear algebra applied to the adjacency matrix or other network matrices such as the graph Laplacian. It begins with a simple example — the calculation of eigenvector centrality — which involves finding the leading eigenvector of the adjacency matrix, and then moves on to some more advanced examples, including Fiedler's spectral partitioning method and algorithms for network community detection. Exercises are provided at the end of the chapter.

Keywords:   network algorithms, network calculations, matrix calculations, linear algebra

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