Partitions of networks that are robust to vertex permutation dynamics

• Autorzy: Gary Froyland , Eric Kwok
• Języki publikacji: EN

Abstrakty

EN

Minimum disconnecting cuts of connected graphs provide fundamental information about the connectivity structure of the graph. Spectral methods are well-known as stable and efficient means of finding good solutions to the balanced minimum cut problem. In this paper we generalise the standard balanced bisection problem for static graphs to a new “dynamic balanced bisection problem”, in which the bisecting cut should be minimal when the vertex-labelled graph is subjected to a general sequence of vertex permutations. We extend the standard spectral method for partitioning static graphs, based on eigenvectors of the Laplacian matrix of the graph, by constructing a new dynamic Laplacian matrix, with eigenvectors that generate good solutions to the dynamic minimum cut problem. We formulate and prove a dynamic Cheeger inequality for graphs, and demonstrate the effectiveness of the dynamic Laplacian matrix for both structured and unstructured graphs.

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-09-23

zaakceptowano

2015-02-13

online

2015-02-25

Twórcy

autor

Gary Froyland

• School of Mathematics and Statistics, The University of New South Wales, Sydney NSW 2052, Australia

autor

Eric Kwok

• School of Mathematics and Statistics, The University of New South Wales, Sydney NSW 2052, Australia

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Identyfikatory

DOI

10.1515/spma-2015-0003