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Research Article

Characterizing Graph Drawing with Eigenvectors^‡

Tomaž Pisanski*

IMFM, Department of Theoretical Computer Science, University of Ljubljana, Ljubljana, Slovenia

John Shawe-Taylor^†

Department of Computer Science, Royal Holloway, University of London, Egham, England

J. Chem. Inf. Comput. Sci., 2000, 40 (3), pp 567–571

DOI: 10.1021/ci9900938

Publication Date (Web): February 18, 2000

‡

Some of the results contained in this paper were presented at the DIMACS International Workshop, GD'94.³

Corresponding author. E-mail: tomaz.pisanski@fmf.uni-lj.si. Supported in part by Ministrstvo za znanost in tehnologijo, Republike Slovenije, Project Nos. J2-6193-0101 and J1-6161-0101.

†

E-mail: jst@dcs.rhbnc.ac.uk. Supported in part by a COST fellowship from the European Union, 1993, and the British Council Exchange Programme ALIS No. 27.

Abstract

Two definitions of the problem of graph drawing are considered, and an analytical solution is provided for each of them. The solutions obtained make use of the eigenvectors of the Laplacian matrix of a related structure. The procedures give good results for symmetrical graphs, and they have already been used for drawing fullerene molecules in the literature. The analysis characterizes precisely what problems the two procedures are solving. It also illuminates why they can perform unsatisfactorily on asymmetrical graphs.

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