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57 lines
1.6 KiB
57 lines
1.6 KiB
pm(1) -- Compute the leading eigenvalue and eigenvector of a graph
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======
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## SYNOPSIS
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`pm` <graph_in> <is_dir> <eps>
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## DESCRIPTION
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`pm` computes the leading eigenvalue and the corresponding eigenvector
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of the matrix given as input, using the Power Method. In particular,
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this implementation uses the Rayleigh iteration, which allows faster
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convergence on undirected graphs.
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## PARAMETERS
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* <graph_in>:
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input graph (edge list) if equal to `-` (dash), read the edge list
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from STDIN (standard input).
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* <is_dir>:
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set either to `0` (zero) for undirected graphs, or to `1` (one)
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for directed graphs.
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* <eps>:
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Required relative error on the approximation of the leading
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eigenvalue. The program terminates when the relative change in the
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approximation of the eigenvalue is smaller than `eps`
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## EXAMPLES
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The following command:
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$ pm er_1000_5000.net 0 0.0000001
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computes the leading eigenvalue and the corresponding eigenvector of
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the undirected graph stored in the file `er_1000_5000.txt`. We can
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store the leading eigenvector in a file, e.g. by using the command:
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$ pm er_1000_5000.net 0 0.0000001 > er_1000_5000.net_eig
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11.0335794552533
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$
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which will save the leading eigenvector in the file
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`er_1000_5000.net_eig`, one component for each row, and shown on
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output the leading eigenvalue of the graph.
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## REFERENCES
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* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Appendix 5, Cambridge University Press
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(2017)
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## AUTHORS
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(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`.
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