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diff --git a/doc/pm.md b/doc/pm.md new file mode 100644 index 0000000..3dea06b --- /dev/null +++ b/doc/pm.md @@ -0,0 +1,57 @@ +pm(1) -- Compute the leading eigenvalue and eigenvector of a graph +====== + +## SYNOPSIS + +`pm` <graph_in> <is_dir> <eps> + +## DESCRIPTION + +`pm` computes the leading eigenvalue and the corresponding eigenvector +of the matrix given as input, using the Power Method. In particular, +this implementation uses the Rayleigh iteration, which allows faster +convergence on undirected graphs. + +## PARAMETERS + +* <graph_in>: + input graph (edge list) if equal to `-` (dash), read the edge list + from STDIN (standard input). + +* <is_dir>: + set either to `0` (zero) for undirected graphs, or to `1` (one) + for directed graphs. + +* <eps>: + Required relative error on the approximation of the leading + eigenvalue. The program terminates when the relative change in the + approximation of the eigenvalue is smaller than `eps` + +## EXAMPLES + +The following command: + + $ pm er_1000_5000.net 0 0.0000001 + +computes the leading eigenvalue and the corresponding eigenvector of +the undirected graph stored in the file `er_1000_5000.txt`. We can +store the leading eigenvector in a file, e.g. by using the command: + + $ pm er_1000_5000.net 0 0.0000001 > er_1000_5000.net_eig + 11.0335794552533 + $ + +which will save the leading eigenvector in the file +`er_1000_5000.net_eig`, one component for each row, and shown on +output the leading eigenvalue of the graph. + +## REFERENCES + +* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, + Methods and Applications", Appendix 5, Cambridge University Press + (2017) + + +## AUTHORS + +(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`. |