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authorKatolaZ <katolaz@freaknet.org>2017-09-27 15:06:31 +0100
committerKatolaZ <katolaz@freaknet.org>2017-09-27 15:06:31 +0100
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+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>`.