1. pm(1)
  2. www.complex-networks.net
  3. pm(1)

NAME

pm - 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

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

AUTHORS

(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.

  1. www.complex-networks.net
  2. October 2020
  3. pm(1)