pm(1) -- Compute the leading eigenvalue and eigenvector of a graph

SYNOPSIS

pm <graph_in> <is_dir>

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.
: 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)

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