pm - Compute the leading eigenvalue and eigenvector of a graph
pm graph_in is_dir eps
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.
input graph (edge list) if equal to - (dash), read the edge list
from STDIN (standard input).
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
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.
(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.