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ws(1) -- Create a small-world graph using the Watts-Strogatz model
======
## SYNOPSIS
`ws` <N> <m> _p_ [SHOW]
## DESCRIPTION
`ws` creates a small-world undirected graph with 'N' nodes using the
Watts-Strogatz small-world network model. The nodes are initially
placed around a circle and each node is connected to its 'm' closest
neighbours on either side. Then, each edge is rewired (independently)
with probability 'p'. The program prints on output the edge-list of
the resulting graph.
## PARAMETERS
* <N>:
Number of nodes in the final graph.
* <m>:
Number of neighbours on the circle graph to which a node is
connected on either side (i.e., each node will initially have
'2m' edges).
* _p_:
Edge rewiring probability.
* SHOW:
If the fourth (optional) parameter is equal to `SHOW`, the program
will print on STDERR the number of edges rewired while constructing
the graph.
## EXAMPLES
The command:
$ ws 100 3 0.1
0 95
0 2
0 3
1 2
1 24
1 4
2 3
....
99 0
99 56
99 2
$
creates a Watts-Strogatz small-world network with 'N=100' nodes and
'K=m*N=300' edges, where each edge is independently rewired with
probability 'p=0.1'. The output of `ws` is the edge-list of the
resulting graph. Notice that in this case the first edge od node `0`
has been rewired and connected to node `95`. In order to be useful,
such edge-list should be saved into a file. The following command:
$ ws 100 300 0.1 SHOW > ws_100_3_0.1.net
Rewired edges: 32
$
will save the resulting graph in the file `ws_100_3_0.1.net`. Notice
the usage of the symbol "\>" to redirect the output of the program to
a file. The line printed on output reports the number of rewired
edges, since `SHOW` was specified as a fourth parameter.
## SEE ALSO
er\_A(1), er\_B(1)
## REFERENCES
* D\. J. Watts and S. H. Strogatz. "Collective dynamics of
'small-world' networks". Nature 393 (1998), 440–442.
* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
Methods and Applications", Chapter 4, Cambridge University Press
(2017)
## AUTHORS
(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`.
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