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