2.3 KiB
ws(1) -- Create a small-world graph using the Watts-Strogatz model
SYNOPSIS
ws 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
-
: Number of nodes in the final graph.
-
: 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>.