ws - Create a small-world graph using the Watts-Strogatz model
ws N m p [SHOW]
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.
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).
Edge rewiring probability.
If the fourth (optional) parameter is equal to
SHOW, the program
will print on STDERR the number of edges rewired while constructing
$ 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
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
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
SHOW was specified as a fourth parameter.
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)
(c) Vincenzo 'KatolaZ' Nicosia 2009-2017