- ws(1)
- www.complex-networks.net
- ws(1)

`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.

`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.

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.

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 `<v.nicosia@qmul.ac.uk>`

.

- www.complex-networks.net
- September 2017
- ws(1)