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diff --git a/doc/ws.md b/doc/ws.md new file mode 100644 index 0000000..242a6c9 --- /dev/null +++ b/doc/ws.md @@ -0,0 +1,85 @@ +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>`. |