`nwsmall`

Generate a small-world network

Syntax

nwsmall 
nodes
,
k(int) 
prob(float) 
[weights(p1, p2,...)
undirected
ntimes(int)
name(newnetname)
labs(lab1 lab2 ...)
xvars]
nwsmall 
nodes
,
k(int) 
shortcuts(integer) 
[weights(p1, p2,...)
undirected
ntimes(int)
name(newnetname)
labs(lab1 lab2 ...)
xvars]


`nodes`	number of nodes
`k(int)`	number of neighhbors on ring-lattice on each side
`prob(float)`	probability for a tie to rewire
`shortcuts(int)`	exact number of ties to rewire
`weights(p1, p2,...)`	probabilities p_k for tie weights k
`undirected`	generate an undirected network; default = directed
`ntimes(int)`	number of small-world networks to be generated; default = 1
`name`(newnetname)	name of the new network
`labs`(lab1 lab2 …)	overwrite node labels
`xvars`	generate Stata variables for the network
`noreplace`	reserved; currently a no-op - the create/replace collision guard on `name()` already applies regardless

Description

nwsmall generates a (un-)directed, (un-)weighted small-world network using the original Watts-Strogatz model (see Watts and Strogatz 1998). The algorithm starts with a ring-lattice where each node has k neighbors on each side. Next, the ties of the ring-lattice are rewired in one of two ways:

1) When option prob() is specified, each tie of the ring-lattice has a certain probability to get rewired. All non-existent ties are valid as rewirings (including the ones produced through previous rewirings).

2) When option shortcuts() is specified, an exact number of ties of the ring-lattice gets rewired. In this algorithm, only ties that had not been in the original ring-lattice are valid rewirings.

Either option prob() or shortcuts() needs to be specified.

With option weights(p1, p2,…) the command generates a weighted network. Here, p_k stands for the probability to sample tie weight k. The probabilities p1, p2…, pn do not necessarily have to sum up to one; they are standardized. For example, the following produces a small-world network with 20 nodes. Furthermore, each one of these sampled ties gets assigned a tie weight because of option weights(). In this case, weights(0.0, 0.3,0.7) indicates that tie weight 1 should be sampled with probability 0.0, tie weight 2 with probability 0.3 and tie weight 3 with probability 0.7.

cmd. nwsmall 20, k(2) prob(.2) weights(0.0, 0.3, 0.7)

Examples

In the first example, each tie on the ring-lattice has a probability to get rewired.

. nwclear
. nwsmall 20, k(2) prob(.2)
. nwplot, layout(circle)

In the second example, there are exactly three shortcuts.

. nwsmall 30, k(2) shortcuts(3) undirected
. nwplot, layout(circle)

Supported network types

Binary: yes (only structural tie placement - see Weighted). Directed: yes, via undirected (default is directed). Weighted: yes, via weights(), independent of the small-world rewiring mechanism itself. Signed: not checked. Two-mode: not applicable - this generator always produces a one-mode network.

Stored results

nwsmall stores the following in r():

Macros

r(netlist) list of new networks

References

Watts, D. J., Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440-442.

nwsmall