`nwpref`

Generate a preferential-attachment network

Syntax

nwpref 
nodes
[,
m0(int) 
m(int) 
prob(float) 
weights(p1, p2,...)
undirected
name(newnetname)
xvars
ntimes(int)]


nodes	number of nodes
`m0(int)`	number of connected nodes at start; default = 2
`m(int)`	number of connections each new node forms; default = 2
`prob(float)`	probability that new node connects to existing nodes uniformly at random; default = 0
`weights(p1, p2,...)`	probabilities p_k for tie weights k
`undirected`	generate an undirected network; default = directed
`name`(newnetname)	name of the new network
`xvars`	generate Stata variables for the network
`ntimes(int)`	number of small-world networks to be generated; default = 1
`noreplace`	reserved; currently a no-op - the create/replace collision guard on `name()` already applies regardless

Description

nwpref generates a (un-)directed, (un-)weighted preferential-attachment network using the Barabasi-Albert (1999) model. The network begins with an initial connected network of m_0 nodes. One new node is added to the network at each time t. The preferential attachment process is stated as follows:

With a probability 0 <= prob <= 1, this new node connects to m <= m_0 nodes uniformly at random.

With a probability 1 - prob, this new node connects to m existing nodes with a probability proportional to their current (in-)degree.

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 assigns a tie weight to each tie 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. nwpref 20, prob(1) undirected weights(0.0, 0.3, 0.7)

Examples

. nwclear
. nwpref 20, undirected
. nwplot, layout(circle)

. nwpref 20, prob(1) undirected
. nwplot, layout(circle)

Supported network types

Binary: yes (only structural attachment - see Weighted). Directed: yes, via undirected (default is directed). Weighted: yes, via weights() - a Stata expression assigning each new tie’s value, independent of the preferential-attachment mechanism itself (which is always driven by degree, not tie value). Signed: not checked. Two-mode: not applicable - this generator always produces a one-mode network.

Stored results

nwpref stores the following in r():

Macros

r(netlist) list of new networks

References

Barabasi, A-L., Albert, R. (1999). Emergence of scaling in random networks. Science 286(54439), 509-512.

nwpref