Watts-Strogatz model

Generates a small-world random graph.

rgraph_ws(
  n,
  k,
  p,
  both.ends = FALSE,
  self = FALSE,
  multiple = FALSE,
  undirected = FALSE
)

Arguments

n	Integer scalar. Set the size of the graph.
k	Integer scalar. Set the initial degree of the ring (must be less than \(n\)).
p	Numeric scalar/vector of length \(T\). Set the probability of changing an edge.
both.ends	Logical scalar. When TRUE rewires both ends.
self	Logical scalar. When TRUE, allows loops (self edges).
multiple	Logical scalar. When TRUE allows multiple edges.
undirected	Logical scalar. Passed to ring_lattice

Value

A random graph of size \(n\times n\) following the small-world model. The resulting graph will have attr(graph, "undirected")=FALSE.

Details

Implemented as in Watts and Strogatz (1998). Starts from an undirected ring with \(n\) vertices all with degree \(k\) (so it must be an even number), and then rewire each edge by setting the endpoint (so now you treat it as a digraph) randomly any vertex in \(N \setminus {i}\) avoiding multiple links (by default) using the rewiring algorithm described on the paper.

References

Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of "small-world" networks. Nature, 393(6684), 440–2. http://dx.doi.org/10.1038/30918

Newman, M. E. J. (2003). The Structure and Function of Complex Networks. SIAM Review, 45(2), 167–256. http://doi.org/10.1137/S003614450342480

See also

Other simulation functions: permute_graph(), rdiffnet(), rewire_graph(), rgraph_ba(), rgraph_er(), ring_lattice()

Examples

library(igraph)
set.seed(7123)
x0 <- graph_from_adjacency_matrix(rgraph_ws(10,2, 0))
x1 <- graph_from_adjacency_matrix(rgraph_ws(10,2, .3))
x2 <- graph_from_adjacency_matrix(rgraph_ws(10,2, 1))

oldpar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(x0, layout=layout_in_circle, edge.curved=TRUE, main="Regular")
plot(x1, layout=layout_in_circle, edge.curved=TRUE, main="Small-world")
plot(x2, layout=layout_in_circle, edge.curved=TRUE, main="Random")
par(oldpar)