rgraph_ws function

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

Returns

A random graph of size $n*n$ 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 $N \ {i}$

avoiding multiple links (by default) using the rewiring algorithm described on the paper.

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)

References

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

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

See Also

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

Author(s)

George G. Vega Yon