1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
|
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/games.R
\name{sample_smallworld}
\alias{sample_smallworld}
\alias{smallworld}
\title{The Watts-Strogatz small-world model}
\usage{
sample_smallworld(dim, size, nei, p, loops = FALSE, multiple = FALSE)
smallworld(...)
}
\arguments{
\item{dim}{Integer constant, the dimension of the starting lattice.}
\item{size}{Integer constant, the size of the lattice along each dimension.}
\item{nei}{Integer constant, the neighborhood within which the vertices of
the lattice will be connected.}
\item{p}{Real constant between zero and one, the rewiring probability.}
\item{loops}{Logical scalar, whether loops edges are allowed in the
generated graph.}
\item{multiple}{Logical scalar, whether multiple edges are allowed int the
generated graph.}
\item{...}{Passed to \code{sample_smallworld()}.}
}
\value{
A graph object.
}
\description{
This function generates networks with the small-world property
based on a variant of the Watts-Strogatz model. The network is obtained
by first creating a periodic undirected lattice, then rewiring both
endpoints of each edge with probability \code{p}, while avoiding the
creation of multi-edges.
}
\details{
Note that this function might create graphs with loops and/or multiple
edges. You can use \code{\link[=simplify]{simplify()}} to get rid of these.
This process differs from the original model of Watts and Strogatz
(see reference) in that it rewires \strong{both} endpoints of edges. Thus in
the limit of \code{p=1}, we obtain a G(n,m) random graph with the
same number of vertices and edges as the original lattice. In comparison,
the original Watts-Strogatz model only rewires a single endpoint of each edge,
thus the network does not become fully random even for \code{p=1}.
For appropriate choices of \code{p}, both models exhibit the property of
simultaneously having short path lengths and high clustering.
}
\examples{
g <- sample_smallworld(1, 100, 5, 0.05)
mean_distance(g)
transitivity(g, type = "average")
}
\references{
Duncan J Watts and Steven H Strogatz: Collective dynamics of
\sQuote{small world} networks, Nature 393, 440-442, 1998.
}
\seealso{
\code{\link[=make_lattice]{make_lattice()}}, \code{\link[=rewire]{rewire()}}
Random graph models (games)
\code{\link{erdos.renyi.game}()},
\code{\link{sample_}()},
\code{\link{sample_bipartite}()},
\code{\link{sample_chung_lu}()},
\code{\link{sample_correlated_gnp}()},
\code{\link{sample_correlated_gnp_pair}()},
\code{\link{sample_degseq}()},
\code{\link{sample_dot_product}()},
\code{\link{sample_fitness}()},
\code{\link{sample_fitness_pl}()},
\code{\link{sample_forestfire}()},
\code{\link{sample_gnm}()},
\code{\link{sample_gnp}()},
\code{\link{sample_grg}()},
\code{\link{sample_growing}()},
\code{\link{sample_hierarchical_sbm}()},
\code{\link{sample_islands}()},
\code{\link{sample_k_regular}()},
\code{\link{sample_last_cit}()},
\code{\link{sample_pa}()},
\code{\link{sample_pa_age}()},
\code{\link{sample_pref}()},
\code{\link{sample_sbm}()},
\code{\link{sample_traits_callaway}()},
\code{\link{sample_tree}()}
}
\author{
Gabor Csardi \email{csardi.gabor@gmail.com}
}
\concept{games}
\keyword{graphs}
|
