sample_smallworld: The Watts-Strogatz small-world model

In igraph: Network Analysis and Visualization

The Watts-Strogatz small-world model

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 p, while avoiding the creation of multi-edges.

Usage

sample_smallworld(dim, size, nei, p, loops = FALSE, multiple = FALSE)

smallworld(...)

Arguments

dim	Integer constant, the dimension of the starting lattice.
size	Integer constant, the size of the lattice along each dimension.
nei	Integer constant, the neighborhood within which the vertices of the lattice will be connected.
p	Real constant between zero and one, the rewiring probability.
loops	Logical scalar, whether loops edges are allowed in the generated graph.
multiple	Logical scalar, whether multiple edges are allowed int the generated graph.
...	Passed to sample_smallworld().

Details

Note that this function might create graphs with loops and/or multiple edges. You can use simplify() to get rid of these.

This process differs from the original model of Watts and Strogatz (see reference) in that it rewires both endpoints of edges. Thus in the limit of 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 p=1. For appropriate choices of p, both models exhibit the property of simultaneously having short path lengths and high clustering.

Value

A graph object.

Author(s)

Gabor Csardi [e-mail]

References

Duncan J Watts and Steven H Strogatz: Collective dynamics of ‘small world’ networks, Nature 393, 440-442, 1998.

See Also

make_lattice(), rewire()

Random graph models (games) erdos.renyi.game(), sample_(), sample_bipartite(), sample_chung_lu(), sample_correlated_gnp(), sample_correlated_gnp_pair(), sample_degseq(), sample_dot_product(), sample_fitness(), sample_fitness_pl(), sample_forestfire(), sample_gnm(), sample_gnp(), sample_grg(), sample_growing(), sample_hierarchical_sbm(), sample_islands(), sample_k_regular(), sample_last_cit(), sample_pa(), sample_pa_age(), sample_pref(), sample_sbm(), sample_traits_callaway(), sample_tree()

Examples

g <- sample_smallworld(1, 100, 5, 0.05)
mean_distance(g)
transitivity(g, type = "average")

igraph documentation built on Oct. 20, 2024, 1:06 a.m.