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.
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.
References
Duncan J Watts and Steven H Strogatz: Collective dynamics of ‘small world’ networks, Nature 393, 440-442, 1998.
See also
Random graph models (games)
bipartite_gnm(),
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()
Author
Gabor Csardi csardi.gabor@gmail.com
Examples
g <- sample_smallworld(1, 100, 5, 0.05)
mean_distance(g)
#> [1] 2.774949
transitivity(g, type = "average")
#> [1] 0.5295533