Small world network

Random network of Watts and Strogatz (1998), which has the short distances of a random network and the high transitivity of a regular one.

Usage

small_world(n, neighbours = 2, p = 0.05)

Arguments

n

The number of nodes

neighbours

The number of closest nodes on each side that every node is tied to in the ring

p

Probability of rewiring each tie

Value

This function returns a symmetric matrix.

Details

The network starts as a ring in which every node is tied to its neighbours closest nodes on each side. Then each tie is rewired with probability p: one of its ends is replaced by a node chosen at random, avoiding loops and repeated ties. With p = 0 the ring is left as it is, and with p = 1 every tie is rewired.

References

Watts, D. J. and Strogatz, S. H. (1998). Collective dynamics of 'small-world' networks. Nature, 393(6684), 440–442. doi:10.1038/30918

Author

Alejandro Espinosa-Rada

Examples

set.seed(18051889)
A <- small_world(20, neighbours = 2, p = 0.05)
gen_degree(A, digraph = FALSE)
#>  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 
#>  5  5  4  4  3  4  4  4  4  4  3  3  4  4  4  4  4  4  4  5