Threshold diffusion

Simulates the diffusion of a behaviour through the network, where an actor adopts it when enough of its neighbours have already adopted it (Granovetter, 1978; Valente, 1996).

Usage

threshold_diffusion(
  A,
  seeds,
  threshold = 0.5,
  mode = c("proportion", "count"),
  steps = NULL
)

Arguments

A

A square matrix

seeds

The actors that have adopted at the beginning, by name or by position

threshold

The threshold of every actor, as a single value or a vector

mode

Whether the threshold is a proportion of the neighbours (default) or a count of them

steps

Maximum number of steps. If NULL, the process runs until nobody else adopts

Value

This function returns who has adopted at every step, the step in which every actor adopted, and the proportion of actors that adopted.

Details

At each step, the actors that have not adopted count how many of their neighbours did. They adopt when that number, or that proportion of their neighbours, reaches their threshold. The actors that adopt never go back, so the process stops when nobody else adopts.

References

Granovetter, M. (1978). Threshold models of collective behavior. American Journal of Sociology, 83(6), 1420–1443. doi:10.1086/226707

Valente, T. W. (1996). Social network thresholds in the diffusion of innovations. Social Networks, 18(1), 69–89. doi:10.1016/0378-8733(95)00256-1

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0,
  1, 0, 1, 0, 0, 0,
  1, 1, 0, 1, 0, 0,
  0, 0, 1, 0, 1, 1,
  0, 0, 0, 1, 0, 1,
  0, 0, 0, 1, 1, 0
), byrow = TRUE, ncol = 6)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)

threshold_diffusion(A, seeds = c("a", "b"), threshold = 0.5)
#> $history
#>       a    b     c     d     e     f
#> t0 TRUE TRUE FALSE FALSE FALSE FALSE
#> t1 TRUE TRUE  TRUE FALSE FALSE FALSE
#> 
#> $time
#>  a  b  c  d  e  f 
#>  0  0  1 NA NA NA 
#> 
#> $adopters
#> [1] 0.5
#>