rdiffnet: Random diffnet network

Description

Simulates a diffusion network by creating a random dynamic network and adoption threshold levels.

Usage

rdiffnet_multiple(R, statistic, ..., ncpus = 1L, cl = NULL)
rdiffnet(
  n,
  t,
  seed.nodes = "random",
  seed.p.adopt = 0.05,
  seed.graph = "scale-free",
  rgraph.args = list(),
  rewire = TRUE,
  rewire.args = list(),
  threshold.dist = runif(n),
  exposure.args = list(),
  name = "A diffusion network",
  behavior = "Random contagion",
  stop.no.diff = TRUE
)

Value

A random diffnet class object.

rdiffnet_multiple returns either a vector or an array depending on what statistic is (see sapply and parSapply).

Arguments

R: Integer scalar. Number of simulations to be done.
statistic: A Function to be applied to each simulated diffusion network.
...: Further arguments to be passed to rdiffnet.
ncpus: Integer scalar. Number of processors to be used (see details).
cl: An object of class c("SOCKcluster", "cluster") (see details).
n: Integer scalar. Number of vertices.
t: Integer scalar. Time length.
seed.nodes: Either a character scalar or a vector. Type of seed nodes (see details).
seed.p.adopt: Numeric scalar. Proportion of early adopters.
seed.graph: Baseline graph used for the simulation (see details).
rgraph.args: List. Arguments to be passed to rgraph.
rewire: Logical scalar. When TRUE, network slices are generated by rewiring (see rewire_graph).
rewire.args: List. Arguments to be passed to rewire_graph.
threshold.dist: Either a function to be applied via sapply, a numeric scalar, or a vector/matrix with \(n\) elements. Sets the adoption threshold for each node.
exposure.args: List. Arguments to be passed to exposure.
name: Character scalar. Passed to as_diffnet.
behavior: Character scalar. Passed to as_diffnet.
stop.no.diff: Logical scalar. When TRUE, the function will return with error if there was no diffusion. Otherwise it throws a warning.

Author

George G. Vega Yon

Details

Instead of randomizing whether an individual adopts the innovation or not, this toy model randomizes threshold levels, seed adopters and network structure, so an individual adopts the innovation in time \(T\) iff his exposure is above or equal to his threshold. The simulation is done in the following steps:

Using seed.graph, a baseline graph is created.
Given the baseline graph, the set of initial adopters is defined using seed.nodes.
Afterwards, if rewire=TRUE \(t-1\) slices of the network are created by iteratively rewiring the baseline graph.
The threshold.dist function is applied to each node in the graph.
Simulation starts at \(t=2\) assigning adopters in each time period accordingly to each vertex's threshold and exposure.

When seed.nodes is a character scalar it can be "marginal", "central" or "random", So each of these values sets the initial adopters using the vertices with lowest degree, with highest degree or completely randomly. The number of early adoptes is set as seed.p.adopt * n. Please note that when marginal nodes are set as seed it may be the case that no diffusion process is attained as the chosen set of first adopters can be isolated. Any other case will be considered as an index (via [<- methods), hence the user can manually set the set of initial adopters, for example if the user sets seed.nodes=c(1, 4, 7) then nodes 1, 4 and 7 will be selected as initial adopters.

The argument seed.graph can be either a function that generates a graph (Any class of accepted graph format (see netdiffuseR-graphs)), a graph itself or a character scalar in which the user sets the algorithm used to generate the first network (network in t=1), this can be either "scale-free" (Barabasi-Albert model using the rgraph_ba function, the default), "bernoulli" (Erdos-Renyi model using the rgraph_er function), or "small-world" (Watts-Strogatz model using the rgraph_ws function). The list rgraph.args passes arguments to the chosen algorithm.

When rewire=TRUE, the networks that follow t=1 will be generated using the rewire_graph function as \(G(t) = R(G(t-1))\), where \(R\) is the rewiring algorithm.

If a function, the argument threshold.dist sets the threshold for each vertex in the graph. It is applied using sapply as follows


sapply(1:n, threshold.dist)

By default sets the threshold to be random for each node in the graph.

If seed.graph is provided, no random graph is generated and the simulation is applied using that graph instead.

rewire.args has the following default options:

`p`	`.1`
`undirected`	`getOption("diffnet.undirected", FALSE)`
`self`	`getOption("diffnet.self", FALSE)`

exposure.args has the following default options:

`outgoing`	`TRUE`
`valued`	`getOption("diffnet.valued", FALSE)`
`normalized`	`TRUE`

The function rdiffnet_multiple is a wrapper of rdiffnet wich allows simulating multiple diffusion networks with the same parameters and apply the same function to all of them. This function is designed to allow the user to perform larger simulation studies in which the distribution of a particular statistic is observed.

When cl is provided, then simulations are done via parSapply. If ncpus is greater than 1, then the function creates a cluster via makeCluster which is stopped (removed) once the process is complete.

Examples

Run this code

# Asimple example -----------------------------------------------------------
set.seed(123)
z <- rdiffnet(100,10)
z
summary(z)

# A more complex example: Adopt if at least one neighbor has adopted --------
y <- rdiffnet(100, 10, threshold.dist=function(x) 1,
    exposure.args=list(valued=FALSE, normalized=FALSE))

# Re thinking the Adoption of Tetracycline ----------------------------------
newMI <- rdiffnet(seed.graph = medInnovationsDiffNet$graph,
 threshold.dist = threshold(medInnovationsDiffNet), rewire=FALSE)


# Simulation study comparing the diffusion with diff sets of seed nodes -----

# Random seed nodes
set.seed(1)
ans0 <- rdiffnet_multiple(R=50, statistic=function(x) sum(!is.na(x$toa)),
    n = 100, t = 4, seed.nodes = "random", stop.no.diff=FALSE)

# Central seed nodes
set.seed(1)
ans1 <- rdiffnet_multiple(R=50, statistic=function(x) sum(!is.na(x$toa)),
    n = 100, t = 4, seed.nodes = "central", stop.no.diff=FALSE)

boxplot(cbind(Random = ans0, Central = ans1), main="Number of adopters")

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