SimulateAdjacency {fake}

Simulation of undirected graph with block structure

Description

Simulates the adjacency matrix of an unweighted, undirected graph with no self-loops. If topology="random", different densities in diagonal (nu_within) compared to off-diagonal (nu_between) blocks can be used.

Usage

SimulateAdjacency(
  pk = 10,
  implementation = HugeAdjacency,
  topology = "random",
  nu_within = 0.1,
  nu_between = 0,
  nu_mat = NULL,
  ...
)

Arguments

pk

vector of the number of variables per group in the simulated dataset. The number of nodes in the simulated graph is sum(pk). With multiple groups, the simulated (partial) correlation matrix has a block structure, where blocks arise from the integration of the length(pk) groups. This argument is only used if theta is not provided.

implementation

function for simulation of the graph. By default, algorithms implemented in huge.generator are used. Alternatively, a user-defined function can be used. It must take pk, topology and nu as arguments and return a (sum(pk)*(sum(pk))) binary and symmetric matrix for which diagonal entries are all equal to zero. This function is only applied if theta is not provided.

topology

topology of the simulated graph. If using implementation=HugeAdjacency, possible values are listed for the argument graph of huge.generator. These are: "random", "hub", "cluster", "band" and "scale-free".

nu_within

probability of having an edge between two nodes belonging to the same group, as defined in pk. If length(pk)=1, this is the expected density of the graph. If implementation=HugeAdjacency, this argument is only used for topology="random" or topology="cluster" (see argument prob in huge.generator). Only used if nu_mat is not provided.

nu_between

probability of having an edge between two nodes belonging to different groups, as defined in pk. By default, the same density is used for within and between blocks (nu_within=nu_between). Only used if length(pk)>1. Only used if nu_mat is not provided.

nu_mat

matrix of probabilities of having an edge between nodes belonging to a given pair of node groups defined in pk.

...

additional arguments passed to the graph simulation function provided in implementation.

Details

Random graphs are simulated using the Erdos-Renyi algorithm. Scale-free graphs are simulated using a preferential attachment algorithm. More details are provided in huge.generator.

Value

A symmetric adjacency matrix encoding an unweighted, undirected graph with no self-loops, and with different densities in diagonal compared to off-diagonal blocks.

References

Bodinier B, Filippi S, Nost TH, Chiquet J, Chadeau-Hyam M (2021). “Automated calibration for stability selection in penalised regression and graphical models: a multi-OMICs network application exploring the molecular response to tobacco smoking.” https://arxiv.org/abs/2106.02521.

Jiang H, Fei X, Liu H, Roeder K, Lafferty J, Wasserman L, Li X, Zhao T (2021). huge: High-Dimensional Undirected Graph Estimation. R package version 1.3.5, https://CRAN.R-project.org/package=huge.

See Also

Other simulation functions: SimulateClustering(), SimulateComponents(), SimulateCorrelation(), SimulateGraphical(), SimulateRegression(), SimulateStructural()

Examples

# Simulation of a scale-free graph with 20 nodes
adjacency <- SimulateAdjacency(pk = 20, topology = "scale-free")
plot(adjacency)

# Simulation of a random graph with three connected components
adjacency <- SimulateAdjacency(
  pk = rep(10, 3),
  nu_within = 0.7, nu_between = 0
)
plot(adjacency)

# Simulation of a random graph with block structure
adjacency <- SimulateAdjacency(
  pk = rep(10, 3),
  nu_within = 0.7, nu_between = 0.03
)
plot(adjacency)

# User-defined function for graph simulation
CentralNode <- function(pk, hub = 1) {
  theta <- matrix(0, nrow = sum(pk), ncol = sum(pk))
  theta[hub, ] <- 1
  theta[, hub] <- 1
  diag(theta) <- 0
  return(theta)
}
simul <- SimulateAdjacency(pk = 10, implementation = CentralNode)
plot(simul) # star
simul <- SimulateAdjacency(pk = 10, implementation = CentralNode, hub = 2)
plot(simul) # variable 2 is the central node