# Simulation of undirected graph with block structure 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. ```r 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 `igraph` 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. Possible arguments are: "random", or "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"`. 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`. ## Returns A symmetric adjacency matrix encoding an unweighted, undirected graph with no self-loops, and with different densities in diagonal compared to off-diagonal blocks. ## Details Random graphs are simulated using the Erdos-Renyi algorithm. Scale-free graphs are simulated using a preferential attachment algorithm. ## Examples ```r # 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 ``` ## References \insertRef ourstabilityselectionfake \insertRef hugefake ## See Also Other simulation functions: `SimulateClustering()`, `SimulateComponents()`, `SimulateCorrelation()`, `SimulateGraphical()`, `SimulateRegression()`, `SimulateStructural()`

SimulateAdjacency function