# Random DAG Generation Generating random directed acyclic graphs (DAGs) with fixed expected number of neighbours. Several different methods are provided, each intentionally biased towards certain properties. The methods are based on the analogue `*.game` functions in the `igraph` package. ```r randDAG(n, d, method ="er", par1=NULL, par2=NULL, DAG = TRUE, weighted = TRUE, wFUN = list(runif, min=0.1, max=1)) ``` ## Arguments - `n`: integer, at least `2`, indicating the number of nodes in the DAG. - `d`: a positive number, corresponding to the expected number of neighbours per node, more precisely the expected sum of the in- and out-degree. - `method`: a string, specifying the method used for generating the random graph. See details below. - `par1, par2`: optional additional arguments, dependent on the method. See details. - `DAG`: logical, if `TRUE`, labelled graph is directed to a labelled acyclic graph. - `weighted`: logical indicating if edge weights are computed according to `wFUN`. - `wFUN`: a `function` for computing the edge weights in the DAG. It takes as first argument a number of edges `m` for which it returns a vector of length `m` containing the weights. Alternatively, `wFUN` can be a `list` consisting of the function in the first entry and of further arguments of the function in the additional entries. The default (only if `weighted` is true) is a uniform weight in c("$[0.1,\n$", "$ 1]$"). See the examples for more. ## Details A (weighted) random graph with `n` nodes and expected number of neighbours `d` is constructed. For `DAG=TRUE`, the graph is oriented to a DAG. There are eight different random graph models provided, each selectable by the parameters `method`, `par1` and `par2`, with `method`, a string, taking one of the following values: - **`regular`:**: Graph where every node has exactly `d` incident edges. `par1` and `par2` are not used. - **`watts`:**: Watts-Strogatz graph that interpolates between the regular (`par1->0`) and Erdoes-Renyi graph (`par1->1`). The parameter `par1` is per default `0.5` and has to be in `(0,1)`. `par2` is not used. - **`er`:**: Erdoes-Renyi graph where every edge is present independently. `par1` and `par2` are not used. - **`power`:**: A graph with power-law degree distribution with expectation `d`.`par1` and `par2` are not used. - **`bipartite`:**: Bipartite graph with at least `par1*n` nodes in group 1 and at most `(1-par1)*n` nodes in group 2. The argument `par1` has to be in `[0,1]` and is per default `0.5`. `par2` is not used. - **`barabasi`:**: A graph with power-law degree distribution and preferential attachement according to parameter `par1`. It must hold that `par1 >= 1` and the default is `par1=1`. `par2` is not used. - **`geometric`:**: A geometric random graph in dimension `par1`, where `par1` can take values from `{2,3,4,5}` and is per default `2`. If `par2="geo"` and `weighted=TRUE`, then the weights are computed according to the Euclidean distance. There are currently no other option for `par2` implemented. - **`interEr`:**: A graph with `par1` islands of Erdoes-Renyi graphs, every pair of those connected by a certain number of edges proportional to `par2` (fraction of inter-connectivity). It is required that $n/s$ be integer and `par2` in $(0,1)$. Defaults are `par1=2` and `par2=0.25`, respectively. ## Returns A graph object of class `graphNEL`. ## References These methods are mainly based on the analogue functions in the `igraph` package. ## Author(s) Markus Kalisch (kalisch@stat.math.ethz.ch ) and Manuel Schuerch. ## Note The output is **not** topologically sorted (as opposed to the output of `randomDAG`). ## See Also the package `igraph`, notably help pages such as `sample_k_regular` or `sample_smallworld`; `unifDAG` from package `unifDAG` for generating uniform random DAGs. `randomDAG` a limited and soon deprecated version of `randDAG`; `rmvDAG` for generating multivariate data according to a DAG. ## Examples ```r set.seed(38) dag1 <- randDAG(10, 4, "regular") dag2 <- randDAG(10, 4, "watts") dag3 <- randDAG(10, 4, "er") dag4 <- randDAG(10, 4, "power") dag5 <- randDAG(10, 4, "bipartite") dag6 <- randDAG(10, 4, "barabasi") dag7 <- randDAG(10, 4, "geometric") dag8 <- randDAG(10, 4, "interEr", par2 = 0.5) if (require(Rgraphviz)) { par(mfrow=c(4,2)) plot(dag1,main="Regular graph") plot(dag2,main="Watts-Strogatz graph") plot(dag3,main="Erdoes-Renyi graph") plot(dag4,main="Power-law graph") plot(dag5,main="Bipartite graph") plot(dag6,main="Barabasi graph") plot(dag7,main="Geometric random graph") plot(dag8,main="Interconnected island graph") } set.seed(45) dag0 <- randDAG(6,3) dag1 <- randDAG(6,3, weighted=FALSE) dag2 <- randDAG(6,3, DAG=FALSE) if (require(Rgraphviz)) { par(mfrow=c(1,2)) plot(dag1) plot(dag2) ## undirected graph } dag0@edgeData ## note the uniform weights between 0.1 and 1 dag1@edgeData ## note the constant weights wFUN <- function(m,lB,uB) { runif(m,lB,uB) } dag <- randDAG(6,3,wFUN=list(wFUN,1,4)) dag@edgeData ## note the uniform weights between 1 and 4 ```

randDAG function