Random DAG Generation

Description

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.

Usage

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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 [0.1, 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.

Value

A graph object of class graphNEL.

Note

The output is not topologically sorted (as opposed to the output of randomDAG).

Author(s)

Markus Kalisch (kalisch@stat.math.ethz.ch) and Manuel Schuerch.

References

These methods are mainly based on the analogue functions in the igraph package.

See Also

the package igraph, notably help pages such as random.graph.game or barabasi.game;

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

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set.seed(37)
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)

## 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)
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

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