bnlearn (version 4.1)

graph generation utilities: Generate empty or random graphs

Description

Generate empty or random directed acyclic graphs from a given set of nodes.

Usage

empty.graph(nodes, num = 1)
random.graph(nodes, num = 1, method = "ordered", ..., debug = FALSE)

Arguments

nodes

a vector of character strings, the labels of the nodes.

num

an integer, the number of graphs to be generated.

method

a character string, the label of a score. Possible values are ordered (full ordering based generation), ic-dag (Ide's and Cozman's Generating Multi-connected DAGs algorithm), melancon (Melancon's and Philippe's Uniform Random Acyclic Digraphs algorithm) and empty (generates empty graphs).

…

additional tuning parameters (see below).

debug

a boolean value. If TRUE a lot of debugging output is printed; otherwise the function is completely silent. Ignored in some generation methods.

Value

Both empty.graph and random.graph return an object of class bn (if num is equal to 1) or a list of objects of class bn (otherwise). If every is greated than 1, random.graph always returns a list, regardless of the number of graphs it contains.

Details

Available graph generation algorithms are:

• full ordering based generation (ordered): generates graphs whose node ordering is given by the order of the labels in the nodes argument. The same algorithm is used in the randomDAG function in package pcalg.
• Ide's and Cozman's Generating Multi-connected DAGs algorithm (ic-dag): generates graphs with a uniform probability distribution over the set of multiconnected graphs.
• Melancon's and Philippe's Uniform Random Acyclic Digraphs algorithm (melancon): generates graphs with a uniform probability distribution over the set of all possible graphs.
• empty graphs (empty): generates graphs without any arc.

Additional arguments for the random.graph function are:

• prob: the probability of each arc to be present in a graph generated by the ordered algorithm. The default value is 2 / (length(nodes) - 1), which results in a sparse graph (the number of arcs should be of the same order as the number of nodes).
• burn.in: the number of iterations for the ic-dag and melancon algorithms to converge to a stationary (and uniform) probability distribution. The default value is 6 * length(nodes)^2.
• every: return only one graph every number of steps instead of all the graphs generated with ic-dag and melancon. Since both algorithms are based on Markov Chain Monte Carlo approaches, high values of every result in a more diverse set of networks. The default value is 1, i.e. to return all the networks that are generated.
• max.degree: the maximum degree for any node in a graph generated by the ic-dag and melancon algorithms. The default value is Inf.
• max.in.degree: the maximum in-degree for any node in a graph generated by the ic-dag and melancon algorithms. The default value is Inf.
• max.out.degree: the maximum out-degree for any node in a graph generated by the ic-dag and melancon algorithms. The default value is Inf.

References

Ide JS, Cozman FG (2002). "Random Generation of Bayesian Networks". In "SBIA '02: Proceedings of the 16th Brazilian Symposium on Artificial Intelligence", pp. 366-375. Springer-Verlag. Melancon G, Dutour I, Bousquet-Melou M (2001). "Random Generation of Directed Acyclic Graphs". Electronic Notes in Discrete Mathematics, 10, 202-207. Melancon G, Philippe F (2004). "Generating Connected Acyclic Digraphs Uniformly at Random". Information Processing Letters, 90(4), 209-213.

Examples

empty.graph(LETTERS[1:8])
random.graph(LETTERS[1:8])
plot(random.graph(LETTERS[1:8], method = "ic-dag", max.in.degree = 2))
plot(random.graph(LETTERS[1:8]))
plot(random.graph(LETTERS[1:8], prob = 0.2))