bnlearn (version 3.1)

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

...

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 orderingbased generation (ordered): generates graphs whose node ordering is given by the order of the labels in thenodesparameter. The same algorithm is used in therandomDAGfunction in packagepcalg.
• Ide's and Cozman'sGenerating Multi-connected DAGsalgorithm (ic-dag): generates graphs with a uniform probability distribution over the set of multiconnected graphs.
• Melancon's and Philippe'sUniform Random Acyclic Digraphsalgorithm (melancon): generates graphs with a uniform probability distribution over the set of all possible graphs.
• empty graphs(empty): generates graphs without any arc.

Additional parameters for the random.graph function are:

• prob: the probability of each arc to be present in a graph generated by theorderedalgorithm. The default value is2 / (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 theic-dagandmelanconalgorithms to converge to a stationary (and uniform) probability distribution. The default value is6 * length(nodes)^2.
• every: return only one grapheverynumber of steps instead of all the graphs generated withic-dagandmelancon. Since both algorithms are based on Markov Chain Monte Carlo approaches, high values ofeveryresult in a more diverse set of networks. The default value is1, i.e. to return all the networks that are generated.
• max.degree: the maximum degree for any node in a graph generated by theic-dagandmelanconalgorithms. The default value isInf.
• max.in.degree: the maximum in-degree for any node in a graph generated by theic-dagandmelanconalgorithms. The default value isInf.
• max.out.degree: the maximum out-degree for any node in a graph generated by theic-dagandmelanconalgorithms. The default value isInf.

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/Generated Bayesian network
#
#  model:
#    [A][B][C][D][E][F][G][H]
#  nodes:                                 8
#  arcs:                                  0
#    undirected arcs:                     0
#    directed arcs:                       0
#  average markov blanket size:           0.00
#  average neighbourhood size:            0.00
#  average branching factor:              0.00
#
#  generation algorithm:                  Empty
#
random.graph(LETTERS[1:8])
# <insert the description of a random graph here>
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))