graph-is: Check properties of graphs.

Description

Check if a graph is 1) a directed acyclic graph (DAG), 2) a directed graph (DG), 3) an undirected graph (UG), 4) a triangulated (chordal) undirected graph (TUG).

Usage

is_dag(object)
is_dagMAT(object)
is_ug(object)
is_ugMAT(object)
is_tug(object)
is_tugMAT(object)
is_dg(object)
is_dgMAT(object)
is_adjMAT(object)
is.adjMAT(object)

Arguments

object

A graph represented as a `graphNEL` (graph package), an `igraph` (igraph package), an adjacency matrix or a sparse adjacency matrix (a `dgCMatrix` from the Matrix package).

Synonymous functions

The functions

* `is.TUG`/`is.DAG`/`is.DG`/`is.UG`/`is.adjMAT`

are synonymous with

* `is_tug`/`is_dag`/`is_dg`/`is_ug`/`is_adjMAT`.

The `is.X` group of functions will be deprecated.

Details

* A non-zero value at entry (i,j) in an adjacency matrix A for a graph means that there is an edge from i to j. If also (j,i) is non-zero there is also an edge from j to i. In this case we may think of a bidirected edge between i and j or we may think of the edge as being undirected. We do not distinguish between undirected and bidirected edges in the gRbase package. On the other hand, graphNEL objects from the graph package makes such a distinction (the function edgemode() will tell if edges are "directed" or "undirected" in a graphNEL object).

* The function is_ug() checks if the adjacency matrix is symmetric (If applied to a graphNEL, the adjacency matrix is created and checked for symmetry.)

* The function is_tug() checks if the graph is undirected and triangulated (also called chordal) by checking if the adjacency matrix is symmetric and the vertices can be given a perfect ordering using maximum cardinality seach.

* The function is_dg() checks if a graph is directed, i.e., that there are no undirected edges. This is done by computing the elementwise product of A and the transpose of A; if there are no non--zero entries in this product then the graph is directed.

* The function is_dag() will return TRUE if all edges are directed and if there are no cycles in the graph. (This is checked by checking if the vertices in the graph can be given a topological ordering which is based on identifying an undirected edge with a bidrected edge).

* There is a special case, namely if the graph has no edges at all (such that the adjacency matrix consists only of zeros). Such a graph is both undirected, triangulated, directed and directed acyclic.

Examples

Run this code

# NOT RUN {
## DAGs
dagNEL  <- dag(~ a:b:c + c:d:e, result="graphNEL")

## Undirected graphs
ugNEL  <- ug(~a:b:c + c:d:e, result="graphNEL")

## Is graph a DAG?
is_dag(dagNEL)
is_dag(ugNEL)

## Is graph an undirected graph
is_ug(dagNEL)
is_ug(ugNEL)
 
## Is graph a triangulated (i.e. chordal) undirected graph
is_tug(dagNEL)
is_tug(ugNEL)

## Example where the graph is not triangulated
ug2NEL  <- ug(~ a:b + b:c + c:d + d:a, result="graphNEL")
is_tug(ug2NEL)

## Bidirected graphs
graph::edgemode(ugNEL)
graph::edgemode(ugNEL) <- "directed"
graph::edgemode(ugNEL)
is_dag(ugNEL)
is_ug(ugNEL)

# }