fundCycles: Fundamental cycles

In ggm: Graphical Markov Models with Mixed Graphs

Description

Finds the list of fundamental cycles of a connected undirected graph.

Usage

fundCycles(amat)

Arguments

amat	a symmetric matrix with dimnames denoting the adjacency matrix of the undirected graph. The graph must be connected, otherwise the function returns an error message.

Details

All the cycles in an UG can be obtained from combination (ring sum) of the set of fundamental cycles.

Value

a list of matrices with two columns. Every component of the list is associated to a cycle. The cycle is described by a k \times 2 matrix whose rows are the edges of the cycle. If there is no cycle the function returns NULL.

Note

This function is used by cycleMatrix and isGident.

Author(s)

Giovanni M. Marchetti

References

Thulasiraman, K. \& Swamy, M.N.S. (1992). Graphs: theory and algorithms. New York: Wiley.

See Also

UG,findPath, cycleMatrix, isGident,bfsearch

Examples

## Three fundamental cycles
fundCycles(UG(~a*b*d + d*e + e*a*f))

Example output

Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union


Attaching package: 'ggm'

The following object is masked from 'package:igraph':

    pa

[[1]]
 [,1] [,2]
    2    1
    1    3
    3    2

[[2]]
 [,1] [,2]
    3    1
    1    4
    4    3

[[3]]
 [,1] [,2]
    4    1
    1    5
    5    4

ggm documentation built on March 26, 2020, 7:49 p.m.