R: Fundamental cycles

fundCycles {ggm} | R Documentation

## Fundamental cycles

### 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))

[Package ggm version 2.3 Index]