R: Fundamental cycles

cycleMatrix {ggm} | R Documentation

## Fundamental cycles

### Description

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

### Usage

    cycleMatrix(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. The matrix of fundamental cycles is a Boolean matrix having as rows the fundamental cycles and as columns the edges of the graph. If an entry is one then the edge associated to that column belongs to the cycle associated to the row.

### Value

a Boolean matrix of the fundamental cycles of the undirected graph. If there is no cycle the function returns `NULL`.

### Note

This function is used by `isGident`. The row sum of the matrix gives the length of the cycles.

### Author(s)

Giovanni M. Marchetti

### References

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

### See Also

`UG`, `findPath`, `fundCycles`, `isGident`, `bfsearch`

### Examples

    ## Three cycles
    cycleMatrix(UG(~a*b*d+d*e+e*a*f))
    ## No cycle
     cycleMatrix(UG(~a*b))
    ## two cycles: the first is even and the second is odd
    cm <- cycleMatrix(UG(~a*b+b*c+c*d+d*a+a*u*v))
    apply(cm, 1, sum)

[Package ggm version 2.3 Index]