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networks

  

fundcyc

  

finds the cycle in a unicyclic undirected graph

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

fundcyc(eset, G)

Parameters

G

-

graph or network

e

-

set of edges of G

Description

• 

Important: The networks package has been deprecated.  Use the superseding command GraphTheory[CycleBasis] instead.

• 

Given a subset e of edges forming a unicyclic subgraph of a graph G, the edges forming the unique cycle are returned as a set.  It is assumed that only one cycle is present.

• 

If no cycle exists then the empty set is returned.

• 

When a spanning tree is known, fundcyc allows one to extract the fundamental cycles of a cycle basis by adding one edge at a time to the tree.

• 

This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[fundcyc](...).

Examples

Important: The networks package has been deprecated.  Use the superseding command GraphTheory[CycleBasis] instead.

withnetworks:

Gcomplete4:

sptreeedgesspantreeG

sptreee1,e3,e6

(1)

eop1,edgesGminussptree

ee2

(2)

fundcycsptreeunione,G

e2,e3,e6

(3)

See Also

GraphTheory

GraphTheory[CycleBasis]

networks(deprecated)[components]

networks(deprecated)[cyclebase]

networks(deprecated)[span]

with