Package org.openscience.cdk.graph
Class MinimumCycleBasis
java.lang.Object
org.openscience.cdk.graph.MinimumCycleBasis
Compute the minimum cycle basis (MCB) of a graph. A cycle basis is a set of
cycles that can be combined to generate all the cycles of a graph. The MCB is
the basis of minimum weight (length). As an example, there are three cycles
in naphthalene.
To generate the three cycles (cycle space) we actually only need two of the
three cycles. The third cycle can be generated by combining the other two.
Each combination of the two cycles is called a cycle basis. There is one
basis with the two rings of size six and two bases with either ring of size
six and the perimeter ring of size 10. The weights of each basis are 12
(6+6), 16 (6+10), 16 (6+10). The basis of the two six member rings has
minimum weight (12) and is thus the MCB of naphthalene.
The Smallest Set of Smallest Rings (SSSR) is normally used interchangeably
with MCB although traditionally their meaning was different [Berger, F. et. al.. J. Chem. Inf. Comput. Sci.. 2004. 44]. Although the MCB can be used to generate all other cycles of a
graph it may not be unique. A compound with a bridged ring system, such as
3quinuclidinol, has three equally valid minimum cycle bases. From
any two six member rings the third ring can be generated by ⊕sum
(xoring) their edges. As there may be more than one MCB it should not be used
as a unique descriptor. The smallest (but potentially exponential)
unique set of short cycles which generates the cycle space is the
union of all minimum cycle bases. This set is known as the
RelevantCycles
. The intersect of all minimum cycle bases (EssentialCycles
) is also unique. Although the number of EssentialCycles
is polynomial it can not always be used to generate the
cycle space. Author:
 John May
 See Also:
 Source code:
 main
 Belongs to CDK module:
 core
 Keywords:
 sssr, smallest set of smallest rings, mcb, minimum cycle basis, cycle, ring, ring perception

Constructor Summary
ConstructorDescriptionMinimumCycleBasis
(int[][] graph) Generate the minimum cycle basis for a graph. 
Method Summary

Constructor Details

MinimumCycleBasis
public MinimumCycleBasis(int[][] graph) Generate the minimum cycle basis for a graph. Parameters:
graph
 undirected adjacency list See Also:


Method Details

paths
public int[][] paths()The paths of all cycles in the minimum cycle basis. Returns:
 array of vertex paths

size
public int size()The number of the cycles in the minimum cycle basis. Returns:
 size of minimum cycle set
