# Cycle Space

In graph theory, an area of mathematics, a cycle space is a vector space defined from an undirected graph; elements of the cycle space represent formal combinations of cycles in the graph. Cycle spaces allow one to use the tools of linear algebra to study graphs. A cycle basis is a set of cycles that generates the cycle space.

### Other articles related to "cycles, space, cycle space":

Cyclomatic Complexity - Description - Formal Definition
... of edges such subgraphs are unions of cycles and isolated vertices ... of a graph is closed under symmetric difference, and may thus be viewed as a vector space over GF(2) this vector space is called the cycle space of the graph ... number of the graph is defined as the dimension of this space ...
The Cycle Space Over A Field or Commutative Ring
... The construction of the integral cycle space can be carried out for any field, abelian group, or (most generally) commutative ring (with unity) R replacing the integers ... If R is a field, the cycle space is a vector space over R with dimension m - n + c, where c is the number of connected components of G ... If R is any commutative ring, the cycle space is a free R-module with rank m - n + c ...

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