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.
Read more about Cycle Space: The Binary Cycle Space, The Integral Cycle Space, The Cycle Space Over A Field or Commutative Ring
Other articles related to "cycles, space, cycle space":
... 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 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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