Cycle Basis
A cycle basis of a graph G is a basis for the vector space over the two-element finite field generated by the incidence vectors of the graph cycles of G. The number of cycles in any cycle basis is the circuit rank of G.
A cycle basis obtained from the fundamental cycles determined by a spanning forest is called a fundamental cycle basis. A fundamental cycle basis can be computed in the Wolfram Language using FindFundamentalCycles [g].
See also
Circuit Rank, Fundamental Cycle, Graph CycleExplore with Wolfram|Alpha
WolframAlpha
References
Gross, J. T. and Yellen, J. Graph Theory and Its Applications, 2nd ed. Boca Raton, FL: CRC Press, pp. 192 and 661, 2006.Cite this as:
Weisstein, Eric W. "Cycle Basis." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CycleBasis.html