Let G be a graph with V(G) = {1,⋯n} and E(G) = {e 1,⋯,e m }. Assign an orientation to each edge of G and let Q be the incidence matrix. The null space of Q is called the cycle subspace of G whereas the row space of Q is called the cut subspace of G. These definitions are justified as follows.
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References and Further Reading
N. Deo, Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall, Inc., New Jersey, 1974.
A. Recski, Matroid Theory and Its Applications in Electric Network Theory and in Statics, Algorithms and Combinatorics, 6. Springer-Verlag, Berlin, 1989.
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(2010). Cycles and Cuts. In: Graphs and Matrices. Universitext. Springer, London. https://doi.org/10.1007/978-1-84882-981-7_5
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