Balanced matrix

In mathematics, a balanced matrix B is a matrix that does not contain any odd order 2-cycle submatricies.

The following matrix is an odd order 2-cycle submatrix:

$A={\begin{bmatrix}1&0&1\\1&1&0\\0&1&1\\\end{bmatrix}}.$

Balanced matricies are important in linear programs as they are naturally integer. Totally unimodular matricies are a subset of balanced matricies, and balanced matricies are a subset of perfect matricies.

References

• Berge, C. (1972), Balanced Matricies, Paris, France: Centre National de Recherche Scientifique