Let \(A \in \mathbb {Q}^{X \times Y}\) be a matrix. If for all \(j \in Y\), one has that \(a_{i,j} = 0\) for all \(i \in X\), or that there exists \(i_1,i_2 \in X\) such that

then we call \(A\) a node-incidence matrix for a (directed) graph whose nodes are indexed by \(X\) and whose edges are indexed by \(Y\).

We say that a matroid is graphic if it can be represented by a node-incidence matrix.

Let \(S\) be a standard representation given by matrix \(B\). The dual of \(S\) is given by \(-B^\intercal \).

We say a matroid is co-graphic if its dual is graphic.

The matroid with standard representation

over \(\mathbb {Z}_2\) is called \(R_{10}.\)