Incidence matrix

Set

 context $n_v,m_e\in \mathbb N$
 definiendum $M\in \mathrm{it}(n_v,m_e)$
 postulate $\mathrm{Matrix}(n_v,m_e,\{0,1,2\})$
 for all $i\in\mathrm{range}(n_v)$
 postulate $\sum_{j=1}^{m_e} M_{ij}=2$

Discussion

The index $i$ in $M_{ij}$ labels the vertices and the index $j$ labels the edges. The definition says that every edge has exactly two endpoints.

Every incidence matrix corresponds to (a representative of the isomorphism class of) a finite undirected graph.