incidence_matrix

Incidence matrix

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

$\sum_{j=1}^{m_e} M_{ij}=2$

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.