# Help:Notation

This page collects some of the mathematical notation used on the website.

Notation Meaning
$x(Z)$ For $x \in {\mathbb R}^V$ and $Z \subseteq V$: sum of $x(v)$ over all $v \in Z$
$\chi^Z$ For $Z \subseteq V$: incidence vector of Z in ${\mathbb R}^V$
$d_G(Z)$ Number of edges in (hyper)graph G with at least one endpoint in Z and at least one endpoint outside of Z
$d_x(Z)$ For (hyper)graph G=(V,E) and $x \in {\mathbb R}^E$: sum of $x(e)$ on edges with at least one endpoint in Z and at least one endpoint outside of Z
$i_G(Z)$ Number of edges in (hyper)graph G induced by Z
$E[Z]$ For (hyper)graph G=(V,E): set of edges induced by Z
$N_G(Z)$ For (hyper)graph G=(V,E): set of nodes not in Z that are contained in a (hyper)edge intersecting Z
$\varrho_D(Z)$ or $d^{in}_D(Z)$ Number of arcs of directed (hyper)graph D with at least one head in Z and at least one tail outside of Z
$\delta_D(Z)$ or $d^{out}_D(Z)$ Number of arcs of directed (hyper)graph D with at least one tail in Z and at least one head outside of Z
$\varrho_x(Z)$ or $d^{in}_x(Z)$ For directed (hyper)graph G=(V,E) and $x \in {\mathbb R}^E$: sum of $x(e)$ on arcs with at least one head in Z and at least one tail outside of Z
$\delta_x(Z)$ or $d^{out}_x(Z)$ For directed (hyper)graph G=(V,E) and $x \in {\mathbb R}^E$: sum of $x(e)$ on arcs with at least one tail in Z and at least one head outside of Z