# Element-connectivity

From Egres Open

Let *G=(V,E)* be an undirected graph, and [math]T \subseteq V[/math] a set of nodes that will be called **terminal nodes**. The nodes not in *T* are called **Steiner nodes**. The **elements** of *G* are the edges and the Steiner nodes. The graph *G* is **k-element-connected** if there are *k* element-disjoint paths between any two terminal nodes.

By Menger's theorem, the maximum number of element-disjoint paths between two terminal nodes equals the minimum number of elements needed to separate the two nodes.

The notion of *k*-element-connectivity can also be defined for directed graphs the same way.