# Network

A collection of nodes, V, sometimes called vertices, plus a collection of arcs, A, which are directed from one node to another. The two sets form a network, denoted $LaTeX: N=[V,A].$ As such, it can be considered a directed graph (see other terms, like special graphs).

• Here are associated functions and data values:
• tail of k-th arc $LaTeX: (i, j)$ is node $LaTeX: i;$ we sometimes write $LaTeX: T(k).$
• head of k-th arc $LaTeX: (i, j)$ is node $LaTeX: j;$ we sometimes write $LaTeX: H(k).$
• in-degree of node $LaTeX: i$ is $LaTeX: \textstyle |\left\{k: H(k)=i\right\}|.$
• out-degree of node $LaTeX: i$ is $LaTeX: \textstyle |\left\{k: T(k)=i\right\}|.$
• arc capacity limits the total flow across the arc at any one time.
• node capacity limits the total flow through a node at any one time.
• supply or demand at a node provides external input or an output requirement.