Network

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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.

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