Network Geometry and Number of Links

Network Geometry and Number of Links

A network is a set of nodes (locations) linked by links (arcs between locations) and a graph is the symbolic representation of a network. The following attributes are characterizing network geometry:

  • For a node to be linked to another node n/2 links are necessary for an even number of nodes and (n+1)/2 links for an odd number.
  • For all nodes to be linked, n-1 links are necessary.
  • For all nodes to be linked to every other nodes n(n-1)/2 links are necessary for a non-planar graph.
  • Given a number of nodes, it is possible to find the number of possible combinations: 2n(n-1)/2.
  • A graph with two dimensions is a planar graph (road networks).
  • A graph with three dimensions is a non-planar graph (air networks).