Network Geometry and Number of Links
A network is a set of nodes (locations) linked by links (arcs between
places). The graph is the symbolic representation of a network. We can
define a few attributes 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.
- With the 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).