Answer:

The Swiss mathematician Leonard Euler (1707 - 83) showed that the numbers of vertices (V), edges (E) and faces (F) of a polyhedron satisfy the formula,
V - E + F = 2

For example for a cube V = 8, E = 12 and F = 6, while for a triangular prism V = 6, E = 9 and F = 5

A similar formula applies to Networks,
N - A + R = 2. where N is the number of nodes, A the number of arcs, and R the number of regions into which a network divides the plane, including the region outside the network.