I have one question regarding the connectivity of polygons.
Given a set of N polygons, each with V number of vertices, as shown here what is the max. number of connections that it is possible to make between all the vertices of all polygons? I assume some lines do not have to be considered twice. Some vertices will not have visibility to other vertices and should not be considered, but at this stage I would also include them and assume that they are connected.
Thanks.
There are $NV$ vertices. Assuming that we are not considering connecting two vertices of the same polygon, each vertex can connect with $(N-1)V$ other vertices. So there are $NV\cdot(N-1)V=N(N-1)V^2$ directed edges (i.e. arrows) from one vertex to another, or $\frac12 N(N-1)V^2$ bidirectional connections.