I have a graph whose vertices represent points in geometric space. The edges of this graph represent line segments between various points. Is it possible to assign a direction to an edge based on the coordinates of the points represented by the nodes? When I say direction I don't mean from A to B, I mean the edge A to B is 90deg or pi from horizontal.
This graph represents cutting paths on a CNC router. It will be used to determine the most efficient path that travels each edge at least once. However, there are some constraints that need to be observed. The tool path cannot stop or change direction at a node of degree 3 that has not been previously visited (these are areas where the wood can be scorched). So the angles of edges will be used to determine the next edge in the path.
Is there a name for this sort of thing? I realise that a graph is defined by a set of nodes or vertices, and a set of edges which are themselves defined by pairs of nodes, but is it possible to also apply information contained within the nodes to the edges? Is this something that would be applied within an algorithm, or an accepted way of doing things? Does it have a name?
As mentioned in the comments, the definition you want is a weighted directed graph.