arc_face_graph

arc_face_graph(k: PlanarDiagram)

Generate an arc-face graph for a given planar diagram.

An arc-face graph is a graph where the nodes represent arcs in the planar diagram, and two arcs are adjacent if they lie on the same face in the planar diagram.

Args:

k (PlanarDiagram): The planar diagram object containing arcs and faces, where arcs define

the edges and faces represent connected regions of the planar diagram.

Returns:

dict: A dictionary where keys are arcs from the planar diagram, and values are sets of arcs that share a face with the key arc.