Add sage code

lib/edge_graph.py

@@ -0,0 +1,42 @@
+"""Utilities for constructing edge graphs from planar graphs."""
+from typing import Any, cast
+from sage.all import Graph
+
+
+def get_edge_graph_pos(edge_graph: Graph, pos_src: dict[Any, Any]) -> dict[Any, tuple[Any, Any]]:
+    """Return a position dict for edge graph vertices, using midpoints of the source positions."""
+    pos: dict[Any, tuple[Any, Any]] = {}
+    for e in cast(list[Any], edge_graph.vertices()):  # type: ignore
+        pos[e] = (
+            (pos_src[e[0]][0] + pos_src[e[1]][0]) / 2,
+            (pos_src[e[0]][1] + pos_src[e[1]][1]) / 2
+        )
+    return pos
+
+
+def get_edge_graph(graph: Graph, set_pos: bool = True) -> Graph:
+    """Return the edge graph of the given graph, optionally setting vertex positions."""
+    pos_src: dict[Any, Any] | None = None
+    pos: dict[Any, tuple[Any, Any]] = {}
+    if set_pos:
+        pos_src = cast(dict[Any, Any], graph.get_pos())  # type: ignore
+
+    g = Graph()
+    for e in cast(list[Any], graph.edges()):  # type: ignore
+        g.add_vertex(e)  # type: ignore
+        if pos_src:
+            pos[e] = (
+                (pos_src[e[0]][0] + pos_src[e[1]][0]) / 2,
+                (pos_src[e[0]][1] + pos_src[e[1]][1]) / 2
+            )
+
+    for v in cast(list[Any], graph.vertices()):  # type: ignore
+        incident_edges = cast(list[Any], graph.edges_incident(v))  # type: ignore
+        if len(incident_edges) == 1:
+            continue
+        for i, e1 in enumerate(incident_edges):
+            e2 = incident_edges[(i + 1) % len(incident_edges)]
+            g.add_edge(e1, e2)  # type: ignore
+    if set_pos:
+        g.set_pos(pos)  # type: ignore
+    return g