add python script to generate morphisms json

data/morphisms.dot

@@ -1,3 +1,4 @@
+digraph {
 "G^{14,14,48}_{0}" -> "G^{14,14,24}_{1}"
 "G^{14,14,48}_{0}" -> "G^{14,14,16}_{1}"
 "G^{14,14,48}_{1}" -> "G^{14,14,24}_{0}"
@@ -302,3 +303,4 @@
 "G^{54,54,54}_{2}" -> "G^{18,54,54}_{0}"
 "G^{54,54,54}_{2}" -> "G^{18,54,54}_{8}"
 "G^{54,54,54}_{2}" -> "G^{18,54,54}_{2}"
+}

scripts/morphisms/connected_components.py

@@ -0,0 +1,41 @@
+import networkx
+import json
+import os
+
+DATA_DIR = os.path.join("..", "..", "data")
+
+MORPHISMS_FILE = os.path.join(DATA_DIR, "morphisms.dot")
+MORPHISMS_JSON = os.path.join(DATA_DIR, "triangle_groups_morphisms.json")
+
+def level(G, node):
+    parents = list(G.predecessors(node))
+    if len(parents) == 0:
+        return 0
+    else:
+        return 1 + max([level(G, n) for n in parents])
+
+def nodes_from_component(G, cc, graph_json):
+    subG = networkx.induced_subgraph(G, cc)
+    assert networkx.is_weakly_connected(subG)
+
+    root = [n for n,d in subG.in_degree() if d==0][0]
+
+    for node in graph_json["nodes"]:
+        if node["id"] in subG:
+            print(node)
+            n = node["id"]
+            node["level"] = level(G, n)
+            node["component_id"] = root
+
+    return graph_json
+
+G = networkx.nx_pydot.read_dot(MORPHISMS_FILE)
+G_json = networkx.node_link_data(G)
+G_components = networkx.weakly_connected_components(G)
+
+for cc in G_components:
+    nodes_from_component(G, cc, G_json)
+
+with open(MORPHISMS_JSON, "w") as file:
+    print("writing to ", MORPHISMS_JSON, "\n")
+    json.dump(G_json, file, indent=4)