.

allgraphs.py

@@ -14,7 +14,15 @@ class Graph:
         g.edges = set(edges)
 
     def __str__(g):
-        return "Graph nodes=%s  edges=%s" % (g.nodes, g.edges)
+        nv = ['%s' % _ for _ in g.nodes]
+        ev = [setstr(_) for _ in g.edges]
+        return "Graph nodes={%s}  edges={%s}" % (','.join(nv), ', '.join(ev))
+
+
+def setstr(s):
+    assert isinstance(s, (set,frozenset)), s
+    v = ['%s' % (_,) for _ in s]
+    return '{%s}' % ','.join(v)
 
 
 # generate all connected graphs with N(nodes) =< N
@@ -25,25 +33,43 @@ def genGraphs(N):
     Sprevedges = set()  # set of edges for all graphs with (i-1) nodes
 
     for i in range(1,N+1):
+        print()
         n = ('r' if i == 1 else 'n%d' % (i-1))
         nodes = nodes + [n]
-        Sedges = set()
 
-        # the graph remains connected if previous (N-1) graph is connected, and n
-        # is connected to at least one node in the previous graph.
+        # only 1 node
+        if i == 1:
+            yield Graph(nodes, set())
+            continue
+
+        # only 2 nodes
+        if i == 2:
+            yield Graph(nodes, set([frozenset(nodes),]))
+            Sprevedges.add(frozenset([frozenset(nodes)]))
+            continue
+
+
+        # induction: the graph remains connected if previous (N-1) graph is
+        # connected, and n is connected to at least one node in the previous graph.
+        Sedges = set()
 
         # for all combinations to which nodes n is connected in the previous graph.
         for j in range(1, 1<<(i-1)):
-            Snewconn = set()
+            newconn = set()
             for k in range(i-1):
                 if j & (1 << k):
-                    Snewconn.add((nodes[k], n))
+                    newconn.add(frozenset([nodes[k], n]))
+
+            #print("j: %d\tnewconn: %s" % (j, newconn))
+            #print("Sprevedges: %s" % Sprevedges)
 
             for edges in Sprevedges:
-                for newconn in Snewconn:
-                    newedges = edges.union(newconn)
-                    Sedges.add(newedges)
-                    yield Graph(nodes, newedges)
+                newedges = edges.union(newconn)
+                #print("edges:    %s" % edges)
+                #print("newconn:  %s" % newconn)
+                #print("newedges: %s" % newedges)
+                Sedges.add(newedges)
+                yield Graph(nodes, newedges)
 
         Sprevedges = Sedges