.

allgraphs.py

+#!/usr/bin/env python
+"""generate all connected graphs up to N nodes"""
+
+from __future__ import print_statement
+
+
+class Graph:
+    # .nodes    {nodes}
+    # .edges    {edges}
+
+    def __init__(nodes, edges):
+        self.nodes = set(nodes)
+        self.edges = set(edges)
+
+    def __str__(self):
+        return "Graph nodes=%s  edges=%s" % (self.nodes, self.edges)
+
+
+# generate all connected graphs with N(nodes) =< N
+def genGraphs(N):
+    assert N >= 1
+
+    nodes  = []         # of all nodes
+    Sprevedges = set()  # set of edges for all graphs with (i-1) nodes
+
+    for i in range(N):
+        n = ('r' if i == 0 else 'n%d' % i)
+        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.
+
+        # for all combinations to which nodes n is connected in the previous graph.
+        for j in range(1,2**(i-1)):
+            Snewconn = set()
+            for k in range(i-1):
+                if j & (1 << k):
+                    Snewconn.add((nodes[k], n))
+
+            for edges in Sprevedges:
+                for newconn in Snewconn:
+                    newedges = edges.union(newconn)
+                    Sedges.add(newedges)
+                    yield Graph(node, newedges)
+
+        Sprevedges = Sedges
+
+
+
+
+def main():
+    N = int(sys.argv[1])
+    for g in genGraphs(N):
+        print(g)
+
+
+
+if __name__ == '__main__':
+    main()