Ticket #7487: trac_7487.patch

sage/graphs/graph_generators.py

@@ -101 +101 @@
         - RandomGNM
         - RandomNewmanWattsStrogatz
         - RandomHolmeKim
+        - RandomInterval
         - RandomLobster
         - RandomTreePowerlaw
         - RandomRegular
@@ -229 +230 @@
                     - RandomGNM
                     - RandomNewmanWattsStrogatz
                     - RandomHolmeKim
+                    - RandomInterval
                     - RandomLobster
                     - RandomTreePowerlaw
                     - RandomRegular
@@ -3330 +3332 @@
         import networkx
         return graph.Graph(networkx.powerlaw_cluster_graph(n, m, p, seed))
 
+    def RandomInterval(self,n):
+        """
+        Returns a random interval graph.
+
+        An interval graph is built from a list `(a_i,b_i)_{1\leq i \leq n}` 
+        of intervals : to each interval of the list is associated one 
+        vertex, two vertices being adjacent if the two corresponding
+        intervals intersect.
+
+        A random interval graph of order `n` is generated by picking
+        random values for the `(a_i,b_j)`, each of the two coordinates
+        being generated from the uniform distribution on the interval 
+        `[0,1]`.
+
+        This definitions follows [boucheron2001]_.
+
+        INPUT:
+
+        - ``n`` (integer) -- the number of vertices in the random
+          graph.
+
+        EXAMPLE:
+
+        As for any interval graph, the chromatic number is equal to
+        the clique number ::
+
+            sage: g = graphs.RandomInterval(15)
+            sage: g.clique_number() == g.chromatic_number()
+            True
+
+        REFERENCE:
+
+        - [boucheron2001] Boucheron, S. and FERNANDEZ de la VEGA, W., 
+          On the Independence Number of Random Interval Graphs,
+          Combinatorics, Probability and Computing v10, issue 05,
+          Pages 385--396,
+          Cambridge Univ Press, 2001
+        """
+
+        from sage.misc.prandom import random
+
+        s = lambda x,y : (x,y) if x<=y else (y,x)
+        intervals = [s(random(), random()) for i in range(n)]
+        intervals.sort(key=lambda x:x[0])
+        edges = []
+        while intervals:
+            x = intervals.pop()
+            for y in intervals:
+                if y[0] <= x[1]:
+                    edges.append((x,y))
+                else:
+                    break
+        g=graph.Graph(vertices=intervals)
+        g.add_edges(edges)
+        return g
+
     def RandomLobster(self, n, p, q, seed=None):
         """
         Returns a random lobster.