text: # -*- coding: utf-8 -*-
  """
  Generators for random graphs.
  
  """
  #    Copyright (C) 2004-2011 by
  #    Aric Hagberg <hagberg@lanl.gov>
  #    Dan Schult <dschult@colgate.edu>
  #    Pieter Swart <swart@lanl.gov>
  #    All rights reserved.
  #    BSD license.
  __author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
                          'Pieter Swart (swart@lanl.gov)',
                          'Dan Schult (dschult@colgate.edu)'])
  import itertools
  import random
  import math
  import networkx as nx
  from networkx.generators.classic import empty_graph, path_graph, complete_graph
  
  from collections import defaultdict
  
  __all__ = ['fast_gnp_random_graph',
             'gnp_random_graph',
             'dense_gnm_random_graph',
             'gnm_random_graph',
             'erdos_renyi_graph',
             'binomial_graph',
             'newman_watts_strogatz_graph',
             'watts_strogatz_graph',
             'connected_watts_strogatz_graph',
             'random_regular_graph',
             'barabasi_albert_graph',
             'powerlaw_cluster_graph',
             'random_lobster',
             'random_shell_graph',
             'random_powerlaw_tree',
             'random_powerlaw_tree_sequence']
  
  
  #-------------------------------------------------------------------------
  #  Some Famous Random Graphs
  #-------------------------------------------------------------------------
  
  
  def fast_gnp_random_graph(n, p, seed=None, directed=False):
      """Return a random graph G_{n,p} (Erdős-Rényi graph, binomial graph).
  
      Parameters
      ----------
      n : int
          The number of nodes.
      p : float
          Probability for edge creation.
      seed : int, optional
          Seed for random number generator (default=None).
      directed : bool, optional (default=False)
          If True return a directed graph
  
      Notes
      -----
      The G_{n,p} graph algorithm chooses each of the [n(n-1)]/2
      (undirected) or n(n-1) (directed) possible edges with probability p.
  
      This algorithm is O(n+m) where m is the expected number of
      edges m=p*n*(n-1)/2.
  
      It should be faster than gnp_random_graph when p is small and
      the expected number of edges is small (sparse graph).
  
      See Also
      --------
      gnp_random_graph
  
      References
      ----------
      .. [1] Vladimir Batagelj and Ulrik Brandes,
         "Efficient generation of large random networks",
         Phys. Rev. E, 71, 036113, 2005.
      """
      G = empty_graph(n)
      G.name="fast_gnp_random_graph(%s,%s)"%(n,p)
  
      if not seed is None:
          random.seed(seed)
  
      if p <= 0 or p >= 1:
          return nx.gnp_random_graph(n,p,directed=directed)
  
      w = -1
      lp = math.log(1.0 - p)
  
      if directed:
          G = nx.DiGraph(G)
          # Nodes in graph are from 0,n-1 (start with v as the first node index).
          v = 0
          while v < n:
              lr = math.log(1.0 - random.random())
              w = w + 1 + int(lr/lp)
              if v == w: # avoid self loops
                  w = w + 1
              while  w >= n and v < n:
                  w = w - n
                  v = v + 1
                  if v == w: # avoid self loops
                      w = w + 1
              if v < n:
                  G.add_edge(v, w)
      else:
          # Nodes in graph are from 0,n-1 (start with v as the second node index).
          v = 1
          while v < n:
              lr = math.log(1.0 - random.random())
              w = w + 1 + int(lr/lp)
              while w >= v and v < n:
                  w = w - v
                  v = v + 1
              if v < n:
                  G.add_edge(v, w)
      return G
  
  
  def gnp_random_graph(n, p, seed=None, directed=False):
      """Return a random graph G_{n,p} (Erdős-Rényi graph, binomial graph).
  
      Chooses each of the possible edges with probability p.
  
      This is also called binomial_graph and erdos_renyi_graph.
  
      Parameters
      ----------
      n : int
          The number of nodes.
      p : float
          Probability for edge creation.
      seed : int, optional
          Seed for random number generator (default=None).
      directed : bool, optional (default=False)
          If True return a directed graph
  
      See Also
      --------
      fast_gnp_random_graph
  
      Notes
      -----
      This is an O(n^2) algorithm.  For sparse graphs (small p) see
      fast_gnp_random_graph for a faster algorithm.
  
      References
      ----------
      .. [1] P. Erdős and A. Rényi, On Random Graphs, Publ. Math. 6, 290 (1959).
      .. [2] E. N. Gilbert, Random Graphs, Ann. Math. Stat., 30, 1141 (1959).
      """
      if directed:
          G=nx.DiGraph()
      else:
          G=nx.Graph()
      G.add_nodes_from(range(n))
      G.name="gnp_random_graph(%s,%s)"%(n,p)
      if p<=0:
          return G
      if p>=1:
          return complete_graph(n,create_using=G)
  
      if not seed is None:
          random.seed(seed)
  
      if G.is_directed():
          edges=itertools.permutations(range(n),2)
      else:
          edges=itertools.combinations(range(n),2)
  
      for e in edges:
          if random.random() < p:
              G.add_edge(*e)
      return G
  
  
  # add some aliases to common names
  binomial_graph=gnp_random_graph
  erdos_renyi_graph=gnp_random_graph
  
  def dense_gnm_random_graph(n, m, seed=None):
      """Return the random graph G_{n,m}.
  
      Gives a graph picked randomly out of the set of all graphs
      with n nodes and m edges.
      This algorithm should be faster than gnm_random_graph for dense graphs.
  
      Parameters
      ----------
      n : int
          The number of nodes.
      m : int
          The number of edges.
      seed : int, optional
          Seed for random number generator (default=None).
  
      See Also
      --------
      gnm_random_graph()
  
      Notes
      -----
      Algorithm by Keith M. Briggs Mar 31, 2006.
      Inspired by Knuth's Algorithm S (Selection sampling technique),
      in section 3.4.2 of [1]_.
  
      References
      ----------
      .. [1] Donald E. Knuth, The Art of Computer Programming,
          Volume 2/Seminumerical algorithms, Third Edition, Addison-Wesley, 1997.
      """
      mmax=n*(n-1)/2
      if m>=mmax:
          G=complete_graph(n)
      else:
          G=empty_graph(n)
      G.name="dense_gnm_random_graph(%s,%s)"%(n,m)
  
      if n==1 or m>=mmax:
          return G
  
      if seed is not None:
          random.seed(seed)
  
      u=0
      v=1
      t=0
      k=0
      while True:
          if random.randrange(mmax-t)<m-k:
              G.add_edge(u,v)
              k+=1
              if k==m: return G
          t+=1
          v+=1
          if v==n: # go to next row of adjacency matrix
              u+=1
              v=u+1
  
  def gnm_random_graph(n, m, seed=None, directed=False):
      """Return the random graph G_{n,m}.
  
      Produces a graph picked randomly out of the set of all graphs
      with n nodes and m edges.
  
      Parameters
      ----------
      n : int
          The number of nodes.
      m : int
          The number of edges.
      seed : int, optional
          Seed for random number generator (default=None).
      directed : bool, optional (default=False)
          If True return a directed graph
      """
      if directed:
          G=nx.DiGraph()
      else:
          G=nx.Graph()
      G.add_nodes_from(range(n))
      G.name="gnm_random_graph(%s,%s)"%(n,m)
  
      if seed is not None:
          random.seed(seed)
  
      if n==1:
          return G
      max_edges=n*(n-1)
      if not directed:
          max_edges/=2.0
      if m>=max_edges:
          return complete_graph(n,create_using=G)
  
      nlist=G.nodes()
      edge_count=0
      while edge_count < m:
          # generate random edge,u,v
          u = random.choice(nlist)
          v = random.choice(nlist)
          if u==v or G.has_edge(u,v):
              continue
          else:
              G.add_edge(u,v)
              edge_count=edge_count+1
      return G
  
  
  def newman_watts_strogatz_graph(n, k, p, seed=None):
      """Return a Newman-Watts-Strogatz small world graph.
  
      Parameters
      ----------
      n : int
          The number of nodes
      k : int
          Each node is connected to k nearest neighbors in ring topology
      p : float
          The probability of adding a new edge for each edge
      seed : int, optional
         seed for random number generator (default=None)
  
      Notes
      -----
      First create a ring over n nodes.  Then each node in the ring is
      connected with its k nearest neighbors (k-1 neighbors if k is odd).
      Then shortcuts are created by adding new edges as follows:
      for each edge u-v in the underlying "n-ring with k nearest neighbors"
      with probability p add a new edge u-w with randomly-chosen existing
      node w.  In contrast with watts_strogatz_graph(), no edges are removed.
  
      See Also
      --------
      watts_strogatz_graph()
  
      References
      ----------
      .. [1] M. E. J. Newman and D. J. Watts,
         Renormalization group analysis of the small-world network model,
         Physics Letters A, 263, 341, 1999.
         http://dx.doi.org/10.1016/S0375-9601(99)00757-4
      """
      if seed is not None:
          random.seed(seed)
      if k>=n:
          raise nx.NetworkXError("k>=n, choose smaller k or larger n")
      G=empty_graph(n)
      G.name="newman_watts_strogatz_graph(%s,%s,%s)"%(n,k,p)
      nlist = G.nodes()
      fromv = nlist
      # connect the k/2 neighbors
      for j in range(1, k // 2+1):
          tov = fromv[j:] + fromv[0:j] # the first j are now last
          for i in range(len(fromv)):
              G.add_edge(fromv[i], tov[i])
      # for each edge u-v, with probability p, randomly select existing
      # node w and add new edge u-w
      e = G.edges()
      for (u, v) in e:
          if random.random() < p:
              w = random.choice(nlist)
              # no self-loops and reject if edge u-w exists
              # is that the correct NWS model?
              while w == u or G.has_edge(u, w):
                  w = random.choice(nlist)
                  if G.degree(u) >= n-1:
                      break # skip this rewiring
              else:
                  G.add_edge(u,w)
      return G
  
  
  def watts_strogatz_graph(n, k, p, seed=None):
      """Return a Watts-Strogatz small-world graph.
  
  
      Parameters
      ----------
      n : int
          The number of nodes
      k : int
          Each node is connected to k nearest neighbors in ring topology
      p : float
          The probability of rewiring each edge
      seed : int, optional
          Seed for random number generator (default=None)
  
      See Also
      --------
      newman_watts_strogatz_graph()
      connected_watts_strogatz_graph()
  
      Notes
      -----
      First create a ring over n nodes.  Then each node in the ring is
      connected with its k nearest neighbors (k-1 neighbors if k is odd).
      Then shortcuts are created by replacing some edges as follows:
      for each edge u-v in the underlying "n-ring with k nearest neighbors"
      with probability p replace it with a new edge u-w with uniformly
      random choice of existing node w.
  
      In contrast with newman_watts_strogatz_graph(), the random
      rewiring does not increase the number of edges. The rewired graph
      is not guaranteed to be connected as in  connected_watts_strogatz_graph().
  
      References
      ----------
      .. [1] Duncan J. Watts and Steven H. Strogatz,
         Collective dynamics of small-world networks,
         Nature, 393, pp. 440--442, 1998.
      """
      if k>=n:
          raise nx.NetworkXError("k>=n, choose smaller k or larger n")
      if seed is not None:
          random.seed(seed)
  
      G = nx.Graph()
      G.name="watts_strogatz_graph(%s,%s,%s)"%(n,k,p)
      nodes = list(range(n)) # nodes are labeled 0 to n-1
      # connect each node to k/2 neighbors
      for j in range(1, k // 2+1):
          targets = nodes[j:] + nodes[0:j] # first j nodes are now last in list
          G.add_edges_from(zip(nodes,targets))
      # rewire edges from each node
      # loop over all nodes in order (label) and neighbors in order (distance)
      # no self loops or multiple edges allowed
      for j in range(1, k // 2+1): # outer loop is neighbors
          targets = nodes[j:] + nodes[0:j] # first j nodes are now last in list
          # inner loop in node order
          for u,v in zip(nodes,targets):
              if random.random() < p:
                  w = random.choice(nodes)
                  # Enforce no self-loops or multiple edges
                  while w == u or G.has_edge(u, w):
                      w = random.choice(nodes)
                      if G.degree(u) >= n-1:
                          break # skip this rewiring
                  else:
                      G.remove_edge(u,v)
                      G.add_edge(u,w)
      return G
  
  def connected_watts_strogatz_graph(n, k, p, tries=100, seed=None):
      """Return a connected Watts-Strogatz small-world graph.
  
      Attempt to generate a connected realization by repeated
      generation of Watts-Strogatz small-world graphs.
      An exception is raised if the maximum number of tries is exceeded.
  
      Parameters
      ----------
      n : int
          The number of nodes
      k : int
          Each node is connected to k nearest neighbors in ring topology
      p : float
          The probability of rewiring each edge
      tries : int
          Number of attempts to generate a connected graph.
      seed : int, optional
           The seed for random number generator.
  
      See Also
      --------
      newman_watts_strogatz_graph()
      watts_strogatz_graph()
  
      """
      G = watts_strogatz_graph(n, k, p, seed)
      t=1
      while not nx.is_connected(G):
          G = watts_strogatz_graph(n, k, p, seed)
          t=t+1
          if t>tries:
              raise nx.NetworkXError("Maximum number of tries exceeded")
      return G
  
  
  def random_regular_graph(d, n, seed=None):
      """Return a random regular graph of n nodes each with degree d.
  
      The resulting graph G has no self-loops or parallel edges.
  
      Parameters
      ----------
      d : int
        Degree
      n : integer
        Number of nodes. The value of n*d must be even.
      seed : hashable object
          The seed for random number generator.
  
      Notes
      -----
      The nodes are numbered form 0 to n-1.
  
      Kim and Vu's paper [2]_ shows that this algorithm samples in an
      asymptotically uniform way from the space of random graphs when
      d = O(n**(1/3-epsilon)).
  
      References
      ----------
      .. [1] A. Steger and N. Wormald,
         Generating random regular graphs quickly,
         Probability and Computing 8 (1999), 377-396, 1999.
         http://citeseer.ist.psu.edu/steger99generating.html
  
      .. [2] Jeong Han Kim and Van H. Vu,
         Generating random regular graphs,
         Proceedings of the thirty-fifth ACM symposium on Theory of computing,
         San Diego, CA, USA, pp 213--222, 2003.
         http://portal.acm.org/citation.cfm?id=780542.780576
      """
      if (n * d) % 2 != 0:
          raise nx.NetworkXError("n * d must be even")
  
      if not 0 <= d < n:
          raise nx.NetworkXError("the 0 <= d < n inequality must be satisfied")
  
      if d == 0:
          return empty_graph(n)
  
      if seed is not None:
          random.seed(seed)
  
      def _suitable(edges, potential_edges):
      # Helper subroutine to check if there are suitable edges remaining
      # If False, the generation of the graph has failed
          if not potential_edges:
              return True
          for s1 in potential_edges:
              for s2 in potential_edges:
                  # Two iterators on the same dictionary are guaranteed
                  # to visit it in the same order if there are no
                  # intervening modifications.
                  if s1 == s2:
                      # Only need to consider s1-s2 pair one time
                      break
                  if s1 > s2:
                      s1, s2 = s2, s1
                  if (s1, s2) not in edges:
                      return True
          return False
  
      def _try_creation():
          # Attempt to create an edge set
  
          edges = set()
          stubs = list(range(n)) * d
  
          while stubs:
              potential_edges = defaultdict(lambda: 0)
              random.shuffle(stubs)
              stubiter = iter(stubs)
              for s1, s2 in zip(stubiter, stubiter):
                  if s1 > s2:
                      s1, s2 = s2, s1
                  if s1 != s2 and ((s1, s2) not in edges):
                      edges.add((s1, s2))
                  else:
                      potential_edges[s1] += 1
                      potential_edges[s2] += 1
  
              if not _suitable(edges, potential_edges):
                  return None # failed to find suitable edge set
  
              stubs = [node for node, potential in potential_edges.items()
                       for _ in range(potential)]
          return edges
  
      # Even though a suitable edge set exists,
      # the generation of such a set is not guaranteed.
      # Try repeatedly to find one.
      edges = _try_creation()
      while edges is None:
          edges = _try_creation()
  
      G = nx.Graph()
      G.name = "random_regular_graph(%s, %s)" % (d, n)
      G.add_edges_from(edges)
  
      return G
  
  def _random_subset(seq,m):
      """ Return m unique elements from seq.
  
      This differs from random.sample which can return repeated
      elements if seq holds repeated elements.
      """
      targets=set()
      while len(targets)<m:
          x=random.choice(seq)
          targets.add(x)
      return targets
  
  def barabasi_albert_graph(n, m, seed=None):
      """Return random graph using Barabási-Albert preferential attachment model.
  
      A graph of n nodes is grown by attaching new nodes each with m
      edges that are preferentially attached to existing nodes with high
      degree.
  
      Parameters
      ----------
      n : int
          Number of nodes
      m : int
          Number of edges to attach from a new node to existing nodes
      seed : int, optional
          Seed for random number generator (default=None).
  
      Returns
      -------
      G : Graph
  
      Notes
      -----
      The initialization is a graph with with m nodes and no edges.
  
      References
      ----------
      .. [1] A. L. Barabási and R. Albert "Emergence of scaling in
         random networks", Science 286, pp 509-512, 1999.
      """
  
      if m < 1 or  m >=n:
          raise nx.NetworkXError(\
                "Barabási-Albert network must have m>=1 and m<n, m=%d,n=%d"%(m,n))
      if seed is not None:
          random.seed(seed)
  
      # Add m initial nodes (m0 in barabasi-speak)
      G=empty_graph(m)
      G.name="barabasi_albert_graph(%s,%s)"%(n,m)
      # Target nodes for new edges
      targets=list(range(m))
      # List of existing nodes, with nodes repeated once for each adjacent edge
      repeated_nodes=[]
      # Start adding the other n-m nodes. The first node is m.
      source=m
      while source<n:
          # Add edges to m nodes from the source.
          G.add_edges_from(zip([source]*m,targets))
          # Add one node to the list for each new edge just created.
          repeated_nodes.extend(targets)
          # And the new node "source" has m edges to add to the list.
          repeated_nodes.extend([source]*m)
          # Now choose m unique nodes from the existing nodes
          # Pick uniformly from repeated_nodes (preferential attachement)
          targets = _random_subset(repeated_nodes,m)
          source += 1
      return G
  
  def powerlaw_cluster_graph(n, m, p, seed=None):
      """Holme and Kim algorithm for growing graphs with powerlaw
      degree distribution and approximate average clustering.
  
      Parameters
      ----------
      n : int
          the number of nodes
      m : int
          the number of random edges to add for each new node
      p : float,
          Probability of adding a triangle after adding a random edge
      seed : int, optional
          Seed for random number generator (default=None).
  
      Notes
      -----
      The average clustering has a hard time getting above
      a certain cutoff that depends on m.  This cutoff is often quite low.
      Note that the transitivity (fraction of triangles to possible
      triangles) seems to go down with network size.
  
      It is essentially the Barabási-Albert (B-A) growth model with an
      extra step that each random edge is followed by a chance of
      making an edge to one of its neighbors too (and thus a triangle).
  
      This algorithm improves on B-A in the sense that it enables a
      higher average clustering to be attained if desired.
  
      It seems possible to have a disconnected graph with this algorithm
      since the initial m nodes may not be all linked to a new node
      on the first iteration like the B-A model.
  
      References
      ----------
      .. [1] P. Holme and B. J. Kim,
         "Growing scale-free networks with tunable clustering",
         Phys. Rev. E, 65, 026107, 2002.
      """
  
      if m < 1 or n < m:
          raise nx.NetworkXError(\
                "NetworkXError must have m>1 and m<n, m=%d,n=%d"%(m,n))
  
      if p > 1 or p < 0:
          raise nx.NetworkXError(\
                "NetworkXError p must be in [0,1], p=%f"%(p))
      if seed is not None:
          random.seed(seed)
  
      G=empty_graph(m) # add m initial nodes (m0 in barabasi-speak)
      G.name="Powerlaw-Cluster Graph"
      repeated_nodes=G.nodes()  # list of existing nodes to sample from
                             # with nodes repeated once for each adjacent edge
      source=m               # next node is m
      while source<n:        # Now add the other n-1 nodes
          possible_targets = _random_subset(repeated_nodes,m)
          # do one preferential attachment for new node
          target=possible_targets.pop()
          G.add_edge(source,target)
          repeated_nodes.append(target) # add one node to list for each new link
          count=1
          while count<m:  # add m-1 more new links
              if random.random()<p: # clustering step: add triangle
                  neighborhood=[nbr for nbr in G.neighbors(target) \
                                 if not G.has_edge(source,nbr) \
                                 and not nbr==source]
                  if neighborhood: # if there is a neighbor without a link
                      nbr=random.choice(neighborhood)
                      G.add_edge(source,nbr) # add triangle
                      repeated_nodes.append(nbr)
                      count=count+1
                      continue # go to top of while loop
              # else do preferential attachment step if above fails
              target=possible_targets.pop()
              G.add_edge(source,target)
              repeated_nodes.append(target)
              count=count+1
  
          repeated_nodes.extend([source]*m)  # add source node to list m times
          source += 1
      return G
  
  def random_lobster(n, p1, p2, seed=None):
      """Return a random lobster.
  
       A lobster is a tree that reduces to a caterpillar when pruning all
       leaf nodes.
  
       A caterpillar is a tree that reduces to a path graph when pruning
       all leaf nodes (p2=0).
  
      Parameters
      ----------
      n : int
          The expected number of nodes in the backbone
      p1 : float
          Probability of adding an edge to the backbone
      p2 : float
          Probability of adding an edge one level beyond backbone
      seed : int, optional
          Seed for random number generator (default=None).
      """
      # a necessary ingredient in any self-respecting graph library
      if seed is not None:
          random.seed(seed)
      llen=int(2*random.random()*n + 0.5)
      L=path_graph(llen)
      L.name="random_lobster(%d,%s,%s)"%(n,p1,p2)
      # build caterpillar: add edges to path graph with probability p1
      current_node=llen-1
      for n in range(llen):
          if random.random()<p1: # add fuzzy caterpillar parts
              current_node+=1
              L.add_edge(n,current_node)
              if random.random()<p2: # add crunchy lobster bits
                  current_node+=1
                  L.add_edge(current_node-1,current_node)
      return L # voila, un lobster!
  
  def random_shell_graph(constructor, seed=None):
      """Return a random shell graph for the constructor given.
  
      Parameters
      ----------
      constructor: a list of three-tuples
          (n,m,d) for each shell starting at the center shell.
      n : int
          The number of nodes in the shell
      m : int
          The number or edges in the shell
      d : float
          The ratio of inter-shell (next) edges to intra-shell edges.
          d=0 means no intra shell edges, d=1 for the last shell
      seed : int, optional
          Seed for random number generator (default=None).
  
      Examples
      --------
      >>> constructor=[(10,20,0.8),(20,40,0.8)]
      >>> G=nx.random_shell_graph(constructor)
  
      """
      G=empty_graph(0)
      G.name="random_shell_graph(constructor)"
  
      if seed is not None:
          random.seed(seed)
  
      glist=[]
      intra_edges=[]
      nnodes=0
      # create gnm graphs for each shell
      for (n,m,d) in constructor:
          inter_edges=int(m*d)
          intra_edges.append(m-inter_edges)
          g=nx.convert_node_labels_to_integers(
              gnm_random_graph(n,inter_edges),
              first_label=nnodes)
          glist.append(g)
          nnodes+=n
          G=nx.operators.union(G,g)
  
      # connect the shells randomly
      for gi in range(len(glist)-1):
          nlist1=glist[gi].nodes()
          nlist2=glist[gi+1].nodes()
          total_edges=intra_edges[gi]
          edge_count=0
          while edge_count < total_edges:
              u = random.choice(nlist1)
              v = random.choice(nlist2)
              if u==v or G.has_edge(u,v):
                  continue
              else:
                  G.add_edge(u,v)
                  edge_count=edge_count+1
      return G
  
  
  def random_powerlaw_tree(n, gamma=3, seed=None, tries=100):
      """Return a tree with a powerlaw degree distribution.
  
      Parameters
      ----------
      n : int,
          The number of nodes
      gamma : float
          Exponent of the power-law
      seed : int, optional
          Seed for random number generator (default=None).
      tries : int
          Number of attempts to adjust sequence to make a tree
  
      Notes
      -----
      A trial powerlaw degree sequence is chosen and then elements are
      swapped with new elements from a powerlaw distribution until
      the sequence makes a tree (#edges=#nodes-1).
  
      """
      from networkx.generators.degree_seq import degree_sequence_tree
      try:
          s=random_powerlaw_tree_sequence(n,
                                          gamma=gamma,
                                          seed=seed,
                                          tries=tries)
      except:
          raise nx.NetworkXError(\
                "Exceeded max (%d) attempts for a valid tree sequence."%tries)
      G=degree_sequence_tree(s)
      G.name="random_powerlaw_tree(%s,%s)"%(n,gamma)
      return G
  
  
  def random_powerlaw_tree_sequence(n, gamma=3, seed=None, tries=100):
      """ Return a degree sequence for a tree with a powerlaw distribution.
  
      Parameters
      ----------
      n : int,
          The number of nodes
      gamma : float
          Exponent of the power-law
      seed : int, optional
          Seed for random number generator (default=None).
      tries : int
          Number of attempts to adjust sequence to make a tree
  
      Notes
      -----
      A trial powerlaw degree sequence is chosen and then elements are
      swapped with new elements from a powerlaw distribution until
      the sequence makes a tree (#edges=#nodes-1).
  
  
      """
      if seed is not None:
          random.seed(seed)
  
      # get trial sequence
      z=nx.utils.powerlaw_sequence(n,exponent=gamma)
      # round to integer values in the range [0,n]
      zseq=[min(n, max( int(round(s)),0 )) for s in z]
  
      # another sequence to swap values from
      z=nx.utils.powerlaw_sequence(tries,exponent=gamma)
      # round to integer values in the range [0,n]
      swap=[min(n, max( int(round(s)),0 )) for s in z]
  
      for deg in swap:
          if n-sum(zseq)/2.0 == 1.0: # is a tree, return sequence
              return zseq
          index=random.randint(0,n-1)
          zseq[index]=swap.pop()
  
      raise nx.NetworkXError(\
            "Exceeded max (%d) attempts for a valid tree sequence."%tries)
      return False
  
  