text: """Generates graphs resembling the Internet Autonomous System network"""
  
  import networkx as nx
  from networkx.utils import py_random_state
  
  __all__ = ['random_internet_as_graph']
  
  
  def uniform_int_from_avg(a, m, seed):
      """ Pick a random integer with uniform probability.
  
      Returns a random integer uniformly taken from a distribution with
      minimum value 'a' and average value 'm', X~U(a,b), E[X]=m, X in N where
      b = 2*m - a.
  
      Notes
      -----
      p = (b-floor(b))/2
      X = X1 + X2; X1~U(a,floor(b)), X2~B(p)
      E[X] = E[X1] + E[X2] = (floor(b)+a)/2 + (b-floor(b))/2 = (b+a)/2 = m
      """
  
      from math import floor
      assert(m >= a)
      b = 2*m - a
      p = (b-floor(b))/2
      X1 = int(round(seed.random()*(floor(b)-a) + a))
      if seed.random() < p:
          X2 = 1
      else:
          X2 = 0
      return X1 + X2
  
  
  def choose_pref_attach(degs, seed):
      """ Pick a random value, with a probability given by its weight.
  
      Returns a random choice among degs keys, each of which has a
      probability proportional to the corresponding dictionary value.
  
      Parameters
      ----------
      degs: dictionary
          It contains the possible values (keys) and the corresponding
          probabilities (values)
      seed: random state
  
      Returns
      -------
      v: object
          A key of degs or None if degs is empty
      """
  
      if len(degs) == 0:
          return None
      s = sum(degs.values())
      if s == 0:
          return seed.choice(list(degs.keys()))
      v = seed.random() * s
  
      nodes = list(degs.keys())
      i = 0
      acc = degs[nodes[i]]
      while v > acc:
          i += 1
          acc += degs[nodes[i]]
      return nodes[i]
  
  
  class AS_graph_generator:
      """ Generates random internet AS graphs.
      """
  
      def __init__(self, n, seed):
          """ Initializes variables. Immediate numbers are taken from [1].
  
          Parameters
          ----------
          n: integer
              Number of graph nodes
          seed: random state
              Indicator of random number generation state.
              See :ref:`Randomness<randomness>`.
  
          Returns
          -------
          GG: AS_graph_generator object
  
          References
          ----------
          [1] A. Elmokashfi, A. Kvalbein and C. Dovrolis, "On the Scalability of
          BGP: The Role of Topology Growth," in IEEE Journal on Selected Areas
          in Communications, vol. 28, no. 8, pp. 1250-1261, October 2010.
          """
  
          self.seed = seed
          self.n_t = min(n, int(round(self.seed.random()*2+4)))  # num of T nodes
          self.n_m = int(round(0.15*n))  # number of M nodes
          self.n_cp = int(round(0.05*n))  # number of CP nodes
          self.n_c = max(0, n-self.n_t-self.n_m-self.n_cp)  # number of C nodes
  
          self.d_m = 2 + (2.5*n)/10000  # average multihoming degree for M nodes
          self.d_cp = 2 + (1.5*n)/10000  # avg multihoming degree for CP nodes
          self.d_c = 1 + (5*n)/100000  # average multihoming degree for C nodes
  
          self.p_m_m = 1 + (2*n)/10000  # avg num of peer edges between M and M
          self.p_cp_m = 0.2 + (2*n)/10000  # avg num of peer edges between CP, M
          self.p_cp_cp = 0.05 + (2*n)/100000  # avg num of peer edges btwn CP, CP
  
          self.t_m = 0.375  # probability M's provider is T
          self.t_cp = 0.375  # probability CP's provider is T
          self.t_c = 0.125  # probability C's provider is T
  
      def t_graph(self):
          """ Generates the core mesh network of tier one nodes of a AS graph.
  
          Returns
          -------
          G: Networkx Graph
              Core network
          """
  
          self.G = nx.Graph()
          for i in range(self.n_t):
              self.G.add_node(i, type="T")
              for r in self.regions:
                  self.regions[r].add(i)
              for j in self.G.nodes():
                  if i != j:
                      self.add_edge(i, j, 'peer')
              self.customers[i] = set()
              self.providers[i] = set()
          return self.G
  
      def add_edge(self, i, j, kind):
          if kind == 'transit':
              customer = str(i)
          else:
              customer = 'none'
          self.G.add_edge(i, j, type=kind, customer=customer)
  
      def choose_peer_pref_attach(self, node_list):
          """ Pick a node with a probability weighted by its peer degree.
  
          Pick a node from node_list with preferential attachment
          computed only on their peer degree
          """
  
          d = {}
          for n in node_list:
              d[n] = self.G.nodes[n]['peers']
          return choose_pref_attach(d, self.seed)
  
      def choose_node_pref_attach(self, node_list):
          """ Pick a node with a probability weighted by its degree.
  
          Pick a node from node_list with preferential attachment
          computed on their degree
          """
  
          degs = dict(self.G.degree(node_list))
          return choose_pref_attach(degs, self.seed)
  
      def add_customer(self, i, j):
          """ Keep the dictionaries 'customers' and 'providers' consistent.
          """
  
          self.customers[j].add(i)
          self.providers[i].add(j)
          for z in self.providers[j]:
              self.customers[z].add(i)
              self.providers[i].add(z)
  
      def add_node(self, i, kind, reg2prob, avg_deg, t_edge_prob):
          """ Add a node and its customer transit edges to the graph.
  
          Parameters
          ----------
          i: object
              Identifier of the new node
          kind: string
              Type of the new node. Options are: 'M' for middle node, 'CP' for
              content provider and 'C' for customer.
          reg2prob: float
              Probability the new node can be in two different regions.
          avg_deg: float
              Average number of transit nodes of which node i is customer.
          t_edge_prob: float
              Probability node i establish a customer transit edge with a tier
              one (T) node
  
          Returns
          -------
          i: object
              Identifier of the new node
          """
  
          regs = 1  # regions in which node resides
          if self.seed.random() < reg2prob:  # node is in two regions
              regs = 2
          node_options = set()
  
          self.G.add_node(i, type=kind, peers=0)
          self.customers[i] = set()
          self.providers[i] = set()
          self.nodes[kind].add(i)
          for r in self.seed.sample(list(self.regions), regs):
              node_options = node_options.union(self.regions[r])
              self.regions[r].add(i)
  
          edge_num = uniform_int_from_avg(1, avg_deg, self.seed)
  
          t_options = node_options.intersection(self.nodes['T'])
          m_options = node_options.intersection(self.nodes['M'])
          if i in m_options:
              m_options.remove(i)
          d = 0
          while d < edge_num and (len(t_options) > 0 or len(m_options) > 0):
              if len(m_options) == 0 or (len(t_options) > 0 and
                                         self.seed.random() < t_edge_prob):  # add edge to a T node
                  j = self.choose_node_pref_attach(t_options)
                  t_options.remove(j)
              else:
                  j = self.choose_node_pref_attach(m_options)
                  m_options.remove(j)
              self.add_edge(i, j, 'transit')
              self.add_customer(i, j)
              d += 1
  
          return i
  
      def add_m_peering_link(self, m, to_kind):
          """ Add a peering link between two middle tier (M) nodes.
  
          Target node j is drawn considering a preferential attachment based on
          other M node peering degree.
  
          Parameters
          ----------
          m: object
              Node identifier
          to_kind: string
              type for target node j (must be always M)
  
          Returns
          -------
          success: boolean
          """
  
          # candidates are of type 'M' and are not customers of m
          node_options = self.nodes['M'].difference(self.customers[m])
          # candidates are not providers of m
          node_options = node_options.difference(self.providers[m])
          # remove self
          if m in node_options:
              node_options.remove(m)
  
          # remove candidates we are already connected to
          for j in self.G.neighbors(m):
              if j in node_options:
                  node_options.remove(j)
  
          if len(node_options) > 0:
              j = self.choose_peer_pref_attach(node_options)
              self.add_edge(m, j, 'peer')
              self.G.nodes[m]['peers'] += 1
              self.G.nodes[j]['peers'] += 1
              return True
          else:
              return False
  
      def add_cp_peering_link(self, cp, to_kind):
          """ Add a peering link to a content provider (CP) node.
  
          Target node j can be CP or M and it is drawn uniformely among the nodes
          belonging to the same region as cp.
  
          Parameters
          ----------
          cp: object
              Node identifier
          to_kind: string
              type for target node j (must be M or CP)
  
          Returns
          -------
          success: boolean
          """
  
          node_options = set()
          for r in self.regions:  # options include nodes in the same region(s)
              if cp in self.regions[r]:
                  node_options = node_options.union(self.regions[r])
  
          # options are restricted to the indicated kind ('M' or 'CP')
          node_options = self.nodes[to_kind].intersection(node_options)
  
          # remove self
          if cp in node_options:
              node_options.remove(cp)
  
          # remove nodes that are cp's providers
          node_options = node_options.difference(self.providers[cp])
  
          # remove nodes we are already connected to
          for j in self.G.neighbors(cp):
              if j in node_options:
                  node_options.remove(j)
  
          if len(node_options) > 0:
              j = self.seed.sample(node_options, 1)[0]
              self.add_edge(cp, j, 'peer')
              self.G.nodes[cp]['peers'] += 1
              self.G.nodes[j]['peers'] += 1
              return True
          else:
              return False
  
      def graph_regions(self, rn):
          """ Initializes AS network regions.
  
          Parameters
          ----------
          rn: integer
              Number of regions
          """
  
          self.regions = {}
          for i in range(rn):
              self.regions["REG"+str(i)] = set()
  
      def add_peering_links(self, from_kind, to_kind):
          """ Utility function to add peering links among node groups.
          """
          peer_link_method = None
          if from_kind == 'M':
              peer_link_method = self.add_m_peering_link
              m = self.p_m_m
          if from_kind == 'CP':
              peer_link_method = self.add_cp_peering_link
              if to_kind == 'M':
                  m = self.p_cp_m
              else:
                  m = self.p_cp_cp
  
          for i in self.nodes[from_kind]:
              num = uniform_int_from_avg(0, m, self.seed)
              for _ in range(num):
                  peer_link_method(i, to_kind)
  
      def generate(self):
          """ Generates a random AS network graph as described in [1].
  
          Returns
          -------
          G: Graph object
  
          Notes
          -----
          The process steps are the following: first we create the core network
          of tier one nodes, then we add the middle tier (M), the content
          provider (CP) and the customer (C) nodes along with their transit edges
          (link i,j means i is customer of j). Finally we add peering links
          between M nodes, between M and CP nodes and between CP node couples.
          For a detailed description of the algorithm, please refer to [1].
  
          References
          ----------
          [1] A. Elmokashfi, A. Kvalbein and C. Dovrolis, "On the Scalability of
          BGP: The Role of Topology Growth," in IEEE Journal on Selected Areas
          in Communications, vol. 28, no. 8, pp. 1250-1261, October 2010.
          """
  
          self.graph_regions(5)
          self.customers = {}
          self.providers = {}
          self.nodes = {'T': set(), 'M': set(), 'CP': set(), 'C': set()}
  
          self.t_graph()
          self.nodes['T'] = set(list(self.G.nodes()))
  
          i = len(self.nodes['T'])
          for _ in range(self.n_m):
              self.nodes['M'].add(self.add_node(i, 'M', 0.2, self.d_m, self.t_m))
              i += 1
          for _ in range(self.n_cp):
              self.nodes['CP'].add(self.add_node(i, 'CP', 0.05, self.d_cp,
                                                 self.t_cp))
              i += 1
          for _ in range(self.n_c):
              self.nodes['C'].add(self.add_node(i, 'C', 0, self.d_c, self.t_c))
              i += 1
  
          self.add_peering_links('M', 'M')
          self.add_peering_links('CP', 'M')
          self.add_peering_links('CP', 'CP')
  
          return self.G
  
  
  @py_random_state(1)
  def random_internet_as_graph(n, seed=None):
      """ Generates a random undirected graph resembling the Internet AS network
  
      Parameters
      ----------
      n: integer in [1000, 10000]
          Number of graph nodes
      seed : integer, random_state, or None (default)
          Indicator of random number generation state.
          See :ref:`Randomness<randomness>`.
  
      Returns
      -------
      G: Networkx Graph object
          A randomly generated undirected graph
  
      Notes
      -----
      This algorithm returns an undirected graph resembling the Internet
      Autonomous System (AS) network, it uses the approach by Elmokashfi et al.
      [1] and it grants the properties described in the related paper [1].
  
      Each node models an autonomous system, with an attribute 'type' specifying
      its kind; tier-1 (T), mid-level (M), customer (C) or content-provider (CP).
      Each edge models an ADV communication link (hence, bidirectional) with
      attributes:
          - type: transit|peer, the kind of commercial agreement between nodes;
          - customer: <node id>, the identifier of the node acting as customer
              ('none' if type is peer).
  
      References
      ----------
      [1] A. Elmokashfi, A. Kvalbein and C. Dovrolis, "On the Scalability of
      BGP: The Role of Topology Growth," in IEEE Journal on Selected Areas
      in Communications, vol. 28, no. 8, pp. 1250-1261, October 2010.
      """
  
      GG = AS_graph_generator(n, seed)
      G = GG.generate()
      return G
  