text: # Copyright 2019 D-Wave Systems Inc.
  #
  #    Licensed under the Apache License, Version 2.0 (the "License");
  #    you may not use this file except in compliance with the License.
  #    You may obtain a copy of the License at
  #
  #        http://www.apache.org/licenses/LICENSE-2.0
  #
  #    Unless required by applicable law or agreed to in writing, software
  #    distributed under the License is distributed on an "AS IS" BASIS,
  #    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  #    See the License for the specific language governing permissions and
  #    limitations under the License.
  
  import itertools
  import collections.abc as abc
  
  from collections import namedtuple
  
  import networkx as nx
  
  
  __all__ = 'markov_network',
  
  
  ###############################################################################
  # The following code is partially based on https://github.com/tbabej/gibbs
  #
  # MIT License
  # ===========
  #
  # Copyright 2017 Tomas Babej
  # https://github.com/tbabej/gibbs
  #
  # This software is released under MIT licence.
  #
  # Permission is hereby granted, free of charge, to any person obtaining
  # a copy of this software and associated documentation files (the
  # "Software"), to deal in the Software without restriction, including
  # without limitation the rights to use, copy, modify, merge, publish,
  # distribute, sublicense, and/or sell copies of the Software, and to
  # permit persons to whom the Software is furnished to do so, subject to
  # the following conditions:
  #
  # The above copyright notice and this permission notice shall be
  # included in all copies or substantial portions of the Software.
  #
  # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  # EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  # MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  # NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
  # LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
  # OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
  # WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  #
  
  
  def markov_network(potentials):
      """Creates a Markov Network from potentials.
  
      A Markov Network is also knows as a `Markov Random Field`_
  
      Parameters
      ----------
      potentials : dict[tuple, dict]
          A dict where the keys are either nodes or edges and the values are a
          dictionary of potentials. The potential dict should map each possible
          assignment of the nodes/edges to their energy.
  
      Returns
      -------
      MN : :obj:`networkx.Graph`
          A markov network as a graph where each node/edge stores its potential
          dict as above.
  
      Examples
      --------
      >>> potentials = {('a', 'b'): {(0, 0): -1,
      ...                            (0, 1): .5,
      ...                            (1, 0): .5,
      ...                            (1, 1): 2}}
      >>> MN = dnx.markov_network(potentials)
      >>> MN['a']['b']['potential'][(0, 0)]
      -1
  
      .. _Markov Random Field: https://en.wikipedia.org/wiki/Markov_random_field
  
      """
  
      G = nx.Graph()
  
      G.name = 'markov_network({!r})'.format(potentials)
  
      # we use 'clique' because the keys of potentials can be either nodes or
      # edges, but in either case they are fully connected.
      for clique, phis in potentials.items():
  
          num_vars = len(clique)
  
          # because this data potentially wont be used for a while, let's do some
          # input checking now and save some debugging issues later
          if not isinstance(phis, abc.Mapping):
              raise TypeError("phis should be a dict")
          elif not all(config in phis for config in itertools.product((0, 1), repeat=num_vars)):
              raise ValueError("not all potentials provided for {!r}".format(clique))
  
          if num_vars == 1:
              u, = clique
              G.add_node(u, potential=phis)
          elif num_vars == 2:
              u, v = clique
              # in python<=3.5 the edge order might not be consistent so we store
              # the relevant order of the variables relative to the potentials
              G.add_edge(u, v, potential=phis, order=(u, v))
          else:
              # developer note: in principle supporting larger cliques can be done
              # using higher-order, but it would make the use of networkx graphs
              # far more difficult
              raise ValueError("Only supports cliques up to size 2")
  
      return G
  