class_docstr: Class for representing factor graph.
  
  DiscreteFactor graph is a bipartite graph representing factorization of a function.
  They allow efficient computation of marginal distributions through sum-product
  algorithm.
  
  A factor graph contains two types of nodes. One type corresponds to random
  variables whereas the second type corresponds to factors over these variables.
  The graph only contains edges between variables and factor nodes. Each factor
  node is associated with one factor whose scope is the set of variables that
  are its neighbors.
  
  Parameters
  ----------
  data: input graph
      Data to initialize graph. If data=None (default) an empty graph is
      created. The data is an edge list.
  
  Examples
  --------
  Create an empty FactorGraph with no nodes and no edges
  
  >>> from pgmpy.models import FactorGraph
  >>> G = FactorGraph()
  
  G can be grown by adding variable nodes as well as factor nodes
  
  **Nodes:**
  
  Add a node at a time or a list of nodes.
  
  >>> G.add_node('a')
  >>> G.add_nodes_from(['a', 'b'])
  >>> phi1 = DiscreteFactor(['a', 'b'], [2, 2], np.random.rand(4))
  >>> G.add_factors(phi1)
  >>> G.add_nodes_from([phi1])
  
  **Edges:**
  
  G can also be grown by adding edges.
  
  >>> G.add_edge('a', phi1)
  
  or a list of edges
  
  >>> G.add_edges_from([('a', phi1), ('b', phi1)])
docstr: Check the model for various errors. This method checks for the following
  errors. In the same time it also updates the cardinalities of all the
  random variables.
  
  * Check whether bipartite property of factor graph is still maintained
    or not.
  * Check whether factors are associated for all the random variables or not.
  * Check if factors are defined for each factor node or not.
  * Check if cardinality information for all the variables is available or not.
  * Check if cardinality of random variable remains same across all the
    factors.
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code: def check_model(self):
      """
      Check the model for various errors. This method checks for the following
      errors. In the same time it also updates the cardinalities of all the
      random variables.
  
      * Check whether bipartite property of factor graph is still maintained
        or not.
      * Check whether factors are associated for all the random variables or not.
      * Check if factors are defined for each factor node or not.
      * Check if cardinality information for all the variables is available or not.
      * Check if cardinality of random variable remains same across all the
        factors.
      """
      variable_nodes = set(
          [x for factor in self.factors for x in factor.scope()]
      )
      factor_nodes = set(self.nodes()) - variable_nodes
  
      if not all(
          isinstance(factor_node, DiscreteFactor)
          for factor_node in factor_nodes
      ):
          raise ValueError(
              "Factors not associated for all the random variables"
          )
  
      if not (bipartite.is_bipartite(self)) or not (
          bipartite.is_bipartite_node_set(self, variable_nodes)
          or bipartite.is_bipartite_node_set(self, variable_nodes)
      ):
          raise ValueError(
              "Edges can only be between variables and factors"
          )
  
      if len(factor_nodes) != len(self.factors):
          raise ValueError(
              "Factors not associated with all the factor nodes."
          )
  
      cardinalities = self.get_cardinality()
      if len(variable_nodes) != len(cardinalities):
          raise ValueError("Factors for all the variables not defined")
  
      for factor in self.factors:
          for variable, cardinality in zip(
              factor.scope(), factor.cardinality
          ):
              if cardinalities[variable] != cardinality:
                  raise ValueError(
                      f"Cardinality of variable {variable} not matching among factors"
                  )
  
      return True
  
imports: import itertools
  from collections import defaultdict
  import numpy
  from networkx.algorithms import bipartite
  from pgmpy.models.MarkovNetwork import MarkovNetwork
  from pgmpy.base import UndirectedGraph
  from pgmpy.factors.discrete import DiscreteFactor
  from pgmpy.factors import factor_product
label_desc: Use image node_id 6 for calling the FactorGraph obj's underlying member method code with example usage: obj.check_model() and returns: True