# Source code for qiskit_optimization.applications.graph_partition

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2021.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""An application class for the graph partitioning."""
from typing import Dict, List, Optional, Union
import networkx as nx
import numpy as np
from docplex.mp.model import Model
from qiskit_optimization.algorithms import OptimizationResult
from qiskit_optimization.problems.quadratic_program import QuadraticProgram
from qiskit_optimization.translators import from_docplex_mp
from .graph_optimization_application import GraphOptimizationApplication
[docs]class GraphPartition(GraphOptimizationApplication):
"""Optimization application for the "graph partition" [1] problem based on a NetworkX graph.
References:
[1]: "Graph partition", https://en.wikipedia.org/wiki/Graph_partition
"""
[docs] def to_quadratic_program(self) -> QuadraticProgram:
"""Convert a graph partition instance into a
:class:`~qiskit_optimization.problems.QuadraticProgram`
Returns:
The :class:`~qiskit_optimization.problems.QuadraticProgram` created
from the graph partition instance.
"""
mdl = Model(name="Graph partition")
n = self._graph.number_of_nodes()
x = {i: mdl.binary_var(name=f"x_{i}") for i in range(n)}
for w, v in self._graph.edges:
self._graph.edges[w, v].setdefault("weight", 1)
objective = mdl.sum(
self._graph.edges[i, j]["weight"] * (x[i] + x[j] - 2 * x[i] * x[j])
for i, j in self._graph.edges
)
mdl.minimize(objective)
mdl.add_constraint(mdl.sum([x[i] for i in x]) == n // 2)
op = from_docplex_mp(mdl)
return op
[docs] def interpret(self, result: Union[OptimizationResult, np.ndarray]) -> List[List[int]]:
"""Interpret a result as a list of node indices
Args:
result : The calculated result of the problem
Returns:
A list of node indices divided into two groups.
"""
x = self._result_to_x(result)
partition = [[], []] # type: List[List[int]]
for i, value in enumerate(x):
if value == 0:
partition[0].append(i)
else:
partition[1].append(i)
return partition
def _draw_result(
self,
result: Union[OptimizationResult, np.ndarray],
pos: Optional[Dict[int, np.ndarray]] = None,
) -> None:
"""Draw the result with colors
Args:
result : The calculated result for the problem
pos: The positions of nodes
"""
x = self._result_to_x(result)
nx.draw(self._graph, node_color=self._node_colors(x), pos=pos, with_labels=True)
def _node_colors(self, x: np.ndarray) -> List[str]:
# Return a list of strings for draw.
# Color a node with red when the corresponding variable is 1.
# Otherwise color it with blue.
return ["r" if x[node] else "b" for node in self._graph.nodes]
```