Project: s41467-024-55462-w | Function: MCES_ILP (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Calculates the exact distance between two molecular graphs using Integer Linear Programming (ILP) to solve the Maximum Common Edge Subgraph problem. Takes two networkx graphs representing molecules and returns the MCES distance.

**KEY TERMS:** {
  "nodepairs": "node mapping variables",
  "edgepairs": "edge mapping variables",
  "MCES": "Maximum Common Edge Subgraph",
  "weight": "edge weights/bond orders"
}

**CONTEXT CODE:** # -*- coding: utf-8 -*-
"""
Created on Mon Oct  5 17:17:41 2020

@author: seipp
"""
import pulp
import networkx as nx

def MCES_ILP(G1, G2, threshold, solver='default', solver_options={}, no_ilp_threshold=False):
    """
     Calculates the exact distance between two molecules using an ILP

     Parameters
     ----------
     G1 : networkx.classes.graph.Graph
         Graph representing the first molecule.
     G2 : networkx.classes.graph.Graph
         Graph representing the second molecule.
     threshold : float
         Threshold for the comparison. Exact distance is only calculated if the distance is lower than the threshold.
     solver: string
         ILP-solver used for solving MCES. Example:CPLEX_CMD
     solver_options: dict
         additional options to pass to solvers. Example: threads=1, msg=False for better multi-threaded performance
     no_ilp_threshold: bool
         if true, always return exact distance even if it is below the threshold (slower)

     Returns:
     -------
     float
         Distance between the molecules
     int
         Type of Distance:
             1 : Exact Distance
             2 : Lower bound (If the exact distance is above the threshold)

    """
    raise NotImplementedError("Function implementation has been masked")


Complete the function implementation replacing "raise NotImplementedError".