code: def _fix_connectivity(X, connectivity, affinity):
      """
      Fixes the connectivity matrix.
  
      The different steps are:
  
      - copies it
      - makes it symmetric
      - converts it to LIL if necessary
      - completes it if necessary.
  
      Parameters
      ----------
      X : array-like of shape (n_samples, n_features)
          Feature matrix representing `n_samples` samples to be clustered.
  
      connectivity : sparse matrix, default=None
          Connectivity matrix. Defines for each sample the neighboring samples
          following a given structure of the data. The matrix is assumed to
          be symmetric and only the upper triangular half is used.
          Default is `None`, i.e, the Ward algorithm is unstructured.
  
      affinity : {"euclidean", "precomputed"}, default="euclidean"
          Which affinity to use. At the moment `precomputed` and
          ``euclidean`` are supported. `euclidean` uses the
          negative squared Euclidean distance between points.
  
      Returns
      -------
      connectivity : sparse matrix
          The fixed connectivity matrix.
  
      n_connected_components : int
          The number of connected components in the graph.
      """
      n_samples = X.shape[0]
      if (
          connectivity.shape[0] != n_samples
          or connectivity.shape[1] != n_samples
      ):
          raise ValueError(
              "Wrong shape for connectivity matrix: %s when X is %s"
              % (connectivity.shape, X.shape)
          )
  
      # Make the connectivity matrix symmetric:
      connectivity = connectivity + connectivity.T
  
      # Convert connectivity matrix to LIL
      if not sparse.issparse(connectivity):
          connectivity = sparse.lil_matrix(connectivity)
  
      # `connectivity` is a sparse matrix at this point
      if connectivity.format != "lil":
          connectivity = connectivity.tolil()
  
      # Compute the number of nodes
      n_connected_components, labels = connected_components(
          connectivity
      )
  
      if n_connected_components > 1:
          warnings.warn(
              "the number of connected components of the "
              "connectivity matrix is %d > 1. Completing it to avoid "
              "stopping the tree early." % n_connected_components,
              stacklevel=2,
          )
          # XXX: Can we do without completing the matrix?
          connectivity = _fix_connected_components(
              X=X,
              graph=connectivity,
              n_connected_components=n_connected_components,
              component_labels=labels,
              metric=affinity,
              mode="connectivity",
          )
  
      return connectivity, n_connected_components
  
imports: import warnings
  from heapq import heapify, heappop, heappush, heappushpop
  from numbers import Integral, Real
  import numpy
  from scipy import sparse
  from scipy.sparse.csgraph import connected_components
  from ..base import BaseEstimator, ClassNamePrefixFeaturesOutMixin, ClusterMixin, _fit_context
  from ..metrics import DistanceMetric
  from ..metrics._dist_metrics import METRIC_MAPPING64
  from ..metrics.pairwise import _VALID_METRICS, paired_distances
  from ..utils import check_array
  from ..utils._fast_dict import IntFloatDict
  from ..utils._param_validation import HasMethods, Hidden, Interval, StrOptions, validate_params
  from ..utils.graph import _fix_connected_components
  from ..utils.validation import check_memory
  from .None import _hierarchical_fast
  from ._feature_agglomeration import AgglomerationTransform
label_desc: Use image node_id 1 for calling a global function with example usage: _fix_connectivity(X, connectivity, affinity) and returns: connectivity,  n_connected_components