code: def spectral_graph_forge(
      G, alpha, transformation="identity", seed=None
  ):
      """Returns a random simple graph with spectrum resembling that of `G`
  
      This algorithm, called Spectral Graph Forge (SGF), computes the
      eigenvectors of a given graph adjacency matrix, filters them and
      builds a random graph with a similar eigenstructure.
      SGF has been proved to be particularly useful for synthesizing
      realistic social networks and it can also be used to anonymize
      graph sensitive data.
  
      Parameters
      ----------
      G : Graph
      alpha :  float
          Ratio representing the percentage of eigenvectors of G to consider,
          values in [0,1].
      transformation : string, optional
          Represents the intended matrix linear transformation, possible values
          are 'identity' and 'modularity'
      seed : integer, random_state, or None (default)
          Indicator of numpy random number generation state.
          See :ref:`Randomness<randomness>`.
  
      Returns
      -------
      H : Graph
          A graph with a similar eigenvector structure of the input one.
  
      Raises
      ------
      NetworkXError
          If transformation has a value different from 'identity' or 'modularity'
  
      Notes
      -----
      Spectral Graph Forge (SGF) generates a random simple graph resembling the
      global properties of the given one.
      It leverages the low-rank approximation of the associated adjacency matrix
      driven by the *alpha* precision parameter.
      SGF preserves the number of nodes of the input graph and their ordering.
      This way, nodes of output graphs resemble the properties of the input one
      and attributes can be directly mapped.
  
      It considers the graph adjacency matrices which can optionally be
      transformed to other symmetric real matrices (currently transformation
      options include *identity* and *modularity*).
      The *modularity* transformation, in the sense of Newman's modularity matrix
      allows the focusing on community structure related properties of the graph.
  
      SGF applies a low-rank approximation whose fixed rank is computed from the
      ratio *alpha* of the input graph adjacency matrix dimension.
      This step performs a filtering on the input eigenvectors similar to the low
      pass filtering common in telecommunications.
  
      The filtered values (after truncation) are used as input to a Bernoulli
      sampling for constructing a random adjacency matrix.
  
      References
      ----------
      ..  [1] L. Baldesi, C. T. Butts, A. Markopoulou, "Spectral Graph Forge:
          Graph Generation Targeting Modularity", IEEE Infocom, '18.
          https://arxiv.org/abs/1801.01715
      ..  [2] M. Newman, "Networks: an introduction", Oxford university press,
          2010
  
      Examples
      --------
      >>> G = nx.karate_club_graph()
      >>> H = nx.spectral_graph_forge(G, 0.3)
      >>>
      """
      import numpy as np
      import scipy as sp
  
      available_transformations = ["identity", "modularity"]
      alpha = np.clip(alpha, 0, 1)
      A = nx.to_numpy_array(G)
      n = A.shape[1]
      level = round(n * alpha)
  
      if transformation not in available_transformations:
          msg = f"{transformation!r} is not a valid transformation. "
          msg += f"Transformations: {available_transformations}"
          raise nx.NetworkXError(msg)
  
      K = np.ones((1, n)) @ A
  
      B = A
      if transformation == "modularity":
          B -= K.T @ K / K.sum()
  
      # Compute low-rank approximation of B
      evals, evecs = np.linalg.eigh(B)
      k = np.argsort(np.abs(evals))[
          ::-1
      ]  # indices of evals in descending order
      evecs[
          :, k[np.arange(level, n)]
      ] = 0  # set smallest eigenvectors to 0
      B = evecs @ np.diag(evals) @ evecs.T
  
      if transformation == "modularity":
          B += K.T @ K / K.sum()
  
      B = np.clip(B, 0, 1)
      np.fill_diagonal(B, 0)
  
      for i in range(n - 1):
          B[i, i + 1 :] = sp.stats.bernoulli.rvs(
              B[i, i + 1 :], random_state=seed
          )
          B[i + 1 :, i] = np.transpose(B[i, i + 1 :])
  
      H = nx.from_numpy_array(B)
  
      return H
  
label_desc: Use image node_id 1 for calling a global function with example usage: spectral_graph_forge(G, alpha, transformation, seed) and returns: H