code: def _sparse_fruchterman_reingold(
      A,
      k=None,
      pos=None,
      fixed=None,
      iterations=50,
      threshold=1e-4,
      dim=2,
      seed=None,
  ):
      # Position nodes in adjacency matrix A using Fruchterman-Reingold
      # Entry point for NetworkX graph is fruchterman_reingold_layout()
      # Sparse version
      import numpy as np
      import scipy as sp
  
      try:
          nnodes, _ = A.shape
      except AttributeError as err:
          msg = "fruchterman_reingold() takes an adjacency matrix as input"
          raise nx.NetworkXError(msg) from err
      # make sure we have a LIst of Lists representation
      try:
          A = A.tolil()
      except AttributeError:
          A = (sp.sparse.coo_array(A)).tolil()
  
      if pos is None:
          # random initial positions
          pos = np.asarray(seed.rand(nnodes, dim), dtype=A.dtype)
      else:
          # make sure positions are of same type as matrix
          pos = pos.astype(A.dtype)
  
      # no fixed nodes
      if fixed is None:
          fixed = []
  
      # optimal distance between nodes
      if k is None:
          k = np.sqrt(1.0 / nnodes)
      # the initial "temperature"  is about .1 of domain area (=1x1)
      # this is the largest step allowed in the dynamics.
      t = (
          max(
              max(pos.T[0]) - min(pos.T[0]),
              max(pos.T[1]) - min(pos.T[1]),
          )
          * 0.1
      )
      # simple cooling scheme.
      # linearly step down by dt on each iteration so last iteration is size dt.
      dt = t / (iterations + 1)
  
      displacement = np.zeros((dim, nnodes))
      for iteration in range(iterations):
          displacement *= 0
          # loop over rows
          for i in range(A.shape[0]):
              if i in fixed:
                  continue
              # difference between this row's node position and all others
              delta = (pos[i] - pos).T
              # distance between points
              distance = np.sqrt((delta**2).sum(axis=0))
              # enforce minimum distance of 0.01
              distance = np.where(distance < 0.01, 0.01, distance)
              # the adjacency matrix row
              Ai = A.getrowview(
                  i
              ).toarray()  # TODO: revisit w/ sparse 1D container
              # displacement "force"
              displacement[:, i] += (
                  delta * (k * k / distance**2 - Ai * distance / k)
              ).sum(axis=1)
          # update positions
          length = np.sqrt((displacement**2).sum(axis=0))
          length = np.where(length < 0.01, 0.1, length)
          delta_pos = (displacement * t / length).T
          pos += delta_pos
          # cool temperature
          t -= dt
          if (np.linalg.norm(delta_pos) / nnodes) < threshold:
              break
      return pos
  
imports: import networkx
  from networkx.utils import np_random_state
label_desc: Use image node_id 8 for calling a global function with example usage: _sparse_fruchterman_reingold(A, k, pos, fixed, iterations, threshold, dim, seed) and returns: pos