def adjacency_to_google ( A ):

#*****************************************************************************80
#
## adjacency_to_google() converts an adjacency matrix to a Google transition matrix.
#
#  Discussion:
#
#    If the input adjacency matrix has a node I with no connectivity,
#    (A(I,1:N) = 0) then we artificially set T(1:N,I)=1/N, so that
#    the transition matrix property of having unit column sums is preserved.
#
#    For nodes with connectivity, we assume that 85 percent of the time
#    we will take a link at random, and 15 percent of the time, we will
#    jump to an arbitrary link.  
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    12 February 2025
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer A(N,N): the adjacency matrix.
#
#  Output:
#
#    real G(N,N): the Google matrix.
#
  import numpy as np

  n = A.shape[0]

  G = np.zeros ( [ n, n ] )

  s = np.sum ( A, axis = 1 )

  for i in range ( 0, n ):
    if ( s[i] == 0.0 ):
      G[i,:] = 1.0 / n
    else:
      G[i,:] = 0.85 * A[i,:] / s[i] + 0.15 / n

  G = np.transpose ( G )

  return G