#! /usr/bin/env python3
#
def sauer_incidence ( ):

#*****************************************************************************80
#
## sauer_incidence() sets up the incidence matrix associated with a network.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 April 2022
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Timothy Sauer,
#    "How search engines rate page quality",
#    Numerical Analysis,
#    Pearson, 2006.
#    ISBN: 0-321-2698-9,
#    LC: QA297.S348
#
#  Output:
#
#    real A(15,15): a sparse incidence matrix.
#
  import numpy as np

  A = np.array ( [ \
    [ 0,1,0,0,0,0,0,0,1,0,0,0,0,0,0 ], \
    [ 0,0,1,0,1,0,1,0,0,0,0,0,0,0,0 ], \
    [ 0,1,0,0,0,1,0,1,0,0,0,0,0,0,0 ], \
    [ 0,0,1,0,0,0,0,0,0,0,0,1,0,0,0 ], \
    [ 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0 ], \
    [ 0,0,0,0,0,0,0,0,0,1,1,0,0,0,0 ], \
    [ 0,0,0,0,0,0,0,0,0,1,1,0,0,0,0 ], \
    [ 0,0,0,1,0,0,0,0,0,0,1,0,0,0,0 ], \
    [ 0,0,0,0,1,1,0,0,0,1,0,0,0,0,0 ], \
    [ 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0 ], \
    [ 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 ], \
    [ 0,0,0,0,0,0,1,1,0,0,1,0,0,0,0 ], \
    [ 0,0,0,0,0,0,0,0,1,0,0,0,0,1,0 ], \
    [ 0,0,0,0,0,0,0,0,0,1,1,0,1,0,1 ], \
    [ 0,0,0,0,0,0,0,0,0,0,0,1,0,1,0 ] ] )

  return A

if ( __name__ == '__main__' ):
  A = sauer_incidence ( )
  print ( A )