Sun Mar 12 15:10:13 2023

graph_adj_test():
  Python version:3.8.10
  Test graph_adj().

graph_adj_degree_test():
  graph_adj_degree() computes the degree of the nodes;

  The graph adjacency matrix:
[[0 0 1 0 0 0 1 0 0 1]
 [0 0 0 0 1 0 0 0 0 1]
 [1 0 0 0 0 1 0 0 1 0]
 [0 0 0 0 0 0 1 1 0 0]
 [0 1 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 1 0]
 [1 0 0 1 0 0 0 0 0 0]
 [0 0 0 1 0 0 0 0 0 1]
 [0 0 1 0 0 1 0 0 0 0]
 [1 1 0 0 0 0 0 1 0 0]]

  The node degrees:
[3 2 3 2 1 2 2 2 2 3]

graph_adj_distance_from_node_test():
  graph_adj_distance_from_node() computes the distance
  from one node to all other nodes in a graph;

  The graph adjacency matrix:
[[0 0 1 0 0 0 1 0 0 1]
 [0 0 0 0 1 0 0 0 0 1]
 [1 0 0 0 0 1 0 0 1 0]
 [0 0 0 0 0 0 1 1 0 0]
 [0 1 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 1 0]
 [1 0 0 1 0 0 0 0 0 0]
 [0 0 0 1 0 0 0 0 0 1]
 [0 0 1 0 0 1 0 0 0 0]
 [1 1 0 0 0 0 0 1 0 0]]

  Distance from node 6
[1. 3. 2. 1. 4. 3. 0. 2. 3. 2.]

graph_adj_edge_count_test():
  graph_adj_edge_count() counts edges in a graph.

  Adjacency matrix for bush example:
[[0 0 0 1 0 0 0]
 [0 0 0 0 1 0 0]
 [0 0 0 0 1 0 0]
 [1 0 0 0 1 1 1]
 [0 1 1 1 0 0 0]
 [0 0 0 1 0 0 0]
 [0 0 0 1 0 0 0]]

  Number of edges is 6

graph_adj_edge_select_test():
  graph_adj_edge_select() selects an edge from
  a graph defined by an adjacency matrix.

  Adjacency matrix for bush example
[[0 0 0 1 0 0 0]
 [0 0 0 0 1 0 0]
 [0 0 0 0 1 0 0]
 [1 0 0 0 1 1 1]
 [0 1 1 1 0 0 0]
 [0 0 0 1 0 0 0]
 [0 0 0 1 0 0 0]]

  An edge of this graph extends from
  node 6 to node 3

graph_adj_is_eulerian_test( ):
  graph_adj_is_eulerian() determines whether a graph
  is eulerian.

  Matrix A:
[[0 0 1 0 0 0 1 0 0 1]
 [0 0 0 0 1 0 0 0 0 1]
 [1 0 0 0 0 1 0 0 1 0]
 [0 0 0 0 0 0 1 1 0 0]
 [0 1 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 1 0]
 [1 0 0 1 0 0 0 0 0 0]
 [0 0 0 1 0 0 0 0 0 1]
 [0 0 1 0 0 1 0 0 0 0]
 [1 1 0 0 0 0 0 1 0 0]]
  circuit_eulerian =  False
  path_eulerian    =  False

  Matrix B:
[[0 0 1 0 1 0 1 0 0 1]
 [0 0 0 0 1 0 0 0 0 1]
 [1 0 0 0 0 1 0 0 1 0]
 [0 0 0 0 0 0 1 1 0 0]
 [1 1 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 1 0]
 [1 0 0 1 0 0 0 0 0 0]
 [0 0 0 1 0 0 0 0 0 1]
 [0 0 1 0 0 1 0 0 0 0]
 [1 1 0 0 0 0 0 1 0 0]]
  circuit_eulerian =  False
  path_eulerian    =  True

  Matrix C:
[[0 0 1 0 1 0 1 0 0 1]
 [0 0 0 0 1 0 0 0 0 1]
 [1 0 0 0 0 1 0 0 1 1]
 [0 0 0 0 0 0 1 1 0 0]
 [1 1 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 1 0]
 [1 0 0 1 0 0 0 0 0 0]
 [0 0 0 1 0 0 0 0 0 1]
 [0 0 1 0 0 1 0 0 0 0]
 [1 1 1 0 0 0 0 1 0 0]]
  circuit_eulerian =  True
  path_eulerian    =  True

graph_adj_is_nodewise_connected_test( ):
  A graph is to be checked for nodewise connectedness.
  graph_adj_is_nodewise_connected_breadth() uses breadth-first search.
  graph_adj_is_nodewise_connected_depth() uses depth-first search.
  graph_adj_is_nodewise_connected_walks() counts the walks from node to node.

  Results for graph A (not connected!)
    breadth:  False
    depth:    False
    walks:    False

  Results for graph B (connected!)
    breadth:  True
    depth:    True
    walks:    True

graph_adj_random_test():
  graph_adj_random() returns a random graph, for which the
  probability of an edge between nodes I and J is PROB.

  Random graph # 1
  node_num    =  100
  edge_num    =  1231
  edge_max    =  4950
  ratio       =  0.24868686868686868
  prob        =  0.25

  Random graph # 2
  node_num    =  100
  edge_num    =  2492
  edge_max    =  4950
  ratio       =  0.5034343434343435
  prob        =  0.5

  Random graph # 3
  node_num    =  100
  edge_num    =  3744
  edge_max    =  4950
  ratio       =  0.7563636363636363
  prob        =  0.75

graph_adj_transitive_closure_test():
  graph_adj_transitive_closure() finds the transitive
  closure of a graph;

  Adjacency matrix A:
[[1 0 0 1 1 0 0 0]
 [0 1 0 0 0 0 0 0]
 [0 0 1 0 0 0 1 1]
 [1 0 0 1 1 0 0 0]
 [1 0 0 1 1 1 0 0]
 [0 0 0 0 1 1 0 0]
 [0 0 1 0 0 0 1 0]
 [0 0 1 0 0 0 0 1]]

  Adjacency for transitive closure:
[[1 0 0 1 1 1 0 0]
 [0 1 0 0 0 0 0 0]
 [0 0 1 0 0 0 1 1]
 [1 0 0 1 1 1 0 0]
 [1 0 0 1 1 1 0 0]
 [1 0 0 1 1 1 0 0]
 [0 0 1 0 0 0 1 1]
 [0 0 1 0 0 0 1 1]]

graph_adj_walks_test( ):
  Count the walks from node I to node J of any length.

  Walks for graph A:
[[141.  33.   0. 107. 181.   0. 181.  74.   0.]
 [ 33.  34.   0. 107.  37.   0.  37.  74.   0.]
 [  0.   0. 171.   0.   0. 170.   0.   0. 170.]
 [107. 107.   0. 396. 144.   0. 144. 288.   0.]
 [181.  37.   0. 144. 252.   0. 251. 107.   0.]
 [  0.   0. 170.   0.   0. 171.   0.   0. 170.]
 [181.  37.   0. 144. 251.   0. 252. 107.   0.]
 [ 74.  74.   0. 288. 107.   0. 107. 215.   0.]
 [  0.   0. 170.   0.   0. 170.   0.   0. 171.]]

  Graph B:
[[0 1 0 1 0 0 0 0 0]
 [1 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 1]
 [1 0 0 0 1 0 1 0 0]
 [0 0 0 1 0 1 0 1 0]
 [0 0 0 0 1 0 0 0 1]
 [0 0 0 1 0 0 0 1 0]
 [0 0 0 0 1 0 1 0 0]
 [0 0 1 0 0 1 0 0 0]]

  Walks for graph B:
[[156.  34.  10. 121. 266.  58. 208.  87.  68.]
 [ 34.  35.  10. 121.  48.  58.  39.  87.  10.]
 [ 10.  10.  24.  58.  31.  54.  17.  48.  23.]
 [121. 121.  58. 509. 218. 276. 169. 387.  58.]
 [266.  48.  31. 218. 518. 129. 388. 170. 160.]
 [ 58.  58.  54. 276. 129. 184.  89. 218.  54.]
 [208.  39.  17. 169. 388.  89. 300. 130. 106.]
 [ 87.  87.  48. 387. 170. 218. 130. 301.  48.]
 [ 68.  10.  23.  58. 160.  54. 106.  48.  78.]]

matrix_is_adjacency_test( ):
  matrix_is_adjacency() requires that a matrix A be:
  * square
  * symmetric
  * zero on the diagonal
  * only have 0 or 1 as values.

  Matrix A:
[[0 0 1]
 [0 0 1]
 [1 1 0]
 [0 0 1]]
  matrix_is_adjacency(A) =  False

  Matrix B:
[[0 0 1]
 [1 0 1]
 [1 1 0]]
  matrix_is_adjacency(B) =  False

  Matrix C:
[[1 0 1]
 [0 1 1]
 [1 1 1]]
  matrix_is_adjacency(C) =  False

  Matrix D:
[[0 1 2]
 [1 0 1]
 [2 1 0]]
  matrix_is_adjacency(D) =  False

  Matrix E:
[[0 1 1]
 [1 0 1]
 [1 1 0]]
  matrix_is_adjacency(E) =  True

graph_adj_test():
  Normal end of execution.
Sun Mar 12 15:10:13 2023