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+"""Generator for Sudoku graphs
+
+This module gives a generator for n-Sudoku graphs. It can be used to develop
+algorithms for solving or generating Sudoku puzzles.
+
+A completed Sudoku grid is a 9x9 array of integers between 1 and 9, with no
+number appearing twice in the same row, column, or 3x3 box.
+
++---------+---------+---------+
+| | 8 6 4 | | 3 7 1 | | 2 5 9 |
+| | 3 2 5 | | 8 4 9 | | 7 6 1 |
+| | 9 7 1 | | 2 6 5 | | 8 4 3 |
++---------+---------+---------+
+| | 4 3 6 | | 1 9 2 | | 5 8 7 |
+| | 1 9 8 | | 6 5 7 | | 4 3 2 |
+| | 2 5 7 | | 4 8 3 | | 9 1 6 |
++---------+---------+---------+
+| | 6 8 9 | | 7 3 4 | | 1 2 5 |
+| | 7 1 3 | | 5 2 8 | | 6 9 4 |
+| | 5 4 2 | | 9 1 6 | | 3 7 8 |
++---------+---------+---------+
+
+
+The Sudoku graph is an undirected graph with 81 vertices, corresponding to
+the cells of a Sudoku grid. It is a regular graph of degree 20. Two distinct
+vertices are adjacent if and only if the corresponding cells belong to the
+same row, column, or box. A completed Sudoku grid corresponds to a vertex
+coloring of the Sudoku graph with nine colors.
+
+More generally, the n-Sudoku graph is a graph with n^4 vertices, corresponding
+to the cells of an n^2 by n^2 grid. Two distinct vertices are adjacent if and
+only if they belong to the same row, column, or n by n box.
+
+References
+----------
+.. [1] Herzberg, A. M., & Murty, M. R. (2007). Sudoku squares and chromatic
+    polynomials. Notices of the AMS, 54(6), 708-717.
+.. [2] Sander, Torsten (2009), "Sudoku graphs are integral",
+    Electronic Journal of Combinatorics, 16 (1): Note 25, 7pp, MR 2529816
+.. [3] Wikipedia contributors. "Glossary of Sudoku." Wikipedia, The Free
+    Encyclopedia, 3 Dec. 2019. Web. 22 Dec. 2019.
+"""
+
+import networkx as nx
+from networkx.exception import NetworkXError
+
+__all__ = ["sudoku_graph"]
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def sudoku_graph(n=3):
+    """Returns the n-Sudoku graph. The default value of n is 3.
+
+    The n-Sudoku graph is a graph with n^4 vertices, corresponding to the
+    cells of an n^2 by n^2 grid. Two distinct vertices are adjacent if and
+    only if they belong to the same row, column, or n-by-n box.
+
+    Parameters
+    ----------
+    n: integer
+       The order of the Sudoku graph, equal to the square root of the
+       number of rows. The default is 3.
+
+    Returns
+    -------
+    NetworkX graph
+        The n-Sudoku graph Sud(n).
+
+    Examples
+    --------
+    >>> G = nx.sudoku_graph()
+    >>> G.number_of_nodes()
+    81
+    >>> G.number_of_edges()
+    810
+    >>> sorted(G.neighbors(42))
+    [6, 15, 24, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 51, 52, 53, 60, 69, 78]
+    >>> G = nx.sudoku_graph(2)
+    >>> G.number_of_nodes()
+    16
+    >>> G.number_of_edges()
+    56
+
+    References
+    ----------
+    .. [1] Herzberg, A. M., & Murty, M. R. (2007). Sudoku squares and chromatic
+       polynomials. Notices of the AMS, 54(6), 708-717.
+    .. [2] Sander, Torsten (2009), "Sudoku graphs are integral",
+       Electronic Journal of Combinatorics, 16 (1): Note 25, 7pp, MR 2529816
+    .. [3] Wikipedia contributors. "Glossary of Sudoku." Wikipedia, The Free
+       Encyclopedia, 3 Dec. 2019. Web. 22 Dec. 2019.
+    """
+
+    if n < 0:
+        raise NetworkXError("The order must be greater than or equal to zero.")
+
+    n2 = n * n
+    n3 = n2 * n
+    n4 = n3 * n
+
+    # Construct an empty graph with n^4 nodes
+    G = nx.empty_graph(n4)
+
+    # A Sudoku graph of order 0 or 1 has no edges
+    if n < 2:
+        return G
+
+    # Add edges for cells in the same row
+    for row_no in range(n2):
+        row_start = row_no * n2
+        for j in range(1, n2):
+            for i in range(j):
+                G.add_edge(row_start + i, row_start + j)
+
+    # Add edges for cells in the same column
+    for col_no in range(n2):
+        for j in range(col_no, n4, n2):
+            for i in range(col_no, j, n2):
+                G.add_edge(i, j)
+
+    # Add edges for cells in the same box
+    for band_no in range(n):
+        for stack_no in range(n):
+            box_start = n3 * band_no + n * stack_no
+            for j in range(1, n2):
+                for i in range(j):
+                    u = box_start + (i % n) + n2 * (i // n)
+                    v = box_start + (j % n) + n2 * (j // n)
+                    G.add_edge(u, v)
+
+    return G