diff env/lib/python3.9/site-packages/networkx/algorithms/distance_regular.py @ 0:4f3585e2f14b draft default tip

"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/env/lib/python3.9/site-packages/networkx/algorithms/distance_regular.py	Mon Mar 22 18:12:50 2021 +0000
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+"""
+=======================
+Distance-regular graphs
+=======================
+"""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+from .distance_measures import diameter
+
+__all__ = [
+    "is_distance_regular",
+    "is_strongly_regular",
+    "intersection_array",
+    "global_parameters",
+]
+
+
+def is_distance_regular(G):
+    """Returns True if the graph is distance regular, False otherwise.
+
+    A connected graph G is distance-regular if for any nodes x,y
+    and any integers i,j=0,1,...,d (where d is the graph
+    diameter), the number of vertices at distance i from x and
+    distance j from y depends only on i,j and the graph distance
+    between x and y, independently of the choice of x and y.
+
+    Parameters
+    ----------
+    G: Networkx graph (undirected)
+
+    Returns
+    -------
+    bool
+      True if the graph is Distance Regular, False otherwise
+
+    Examples
+    --------
+    >>> G = nx.hypercube_graph(6)
+    >>> nx.is_distance_regular(G)
+    True
+
+    See Also
+    --------
+    intersection_array, global_parameters
+
+    Notes
+    -----
+    For undirected and simple graphs only
+
+    References
+    ----------
+    .. [1] Brouwer, A. E.; Cohen, A. M.; and Neumaier, A.
+        Distance-Regular Graphs. New York: Springer-Verlag, 1989.
+    .. [2] Weisstein, Eric W. "Distance-Regular Graph."
+        http://mathworld.wolfram.com/Distance-RegularGraph.html
+
+    """
+    try:
+        intersection_array(G)
+        return True
+    except nx.NetworkXError:
+        return False
+
+
+def global_parameters(b, c):
+    """Returns global parameters for a given intersection array.
+
+    Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d
+    such that for any 2 vertices x,y in G at a distance i=d(x,y), there
+    are exactly c_i neighbors of y at a distance of i-1 from x and b_i
+    neighbors of y at a distance of i+1 from x.
+
+    Thus, a distance regular graph has the global parameters,
+    [[c_0,a_0,b_0],[c_1,a_1,b_1],......,[c_d,a_d,b_d]] for the
+    intersection array  [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d]
+    where a_i+b_i+c_i=k , k= degree of every vertex.
+
+    Parameters
+    ----------
+    b : list
+
+    c : list
+
+    Returns
+    -------
+    iterable
+       An iterable over three tuples.
+
+    Examples
+    --------
+    >>> G = nx.dodecahedral_graph()
+    >>> b, c = nx.intersection_array(G)
+    >>> list(nx.global_parameters(b, c))
+    [(0, 0, 3), (1, 0, 2), (1, 1, 1), (1, 1, 1), (2, 0, 1), (3, 0, 0)]
+
+    References
+    ----------
+    .. [1] Weisstein, Eric W. "Global Parameters."
+       From MathWorld--A Wolfram Web Resource.
+       http://mathworld.wolfram.com/GlobalParameters.html
+
+    See Also
+    --------
+    intersection_array
+    """
+    return ((y, b[0] - x - y, x) for x, y in zip(b + [0], [0] + c))
+
+
+@not_implemented_for("directed", "multigraph")
+def intersection_array(G):
+    """Returns the intersection array of a distance-regular graph.
+
+    Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d
+    such that for any 2 vertices x,y in G at a distance i=d(x,y), there
+    are exactly c_i neighbors of y at a distance of i-1 from x and b_i
+    neighbors of y at a distance of i+1 from x.
+
+    A distance regular graph's intersection array is given by,
+    [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d]
+
+    Parameters
+    ----------
+    G: Networkx graph (undirected)
+
+    Returns
+    -------
+    b,c: tuple of lists
+
+    Examples
+    --------
+    >>> G = nx.icosahedral_graph()
+    >>> nx.intersection_array(G)
+    ([5, 2, 1], [1, 2, 5])
+
+    References
+    ----------
+    .. [1] Weisstein, Eric W. "Intersection Array."
+       From MathWorld--A Wolfram Web Resource.
+       http://mathworld.wolfram.com/IntersectionArray.html
+
+    See Also
+    --------
+    global_parameters
+    """
+    # test for regular graph (all degrees must be equal)
+    degree = iter(G.degree())
+    (_, k) = next(degree)
+    for _, knext in degree:
+        if knext != k:
+            raise nx.NetworkXError("Graph is not distance regular.")
+        k = knext
+    path_length = dict(nx.all_pairs_shortest_path_length(G))
+    diameter = max([max(path_length[n].values()) for n in path_length])
+    bint = {}  # 'b' intersection array
+    cint = {}  # 'c' intersection array
+    for u in G:
+        for v in G:
+            try:
+                i = path_length[u][v]
+            except KeyError as e:  # graph must be connected
+                raise nx.NetworkXError("Graph is not distance regular.") from e
+            # number of neighbors of v at a distance of i-1 from u
+            c = len([n for n in G[v] if path_length[n][u] == i - 1])
+            # number of neighbors of v at a distance of i+1 from u
+            b = len([n for n in G[v] if path_length[n][u] == i + 1])
+            # b,c are independent of u and v
+            if cint.get(i, c) != c or bint.get(i, b) != b:
+                raise nx.NetworkXError("Graph is not distance regular")
+            bint[i] = b
+            cint[i] = c
+    return (
+        [bint.get(j, 0) for j in range(diameter)],
+        [cint.get(j + 1, 0) for j in range(diameter)],
+    )
+
+
+# TODO There is a definition for directed strongly regular graphs.
+@not_implemented_for("directed", "multigraph")
+def is_strongly_regular(G):
+    """Returns True if and only if the given graph is strongly
+    regular.
+
+    An undirected graph is *strongly regular* if
+
+    * it is regular,
+    * each pair of adjacent vertices has the same number of neighbors in
+      common,
+    * each pair of nonadjacent vertices has the same number of neighbors
+      in common.
+
+    Each strongly regular graph is a distance-regular graph.
+    Conversely, if a distance-regular graph has diameter two, then it is
+    a strongly regular graph. For more information on distance-regular
+    graphs, see :func:`is_distance_regular`.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    Returns
+    -------
+    bool
+        Whether `G` is strongly regular.
+
+    Examples
+    --------
+
+    The cycle graph on five vertices is strongly regular. It is
+    two-regular, each pair of adjacent vertices has no shared neighbors,
+    and each pair of nonadjacent vertices has one shared neighbor::
+
+        >>> G = nx.cycle_graph(5)
+        >>> nx.is_strongly_regular(G)
+        True
+
+    """
+    # Here is an alternate implementation based directly on the
+    # definition of strongly regular graphs:
+    #
+    #     return (all_equal(G.degree().values())
+    #             and all_equal(len(common_neighbors(G, u, v))
+    #                           for u, v in G.edges())
+    #             and all_equal(len(common_neighbors(G, u, v))
+    #                           for u, v in non_edges(G)))
+    #
+    # We instead use the fact that a distance-regular graph of diameter
+    # two is strongly regular.
+    return is_distance_regular(G) and diameter(G) == 2