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0000000000000000000000000000000000000000..46d6300649d3b4658a7263cad04354988b4da312 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/base_test.py @@ -0,0 +1,81 @@ +import networkx as nx + + +class BaseTestAttributeMixing: + @classmethod + def setup_class(cls): + G = nx.Graph() + G.add_nodes_from([0, 1], fish="one") + G.add_nodes_from([2, 3], fish="two") + G.add_nodes_from([4], fish="red") + G.add_nodes_from([5], fish="blue") + G.add_edges_from([(0, 1), (2, 3), (0, 4), (2, 5)]) + cls.G = G + + D = nx.DiGraph() + D.add_nodes_from([0, 1], fish="one") + D.add_nodes_from([2, 3], fish="two") + D.add_nodes_from([4], fish="red") + D.add_nodes_from([5], fish="blue") + D.add_edges_from([(0, 1), (2, 3), (0, 4), (2, 5)]) + cls.D = D + + M = nx.MultiGraph() + M.add_nodes_from([0, 1], fish="one") + M.add_nodes_from([2, 3], fish="two") + M.add_nodes_from([4], fish="red") + M.add_nodes_from([5], fish="blue") + M.add_edges_from([(0, 1), (0, 1), (2, 3)]) + cls.M = M + + S = nx.Graph() + S.add_nodes_from([0, 1], fish="one") + S.add_nodes_from([2, 3], fish="two") + S.add_nodes_from([4], fish="red") + S.add_nodes_from([5], fish="blue") + S.add_edge(0, 0) + S.add_edge(2, 2) + cls.S = S + + N = nx.Graph() + N.add_nodes_from([0, 1], margin=-2) + N.add_nodes_from([2, 3], margin=-2) + N.add_nodes_from([4], margin=-3) + N.add_nodes_from([5], margin=-4) + N.add_edges_from([(0, 1), (2, 3), (0, 4), (2, 5)]) + cls.N = N + + F = nx.Graph() + F.add_edges_from([(0, 3), (1, 3), (2, 3)], weight=0.5) + F.add_edge(0, 2, weight=1) + nx.set_node_attributes(F, dict(F.degree(weight="weight")), "margin") + cls.F = F + + K = nx.Graph() + K.add_nodes_from([1, 2], margin=-1) + K.add_nodes_from([3], margin=1) + K.add_nodes_from([4], margin=2) + K.add_edges_from([(3, 4), (1, 2), (1, 3)]) + cls.K = K + + +class BaseTestDegreeMixing: + @classmethod + def setup_class(cls): + cls.P4 = nx.path_graph(4) + cls.D = nx.DiGraph() + cls.D.add_edges_from([(0, 2), (0, 3), (1, 3), (2, 3)]) + cls.D2 = nx.DiGraph() + cls.D2.add_edges_from([(0, 3), (1, 0), (1, 2), (2, 4), (4, 1), (4, 3), (4, 2)]) + cls.M = nx.MultiGraph() + nx.add_path(cls.M, range(4)) + cls.M.add_edge(0, 1) + cls.S = nx.Graph() + cls.S.add_edges_from([(0, 0), (1, 1)]) + cls.W = nx.Graph() + cls.W.add_edges_from([(0, 3), (1, 3), (2, 3)], weight=0.5) + cls.W.add_edge(0, 2, weight=1) + S1 = nx.star_graph(4) + S2 = nx.star_graph(4) + cls.DS = nx.disjoint_union(S1, S2) + cls.DS.add_edge(4, 5) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/test_pairs.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/test_pairs.py new file mode 100644 index 0000000000000000000000000000000000000000..3984292be84dd7b306066809fb3c50a7cf0424f4 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/test_pairs.py @@ -0,0 +1,87 @@ +import networkx as nx + +from .base_test import BaseTestAttributeMixing, BaseTestDegreeMixing + + +class TestAttributeMixingXY(BaseTestAttributeMixing): + def test_node_attribute_xy_undirected(self): + attrxy = sorted(nx.node_attribute_xy(self.G, "fish")) + attrxy_result = sorted( + [ + ("one", "one"), + ("one", "one"), + ("two", "two"), + ("two", "two"), + ("one", "red"), + ("red", "one"), + ("blue", "two"), + ("two", "blue"), + ] + ) + assert attrxy == attrxy_result + + def test_node_attribute_xy_undirected_nodes(self): + attrxy = sorted(nx.node_attribute_xy(self.G, "fish", nodes=["one", "yellow"])) + attrxy_result = sorted([]) + assert attrxy == attrxy_result + + def test_node_attribute_xy_directed(self): + attrxy = sorted(nx.node_attribute_xy(self.D, "fish")) + attrxy_result = sorted( + [("one", "one"), ("two", "two"), ("one", "red"), ("two", "blue")] + ) + assert attrxy == attrxy_result + + def test_node_attribute_xy_multigraph(self): + attrxy = sorted(nx.node_attribute_xy(self.M, "fish")) + attrxy_result = [ + ("one", "one"), + ("one", "one"), + ("one", "one"), + ("one", "one"), + ("two", "two"), + ("two", "two"), + ] + assert attrxy == attrxy_result + + def test_node_attribute_xy_selfloop(self): + attrxy = sorted(nx.node_attribute_xy(self.S, "fish")) + attrxy_result = [("one", "one"), ("two", "two")] + assert attrxy == attrxy_result + + +class TestDegreeMixingXY(BaseTestDegreeMixing): + def test_node_degree_xy_undirected(self): + xy = sorted(nx.node_degree_xy(self.P4)) + xy_result = sorted([(1, 2), (2, 1), (2, 2), (2, 2), (1, 2), (2, 1)]) + assert xy == xy_result + + def test_node_degree_xy_undirected_nodes(self): + xy = sorted(nx.node_degree_xy(self.P4, nodes=[0, 1, -1])) + xy_result = sorted([(1, 2), (2, 1)]) + assert xy == xy_result + + def test_node_degree_xy_directed(self): + xy = sorted(nx.node_degree_xy(self.D)) + xy_result = sorted([(2, 1), (2, 3), (1, 3), (1, 3)]) + assert xy == xy_result + + def test_node_degree_xy_multigraph(self): + xy = sorted(nx.node_degree_xy(self.M)) + xy_result = sorted( + [(2, 3), (2, 3), (3, 2), (3, 2), (2, 3), (3, 2), (1, 2), (2, 1)] + ) + assert xy == xy_result + + def test_node_degree_xy_selfloop(self): + xy = sorted(nx.node_degree_xy(self.S)) + xy_result = sorted([(2, 2), (2, 2)]) + assert xy == xy_result + + def test_node_degree_xy_weighted(self): + G = nx.Graph() + G.add_edge(1, 2, weight=7) + G.add_edge(2, 3, weight=10) + xy = sorted(nx.node_degree_xy(G, weight="weight")) + xy_result = sorted([(7, 17), (17, 10), (17, 7), (10, 17)]) + assert xy == xy_result diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/__pycache__/__init__.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..dcfa8d12f09fa560dbd0a1e160e22346c7d46aff Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/__pycache__/__init__.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/__pycache__/greedy_coloring.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/__pycache__/greedy_coloring.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..1226c6ac8b81bf0517645eac0de1f5a9a9843e3e Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/__pycache__/greedy_coloring.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/equitable_coloring.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/equitable_coloring.py new file mode 100644 index 0000000000000000000000000000000000000000..e464a07447045fcdaa8e7ca4ea56552fb00e2826 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/equitable_coloring.py @@ -0,0 +1,505 @@ +""" +Equitable coloring of graphs with bounded degree. +""" + +from collections import defaultdict + +import networkx as nx + +__all__ = ["equitable_color"] + + +@nx._dispatchable +def is_coloring(G, coloring): + """Determine if the coloring is a valid coloring for the graph G.""" + # Verify that the coloring is valid. + return all(coloring[s] != coloring[d] for s, d in G.edges) + + +@nx._dispatchable +def is_equitable(G, coloring, num_colors=None): + """Determines if the coloring is valid and equitable for the graph G.""" + + if not is_coloring(G, coloring): + return False + + # Verify whether it is equitable. + color_set_size = defaultdict(int) + for color in coloring.values(): + color_set_size[color] += 1 + + if num_colors is not None: + for color in range(num_colors): + if color not in color_set_size: + # These colors do not have any vertices attached to them. + color_set_size[color] = 0 + + # If there are more than 2 distinct values, the coloring cannot be equitable + all_set_sizes = set(color_set_size.values()) + if len(all_set_sizes) == 0 and num_colors is None: # Was an empty graph + return True + elif len(all_set_sizes) == 1: + return True + elif len(all_set_sizes) == 2: + a, b = list(all_set_sizes) + return abs(a - b) <= 1 + else: # len(all_set_sizes) > 2: + return False + + +def make_C_from_F(F): + C = defaultdict(list) + for node, color in F.items(): + C[color].append(node) + + return C + + +def make_N_from_L_C(L, C): + nodes = L.keys() + colors = C.keys() + return { + (node, color): sum(1 for v in L[node] if v in C[color]) + for node in nodes + for color in colors + } + + +def make_H_from_C_N(C, N): + return { + (c1, c2): sum(1 for node in C[c1] if N[(node, c2)] == 0) for c1 in C for c2 in C + } + + +def change_color(u, X, Y, N, H, F, C, L): + """Change the color of 'u' from X to Y and update N, H, F, C.""" + assert F[u] == X and X != Y + + # Change the class of 'u' from X to Y + F[u] = Y + + for k in C: + # 'u' witnesses an edge from k -> Y instead of from k -> X now. + if N[u, k] == 0: + H[(X, k)] -= 1 + H[(Y, k)] += 1 + + for v in L[u]: + # 'v' has lost a neighbor in X and gained one in Y + N[(v, X)] -= 1 + N[(v, Y)] += 1 + + if N[(v, X)] == 0: + # 'v' witnesses F[v] -> X + H[(F[v], X)] += 1 + + if N[(v, Y)] == 1: + # 'v' no longer witnesses F[v] -> Y + H[(F[v], Y)] -= 1 + + C[X].remove(u) + C[Y].append(u) + + +def move_witnesses(src_color, dst_color, N, H, F, C, T_cal, L): + """Move witness along a path from src_color to dst_color.""" + X = src_color + while X != dst_color: + Y = T_cal[X] + # Move _any_ witness from X to Y = T_cal[X] + w = next(x for x in C[X] if N[(x, Y)] == 0) + change_color(w, X, Y, N=N, H=H, F=F, C=C, L=L) + X = Y + + +@nx._dispatchable(mutates_input=True) +def pad_graph(G, num_colors): + """Add a disconnected complete clique K_p such that the number of nodes in + the graph becomes a multiple of `num_colors`. + + Assumes that the graph's nodes are labelled using integers. + + Returns the number of nodes with each color. + """ + + n_ = len(G) + r = num_colors - 1 + + # Ensure that the number of nodes in G is a multiple of (r + 1) + s = n_ // (r + 1) + if n_ != s * (r + 1): + p = (r + 1) - n_ % (r + 1) + s += 1 + + # Complete graph K_p between (imaginary) nodes [n_, ... , n_ + p] + K = nx.relabel_nodes(nx.complete_graph(p), {idx: idx + n_ for idx in range(p)}) + G.add_edges_from(K.edges) + + return s + + +def procedure_P(V_minus, V_plus, N, H, F, C, L, excluded_colors=None): + """Procedure P as described in the paper.""" + + if excluded_colors is None: + excluded_colors = set() + + A_cal = set() + T_cal = {} + R_cal = [] + + # BFS to determine A_cal, i.e. colors reachable from V- + reachable = [V_minus] + marked = set(reachable) + idx = 0 + + while idx < len(reachable): + pop = reachable[idx] + idx += 1 + + A_cal.add(pop) + R_cal.append(pop) + + # TODO: Checking whether a color has been visited can be made faster by + # using a look-up table instead of testing for membership in a set by a + # logarithmic factor. + next_layer = [] + for k in C: + if ( + H[(k, pop)] > 0 + and k not in A_cal + and k not in excluded_colors + and k not in marked + ): + next_layer.append(k) + + for dst in next_layer: + # Record that `dst` can reach `pop` + T_cal[dst] = pop + + marked.update(next_layer) + reachable.extend(next_layer) + + # Variables for the algorithm + b = len(C) - len(A_cal) + + if V_plus in A_cal: + # Easy case: V+ is in A_cal + # Move one node from V+ to V- using T_cal to find the parents. + move_witnesses(V_plus, V_minus, N=N, H=H, F=F, C=C, T_cal=T_cal, L=L) + else: + # If there is a solo edge, we can resolve the situation by + # moving witnesses from B to A, making G[A] equitable and then + # recursively balancing G[B - w] with a different V_minus and + # but the same V_plus. + + A_0 = set() + A_cal_0 = set() + num_terminal_sets_found = 0 + made_equitable = False + + for W_1 in R_cal[::-1]: + for v in C[W_1]: + X = None + + for U in C: + if N[(v, U)] == 0 and U in A_cal and U != W_1: + X = U + + # v does not witness an edge in H[A_cal] + if X is None: + continue + + for U in C: + # Note: Departing from the paper here. + if N[(v, U)] >= 1 and U not in A_cal: + X_prime = U + w = v + + try: + # Finding the solo neighbor of w in X_prime + y = next( + node + for node in L[w] + if F[node] == X_prime and N[(node, W_1)] == 1 + ) + except StopIteration: + pass + else: + W = W_1 + + # Move w from W to X, now X has one extra node. + change_color(w, W, X, N=N, H=H, F=F, C=C, L=L) + + # Move witness from X to V_minus, making the coloring + # equitable. + move_witnesses( + src_color=X, + dst_color=V_minus, + N=N, + H=H, + F=F, + C=C, + T_cal=T_cal, + L=L, + ) + + # Move y from X_prime to W, making W the correct size. + change_color(y, X_prime, W, N=N, H=H, F=F, C=C, L=L) + + # Then call the procedure on G[B - y] + procedure_P( + V_minus=X_prime, + V_plus=V_plus, + N=N, + H=H, + C=C, + F=F, + L=L, + excluded_colors=excluded_colors.union(A_cal), + ) + made_equitable = True + break + + if made_equitable: + break + else: + # No node in W_1 was found such that + # it had a solo-neighbor. + A_cal_0.add(W_1) + A_0.update(C[W_1]) + num_terminal_sets_found += 1 + + if num_terminal_sets_found == b: + # Otherwise, construct the maximal independent set and find + # a pair of z_1, z_2 as in Case II. + + # BFS to determine B_cal': the set of colors reachable from V+ + B_cal_prime = set() + T_cal_prime = {} + + reachable = [V_plus] + marked = set(reachable) + idx = 0 + while idx < len(reachable): + pop = reachable[idx] + idx += 1 + + B_cal_prime.add(pop) + + # No need to check for excluded_colors here because + # they only exclude colors from A_cal + next_layer = [ + k + for k in C + if H[(pop, k)] > 0 and k not in B_cal_prime and k not in marked + ] + + for dst in next_layer: + T_cal_prime[pop] = dst + + marked.update(next_layer) + reachable.extend(next_layer) + + # Construct the independent set of G[B'] + I_set = set() + I_covered = set() + W_covering = {} + + B_prime = [node for k in B_cal_prime for node in C[k]] + + # Add the nodes in V_plus to I first. + for z in C[V_plus] + B_prime: + if z in I_covered or F[z] not in B_cal_prime: + continue + + I_set.add(z) + I_covered.add(z) + I_covered.update(list(L[z])) + + for w in L[z]: + if F[w] in A_cal_0 and N[(z, F[w])] == 1: + if w not in W_covering: + W_covering[w] = z + else: + # Found z1, z2 which have the same solo + # neighbor in some W + z_1 = W_covering[w] + # z_2 = z + + Z = F[z_1] + W = F[w] + + # shift nodes along W, V- + move_witnesses( + W, V_minus, N=N, H=H, F=F, C=C, T_cal=T_cal, L=L + ) + + # shift nodes along V+ to Z + move_witnesses( + V_plus, + Z, + N=N, + H=H, + F=F, + C=C, + T_cal=T_cal_prime, + L=L, + ) + + # change color of z_1 to W + change_color(z_1, Z, W, N=N, H=H, F=F, C=C, L=L) + + # change color of w to some color in B_cal + W_plus = next( + k for k in C if N[(w, k)] == 0 and k not in A_cal + ) + change_color(w, W, W_plus, N=N, H=H, F=F, C=C, L=L) + + # recurse with G[B \cup W*] + excluded_colors.update( + [k for k in C if k != W and k not in B_cal_prime] + ) + procedure_P( + V_minus=W, + V_plus=W_plus, + N=N, + H=H, + C=C, + F=F, + L=L, + excluded_colors=excluded_colors, + ) + + made_equitable = True + break + + if made_equitable: + break + else: + assert False, ( + "Must find a w which is the solo neighbor " + "of two vertices in B_cal_prime." + ) + + if made_equitable: + break + + +@nx._dispatchable +def equitable_color(G, num_colors): + """Provides an equitable coloring for nodes of `G`. + + Attempts to color a graph using `num_colors` colors, where no neighbors of + a node can have same color as the node itself and the number of nodes with + each color differ by at most 1. `num_colors` must be greater than the + maximum degree of `G`. The algorithm is described in [1]_ and has + complexity O(num_colors * n**2). + + Parameters + ---------- + G : networkX graph + The nodes of this graph will be colored. + + num_colors : number of colors to use + This number must be at least one more than the maximum degree of nodes + in the graph. + + Returns + ------- + A dictionary with keys representing nodes and values representing + corresponding coloring. + + Examples + -------- + >>> G = nx.cycle_graph(4) + >>> nx.coloring.equitable_color(G, num_colors=3) # doctest: +SKIP + {0: 2, 1: 1, 2: 2, 3: 0} + + Raises + ------ + NetworkXAlgorithmError + If `num_colors` is not at least the maximum degree of the graph `G` + + References + ---------- + .. [1] Kierstead, H. A., Kostochka, A. V., Mydlarz, M., & Szemerédi, E. + (2010). A fast algorithm for equitable coloring. Combinatorica, 30(2), + 217-224. + """ + + # Map nodes to integers for simplicity later. + nodes_to_int = {} + int_to_nodes = {} + + for idx, node in enumerate(G.nodes): + nodes_to_int[node] = idx + int_to_nodes[idx] = node + + G = nx.relabel_nodes(G, nodes_to_int, copy=True) + + # Basic graph statistics and sanity check. + if len(G.nodes) > 0: + r_ = max(G.degree(node) for node in G.nodes) + else: + r_ = 0 + + if r_ >= num_colors: + raise nx.NetworkXAlgorithmError( + f"Graph has maximum degree {r_}, needs " + f"{r_ + 1} (> {num_colors}) colors for guaranteed coloring." + ) + + # Ensure that the number of nodes in G is a multiple of (r + 1) + pad_graph(G, num_colors) + + # Starting the algorithm. + # L = {node: list(G.neighbors(node)) for node in G.nodes} + L_ = {node: [] for node in G.nodes} + + # Arbitrary equitable allocation of colors to nodes. + F = {node: idx % num_colors for idx, node in enumerate(G.nodes)} + + C = make_C_from_F(F) + + # The neighborhood is empty initially. + N = make_N_from_L_C(L_, C) + + # Currently all nodes witness all edges. + H = make_H_from_C_N(C, N) + + # Start of algorithm. + edges_seen = set() + + for u in sorted(G.nodes): + for v in sorted(G.neighbors(u)): + # Do not double count edges if (v, u) has already been seen. + if (v, u) in edges_seen: + continue + + edges_seen.add((u, v)) + + L_[u].append(v) + L_[v].append(u) + + N[(u, F[v])] += 1 + N[(v, F[u])] += 1 + + if F[u] != F[v]: + # Were 'u' and 'v' witnesses for F[u] -> F[v] or F[v] -> F[u]? + if N[(u, F[v])] == 1: + H[F[u], F[v]] -= 1 # u cannot witness an edge between F[u], F[v] + + if N[(v, F[u])] == 1: + H[F[v], F[u]] -= 1 # v cannot witness an edge between F[v], F[u] + + if N[(u, F[u])] != 0: + # Find the first color where 'u' does not have any neighbors. + Y = next(k for k in C if N[(u, k)] == 0) + X = F[u] + change_color(u, X, Y, N=N, H=H, F=F, C=C, L=L_) + + # Procedure P + procedure_P(V_minus=X, V_plus=Y, N=N, H=H, F=F, C=C, L=L_) + + return {int_to_nodes[x]: F[x] for x in int_to_nodes} diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/tests/__pycache__/__init__.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/tests/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..1a05bdffac4fe0279d22e81697b87c0765e71c4c Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/tests/__pycache__/__init__.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/tests/__pycache__/test_coloring.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/tests/__pycache__/test_coloring.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..925aeb5d3781c8d08d394bedbf7247d4199592e5 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/coloring/tests/__pycache__/test_coloring.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/__init__.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..f9ae2caba856daba534037f4a6f967abfad49552 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/__init__.py @@ -0,0 +1,6 @@ +from .connected import * +from .strongly_connected import * +from .weakly_connected import * +from .attracting import * +from .biconnected import * +from .semiconnected import * diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/__pycache__/__init__.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..8dfe4560c28028310848a2b0009b1408a6bc5c17 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/__pycache__/__init__.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/__pycache__/strongly_connected.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/__pycache__/strongly_connected.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..3b42f06189892fb8de40f0d8d1e9355e5aa08173 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/__pycache__/strongly_connected.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/attracting.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/attracting.py new file mode 100644 index 0000000000000000000000000000000000000000..3d77cd93d70efab5f29c77c7d135f4730e4c3a4a --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/attracting.py @@ -0,0 +1,115 @@ +"""Attracting components.""" + +import networkx as nx +from networkx.utils.decorators import not_implemented_for + +__all__ = [ + "number_attracting_components", + "attracting_components", + "is_attracting_component", +] + + +@not_implemented_for("undirected") +@nx._dispatchable +def attracting_components(G): + """Generates the attracting components in `G`. + + An attracting component in a directed graph `G` is a strongly connected + component with the property that a random walker on the graph will never + leave the component, once it enters the component. + + The nodes in attracting components can also be thought of as recurrent + nodes. If a random walker enters the attractor containing the node, then + the node will be visited infinitely often. + + To obtain induced subgraphs on each component use: + ``(G.subgraph(c).copy() for c in attracting_components(G))`` + + Parameters + ---------- + G : DiGraph, MultiDiGraph + The graph to be analyzed. + + Returns + ------- + attractors : generator of sets + A generator of sets of nodes, one for each attracting component of G. + + Raises + ------ + NetworkXNotImplemented + If the input graph is undirected. + + See Also + -------- + number_attracting_components + is_attracting_component + + """ + scc = list(nx.strongly_connected_components(G)) + cG = nx.condensation(G, scc) + for n in cG: + if cG.out_degree(n) == 0: + yield scc[n] + + +@not_implemented_for("undirected") +@nx._dispatchable +def number_attracting_components(G): + """Returns the number of attracting components in `G`. + + Parameters + ---------- + G : DiGraph, MultiDiGraph + The graph to be analyzed. + + Returns + ------- + n : int + The number of attracting components in G. + + Raises + ------ + NetworkXNotImplemented + If the input graph is undirected. + + See Also + -------- + attracting_components + is_attracting_component + + """ + return sum(1 for ac in attracting_components(G)) + + +@not_implemented_for("undirected") +@nx._dispatchable +def is_attracting_component(G): + """Returns True if `G` consists of a single attracting component. + + Parameters + ---------- + G : DiGraph, MultiDiGraph + The graph to be analyzed. + + Returns + ------- + attracting : bool + True if `G` has a single attracting component. Otherwise, False. + + Raises + ------ + NetworkXNotImplemented + If the input graph is undirected. + + See Also + -------- + attracting_components + number_attracting_components + + """ + ac = list(attracting_components(G)) + if len(ac) == 1: + return len(ac[0]) == len(G) + return False diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/biconnected.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/biconnected.py new file mode 100644 index 0000000000000000000000000000000000000000..fd0f3865bb18e9c9eb37d768c7fd3caceb1cde86 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/biconnected.py @@ -0,0 +1,394 @@ +"""Biconnected components and articulation points.""" + +from itertools import chain + +import networkx as nx +from networkx.utils.decorators import not_implemented_for + +__all__ = [ + "biconnected_components", + "biconnected_component_edges", + "is_biconnected", + "articulation_points", +] + + +@not_implemented_for("directed") +@nx._dispatchable +def is_biconnected(G): + """Returns True if the graph is biconnected, False otherwise. + + A graph is biconnected if, and only if, it cannot be disconnected by + removing only one node (and all edges incident on that node). If + removing a node increases the number of disconnected components + in the graph, that node is called an articulation point, or cut + vertex. A biconnected graph has no articulation points. + + Parameters + ---------- + G : NetworkX Graph + An undirected graph. + + Returns + ------- + biconnected : bool + True if the graph is biconnected, False otherwise. + + Raises + ------ + NetworkXNotImplemented + If the input graph is not undirected. + + Examples + -------- + >>> G = nx.path_graph(4) + >>> print(nx.is_biconnected(G)) + False + >>> G.add_edge(0, 3) + >>> print(nx.is_biconnected(G)) + True + + See Also + -------- + biconnected_components + articulation_points + biconnected_component_edges + is_strongly_connected + is_weakly_connected + is_connected + is_semiconnected + + Notes + ----- + The algorithm to find articulation points and biconnected + components is implemented using a non-recursive depth-first-search + (DFS) that keeps track of the highest level that back edges reach + in the DFS tree. A node `n` is an articulation point if, and only + if, there exists a subtree rooted at `n` such that there is no + back edge from any successor of `n` that links to a predecessor of + `n` in the DFS tree. By keeping track of all the edges traversed + by the DFS we can obtain the biconnected components because all + edges of a bicomponent will be traversed consecutively between + articulation points. + + References + ---------- + .. [1] Hopcroft, J.; Tarjan, R. (1973). + "Efficient algorithms for graph manipulation". + Communications of the ACM 16: 372–378. doi:10.1145/362248.362272 + + """ + bccs = biconnected_components(G) + try: + bcc = next(bccs) + except StopIteration: + # No bicomponents (empty graph?) + return False + try: + next(bccs) + except StopIteration: + # Only one bicomponent + return len(bcc) == len(G) + else: + # Multiple bicomponents + return False + + +@not_implemented_for("directed") +@nx._dispatchable +def biconnected_component_edges(G): + """Returns a generator of lists of edges, one list for each biconnected + component of the input graph. + + Biconnected components are maximal subgraphs such that the removal of a + node (and all edges incident on that node) will not disconnect the + subgraph. Note that nodes may be part of more than one biconnected + component. Those nodes are articulation points, or cut vertices. + However, each edge belongs to one, and only one, biconnected component. + + Notice that by convention a dyad is considered a biconnected component. + + Parameters + ---------- + G : NetworkX Graph + An undirected graph. + + Returns + ------- + edges : generator of lists + Generator of lists of edges, one list for each bicomponent. + + Raises + ------ + NetworkXNotImplemented + If the input graph is not undirected. + + Examples + -------- + >>> G = nx.barbell_graph(4, 2) + >>> print(nx.is_biconnected(G)) + False + >>> bicomponents_edges = list(nx.biconnected_component_edges(G)) + >>> len(bicomponents_edges) + 5 + >>> G.add_edge(2, 8) + >>> print(nx.is_biconnected(G)) + True + >>> bicomponents_edges = list(nx.biconnected_component_edges(G)) + >>> len(bicomponents_edges) + 1 + + See Also + -------- + is_biconnected, + biconnected_components, + articulation_points, + + Notes + ----- + The algorithm to find articulation points and biconnected + components is implemented using a non-recursive depth-first-search + (DFS) that keeps track of the highest level that back edges reach + in the DFS tree. A node `n` is an articulation point if, and only + if, there exists a subtree rooted at `n` such that there is no + back edge from any successor of `n` that links to a predecessor of + `n` in the DFS tree. By keeping track of all the edges traversed + by the DFS we can obtain the biconnected components because all + edges of a bicomponent will be traversed consecutively between + articulation points. + + References + ---------- + .. [1] Hopcroft, J.; Tarjan, R. (1973). + "Efficient algorithms for graph manipulation". + Communications of the ACM 16: 372–378. doi:10.1145/362248.362272 + + """ + yield from _biconnected_dfs(G, components=True) + + +@not_implemented_for("directed") +@nx._dispatchable +def biconnected_components(G): + """Returns a generator of sets of nodes, one set for each biconnected + component of the graph + + Biconnected components are maximal subgraphs such that the removal of a + node (and all edges incident on that node) will not disconnect the + subgraph. Note that nodes may be part of more than one biconnected + component. Those nodes are articulation points, or cut vertices. The + removal of articulation points will increase the number of connected + components of the graph. + + Notice that by convention a dyad is considered a biconnected component. + + Parameters + ---------- + G : NetworkX Graph + An undirected graph. + + Returns + ------- + nodes : generator + Generator of sets of nodes, one set for each biconnected component. + + Raises + ------ + NetworkXNotImplemented + If the input graph is not undirected. + + Examples + -------- + >>> G = nx.lollipop_graph(5, 1) + >>> print(nx.is_biconnected(G)) + False + >>> bicomponents = list(nx.biconnected_components(G)) + >>> len(bicomponents) + 2 + >>> G.add_edge(0, 5) + >>> print(nx.is_biconnected(G)) + True + >>> bicomponents = list(nx.biconnected_components(G)) + >>> len(bicomponents) + 1 + + You can generate a sorted list of biconnected components, largest + first, using sort. + + >>> G.remove_edge(0, 5) + >>> [len(c) for c in sorted(nx.biconnected_components(G), key=len, reverse=True)] + [5, 2] + + If you only want the largest connected component, it's more + efficient to use max instead of sort. + + >>> Gc = max(nx.biconnected_components(G), key=len) + + To create the components as subgraphs use: + ``(G.subgraph(c).copy() for c in biconnected_components(G))`` + + See Also + -------- + is_biconnected + articulation_points + biconnected_component_edges + k_components : this function is a special case where k=2 + bridge_components : similar to this function, but is defined using + 2-edge-connectivity instead of 2-node-connectivity. + + Notes + ----- + The algorithm to find articulation points and biconnected + components is implemented using a non-recursive depth-first-search + (DFS) that keeps track of the highest level that back edges reach + in the DFS tree. A node `n` is an articulation point if, and only + if, there exists a subtree rooted at `n` such that there is no + back edge from any successor of `n` that links to a predecessor of + `n` in the DFS tree. By keeping track of all the edges traversed + by the DFS we can obtain the biconnected components because all + edges of a bicomponent will be traversed consecutively between + articulation points. + + References + ---------- + .. [1] Hopcroft, J.; Tarjan, R. (1973). + "Efficient algorithms for graph manipulation". + Communications of the ACM 16: 372–378. doi:10.1145/362248.362272 + + """ + for comp in _biconnected_dfs(G, components=True): + yield set(chain.from_iterable(comp)) + + +@not_implemented_for("directed") +@nx._dispatchable +def articulation_points(G): + """Yield the articulation points, or cut vertices, of a graph. + + An articulation point or cut vertex is any node whose removal (along with + all its incident edges) increases the number of connected components of + a graph. An undirected connected graph without articulation points is + biconnected. Articulation points belong to more than one biconnected + component of a graph. + + Notice that by convention a dyad is considered a biconnected component. + + Parameters + ---------- + G : NetworkX Graph + An undirected graph. + + Yields + ------ + node + An articulation point in the graph. + + Raises + ------ + NetworkXNotImplemented + If the input graph is not undirected. + + Examples + -------- + + >>> G = nx.barbell_graph(4, 2) + >>> print(nx.is_biconnected(G)) + False + >>> len(list(nx.articulation_points(G))) + 4 + >>> G.add_edge(2, 8) + >>> print(nx.is_biconnected(G)) + True + >>> len(list(nx.articulation_points(G))) + 0 + + See Also + -------- + is_biconnected + biconnected_components + biconnected_component_edges + + Notes + ----- + The algorithm to find articulation points and biconnected + components is implemented using a non-recursive depth-first-search + (DFS) that keeps track of the highest level that back edges reach + in the DFS tree. A node `n` is an articulation point if, and only + if, there exists a subtree rooted at `n` such that there is no + back edge from any successor of `n` that links to a predecessor of + `n` in the DFS tree. By keeping track of all the edges traversed + by the DFS we can obtain the biconnected components because all + edges of a bicomponent will be traversed consecutively between + articulation points. + + References + ---------- + .. [1] Hopcroft, J.; Tarjan, R. (1973). + "Efficient algorithms for graph manipulation". + Communications of the ACM 16: 372–378. doi:10.1145/362248.362272 + + """ + seen = set() + for articulation in _biconnected_dfs(G, components=False): + if articulation not in seen: + seen.add(articulation) + yield articulation + + +@not_implemented_for("directed") +def _biconnected_dfs(G, components=True): + # depth-first search algorithm to generate articulation points + # and biconnected components + visited = set() + for start in G: + if start in visited: + continue + discovery = {start: 0} # time of first discovery of node during search + low = {start: 0} + root_children = 0 + visited.add(start) + edge_stack = [] + stack = [(start, start, iter(G[start]))] + edge_index = {} + while stack: + grandparent, parent, children = stack[-1] + try: + child = next(children) + if grandparent == child: + continue + if child in visited: + if discovery[child] <= discovery[parent]: # back edge + low[parent] = min(low[parent], discovery[child]) + if components: + edge_index[parent, child] = len(edge_stack) + edge_stack.append((parent, child)) + else: + low[child] = discovery[child] = len(discovery) + visited.add(child) + stack.append((parent, child, iter(G[child]))) + if components: + edge_index[parent, child] = len(edge_stack) + edge_stack.append((parent, child)) + + except StopIteration: + stack.pop() + if len(stack) > 1: + if low[parent] >= discovery[grandparent]: + if components: + ind = edge_index[grandparent, parent] + yield edge_stack[ind:] + del edge_stack[ind:] + + else: + yield grandparent + low[grandparent] = min(low[parent], low[grandparent]) + elif stack: # length 1 so grandparent is root + root_children += 1 + if components: + ind = edge_index[grandparent, parent] + yield edge_stack[ind:] + del edge_stack[ind:] + if not components: + # root node is articulation point if it has more than 1 child + if root_children > 1: + yield start diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/connected.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/connected.py new file mode 100644 index 0000000000000000000000000000000000000000..ebe0d8c157b57fe68589210f2fa5dcf1219cebc5 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/connected.py @@ -0,0 +1,216 @@ +"""Connected components.""" + +import networkx as nx +from networkx.utils.decorators import not_implemented_for + +from ...utils import arbitrary_element + +__all__ = [ + "number_connected_components", + "connected_components", + "is_connected", + "node_connected_component", +] + + +@not_implemented_for("directed") +@nx._dispatchable +def connected_components(G): + """Generate connected components. + + Parameters + ---------- + G : NetworkX graph + An undirected graph + + Returns + ------- + comp : generator of sets + A generator of sets of nodes, one for each component of G. + + Raises + ------ + NetworkXNotImplemented + If G is directed. + + Examples + -------- + Generate a sorted list of connected components, largest first. + + >>> G = nx.path_graph(4) + >>> nx.add_path(G, [10, 11, 12]) + >>> [len(c) for c in sorted(nx.connected_components(G), key=len, reverse=True)] + [4, 3] + + If you only want the largest connected component, it's more + efficient to use max instead of sort. + + >>> largest_cc = max(nx.connected_components(G), key=len) + + To create the induced subgraph of each component use: + + >>> S = [G.subgraph(c).copy() for c in nx.connected_components(G)] + + See Also + -------- + strongly_connected_components + weakly_connected_components + + Notes + ----- + For undirected graphs only. + + """ + seen = set() + n = len(G) + for v in G: + if v not in seen: + c = _plain_bfs(G, n, v) + seen.update(c) + yield c + + +@not_implemented_for("directed") +@nx._dispatchable +def number_connected_components(G): + """Returns the number of connected components. + + Parameters + ---------- + G : NetworkX graph + An undirected graph. + + Returns + ------- + n : integer + Number of connected components + + Raises + ------ + NetworkXNotImplemented + If G is directed. + + Examples + -------- + >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)]) + >>> nx.number_connected_components(G) + 3 + + See Also + -------- + connected_components + number_weakly_connected_components + number_strongly_connected_components + + Notes + ----- + For undirected graphs only. + + """ + return sum(1 for cc in connected_components(G)) + + +@not_implemented_for("directed") +@nx._dispatchable +def is_connected(G): + """Returns True if the graph is connected, False otherwise. + + Parameters + ---------- + G : NetworkX Graph + An undirected graph. + + Returns + ------- + connected : bool + True if the graph is connected, false otherwise. + + Raises + ------ + NetworkXNotImplemented + If G is directed. + + Examples + -------- + >>> G = nx.path_graph(4) + >>> print(nx.is_connected(G)) + True + + See Also + -------- + is_strongly_connected + is_weakly_connected + is_semiconnected + is_biconnected + connected_components + + Notes + ----- + For undirected graphs only. + + """ + n = len(G) + if n == 0: + raise nx.NetworkXPointlessConcept( + "Connectivity is undefined for the null graph." + ) + return sum(1 for node in _plain_bfs(G, n, arbitrary_element(G))) == len(G) + + +@not_implemented_for("directed") +@nx._dispatchable +def node_connected_component(G, n): + """Returns the set of nodes in the component of graph containing node n. + + Parameters + ---------- + G : NetworkX Graph + An undirected graph. + + n : node label + A node in G + + Returns + ------- + comp : set + A set of nodes in the component of G containing node n. + + Raises + ------ + NetworkXNotImplemented + If G is directed. + + Examples + -------- + >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)]) + >>> nx.node_connected_component(G, 0) # nodes of component that contains node 0 + {0, 1, 2} + + See Also + -------- + connected_components + + Notes + ----- + For undirected graphs only. + + """ + return _plain_bfs(G, len(G), n) + + +def _plain_bfs(G, n, source): + """A fast BFS node generator""" + adj = G._adj + seen = {source} + nextlevel = [source] + while nextlevel: + thislevel = nextlevel + nextlevel = [] + for v in thislevel: + for w in adj[v]: + if w not in seen: + seen.add(w) + nextlevel.append(w) + if len(seen) == n: + return seen + return seen diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/semiconnected.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/semiconnected.py new file mode 100644 index 0000000000000000000000000000000000000000..9ca5d762ca882524d1406f9295fa3a238fedb724 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/semiconnected.py @@ -0,0 +1,71 @@ +"""Semiconnectedness.""" + +import networkx as nx +from networkx.utils import not_implemented_for, pairwise + +__all__ = ["is_semiconnected"] + + +@not_implemented_for("undirected") +@nx._dispatchable +def is_semiconnected(G): + r"""Returns True if the graph is semiconnected, False otherwise. + + A graph is semiconnected if and only if for any pair of nodes, either one + is reachable from the other, or they are mutually reachable. + + This function uses a theorem that states that a DAG is semiconnected + if for any topological sort, for node $v_n$ in that sort, there is an + edge $(v_i, v_{i+1})$. That allows us to check if a non-DAG `G` is + semiconnected by condensing the graph: i.e. constructing a new graph `H` + with nodes being the strongly connected components of `G`, and edges + (scc_1, scc_2) if there is a edge $(v_1, v_2)$ in `G` for some + $v_1 \in scc_1$ and $v_2 \in scc_2$. That results in a DAG, so we compute + the topological sort of `H` and check if for every $n$ there is an edge + $(scc_n, scc_{n+1})$. + + Parameters + ---------- + G : NetworkX graph + A directed graph. + + Returns + ------- + semiconnected : bool + True if the graph is semiconnected, False otherwise. + + Raises + ------ + NetworkXNotImplemented + If the input graph is undirected. + + NetworkXPointlessConcept + If the graph is empty. + + Examples + -------- + >>> G = nx.path_graph(4, create_using=nx.DiGraph()) + >>> print(nx.is_semiconnected(G)) + True + >>> G = nx.DiGraph([(1, 2), (3, 2)]) + >>> print(nx.is_semiconnected(G)) + False + + See Also + -------- + is_strongly_connected + is_weakly_connected + is_connected + is_biconnected + """ + if len(G) == 0: + raise nx.NetworkXPointlessConcept( + "Connectivity is undefined for the null graph." + ) + + if not nx.is_weakly_connected(G): + return False + + H = nx.condensation(G) + + return all(H.has_edge(u, v) for u, v in pairwise(nx.topological_sort(H))) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/strongly_connected.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/strongly_connected.py new file mode 100644 index 0000000000000000000000000000000000000000..393728ffe1f25a077aee6691fe913a81570ef0f1 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/strongly_connected.py @@ -0,0 +1,351 @@ +"""Strongly connected components.""" + +import networkx as nx +from networkx.utils.decorators import not_implemented_for + +__all__ = [ + "number_strongly_connected_components", + "strongly_connected_components", + "is_strongly_connected", + "kosaraju_strongly_connected_components", + "condensation", +] + + +@not_implemented_for("undirected") +@nx._dispatchable +def strongly_connected_components(G): + """Generate nodes in strongly connected components of graph. + + Parameters + ---------- + G : NetworkX Graph + A directed graph. + + Returns + ------- + comp : generator of sets + A generator of sets of nodes, one for each strongly connected + component of G. + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + Examples + -------- + Generate a sorted list of strongly connected components, largest first. + + >>> G = nx.cycle_graph(4, create_using=nx.DiGraph()) + >>> nx.add_cycle(G, [10, 11, 12]) + >>> [ + ... len(c) + ... for c in sorted(nx.strongly_connected_components(G), key=len, reverse=True) + ... ] + [4, 3] + + If you only want the largest component, it's more efficient to + use max instead of sort. + + >>> largest = max(nx.strongly_connected_components(G), key=len) + + See Also + -------- + connected_components + weakly_connected_components + kosaraju_strongly_connected_components + + Notes + ----- + Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_. + Nonrecursive version of algorithm. + + References + ---------- + .. [1] Depth-first search and linear graph algorithms, R. Tarjan + SIAM Journal of Computing 1(2):146-160, (1972). + + .. [2] On finding the strongly connected components in a directed graph. + E. Nuutila and E. Soisalon-Soinen + Information Processing Letters 49(1): 9-14, (1994).. + + """ + preorder = {} + lowlink = {} + scc_found = set() + scc_queue = [] + i = 0 # Preorder counter + neighbors = {v: iter(G[v]) for v in G} + for source in G: + if source not in scc_found: + queue = [source] + while queue: + v = queue[-1] + if v not in preorder: + i = i + 1 + preorder[v] = i + done = True + for w in neighbors[v]: + if w not in preorder: + queue.append(w) + done = False + break + if done: + lowlink[v] = preorder[v] + for w in G[v]: + if w not in scc_found: + if preorder[w] > preorder[v]: + lowlink[v] = min([lowlink[v], lowlink[w]]) + else: + lowlink[v] = min([lowlink[v], preorder[w]]) + queue.pop() + if lowlink[v] == preorder[v]: + scc = {v} + while scc_queue and preorder[scc_queue[-1]] > preorder[v]: + k = scc_queue.pop() + scc.add(k) + scc_found.update(scc) + yield scc + else: + scc_queue.append(v) + + +@not_implemented_for("undirected") +@nx._dispatchable +def kosaraju_strongly_connected_components(G, source=None): + """Generate nodes in strongly connected components of graph. + + Parameters + ---------- + G : NetworkX Graph + A directed graph. + + Returns + ------- + comp : generator of sets + A generator of sets of nodes, one for each strongly connected + component of G. + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + Examples + -------- + Generate a sorted list of strongly connected components, largest first. + + >>> G = nx.cycle_graph(4, create_using=nx.DiGraph()) + >>> nx.add_cycle(G, [10, 11, 12]) + >>> [ + ... len(c) + ... for c in sorted( + ... nx.kosaraju_strongly_connected_components(G), key=len, reverse=True + ... ) + ... ] + [4, 3] + + If you only want the largest component, it's more efficient to + use max instead of sort. + + >>> largest = max(nx.kosaraju_strongly_connected_components(G), key=len) + + See Also + -------- + strongly_connected_components + + Notes + ----- + Uses Kosaraju's algorithm. + + """ + post = list(nx.dfs_postorder_nodes(G.reverse(copy=False), source=source)) + + seen = set() + while post: + r = post.pop() + if r in seen: + continue + c = nx.dfs_preorder_nodes(G, r) + new = {v for v in c if v not in seen} + seen.update(new) + yield new + + +@not_implemented_for("undirected") +@nx._dispatchable +def number_strongly_connected_components(G): + """Returns number of strongly connected components in graph. + + Parameters + ---------- + G : NetworkX graph + A directed graph. + + Returns + ------- + n : integer + Number of strongly connected components + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + Examples + -------- + >>> G = nx.DiGraph( + ... [(0, 1), (1, 2), (2, 0), (2, 3), (4, 5), (3, 4), (5, 6), (6, 3), (6, 7)] + ... ) + >>> nx.number_strongly_connected_components(G) + 3 + + See Also + -------- + strongly_connected_components + number_connected_components + number_weakly_connected_components + + Notes + ----- + For directed graphs only. + """ + return sum(1 for scc in strongly_connected_components(G)) + + +@not_implemented_for("undirected") +@nx._dispatchable +def is_strongly_connected(G): + """Test directed graph for strong connectivity. + + A directed graph is strongly connected if and only if every vertex in + the graph is reachable from every other vertex. + + Parameters + ---------- + G : NetworkX Graph + A directed graph. + + Returns + ------- + connected : bool + True if the graph is strongly connected, False otherwise. + + Examples + -------- + >>> G = nx.DiGraph([(0, 1), (1, 2), (2, 3), (3, 0), (2, 4), (4, 2)]) + >>> nx.is_strongly_connected(G) + True + >>> G.remove_edge(2, 3) + >>> nx.is_strongly_connected(G) + False + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + See Also + -------- + is_weakly_connected + is_semiconnected + is_connected + is_biconnected + strongly_connected_components + + Notes + ----- + For directed graphs only. + """ + if len(G) == 0: + raise nx.NetworkXPointlessConcept( + """Connectivity is undefined for the null graph.""" + ) + + return len(next(strongly_connected_components(G))) == len(G) + + +@not_implemented_for("undirected") +@nx._dispatchable(returns_graph=True) +def condensation(G, scc=None): + """Returns the condensation of G. + + The condensation of G is the graph with each of the strongly connected + components contracted into a single node. + + Parameters + ---------- + G : NetworkX DiGraph + A directed graph. + + scc: list or generator (optional, default=None) + Strongly connected components. If provided, the elements in + `scc` must partition the nodes in `G`. If not provided, it will be + calculated as scc=nx.strongly_connected_components(G). + + Returns + ------- + C : NetworkX DiGraph + The condensation graph C of G. The node labels are integers + corresponding to the index of the component in the list of + strongly connected components of G. C has a graph attribute named + 'mapping' with a dictionary mapping the original nodes to the + nodes in C to which they belong. Each node in C also has a node + attribute 'members' with the set of original nodes in G that + form the SCC that the node in C represents. + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + Examples + -------- + Contracting two sets of strongly connected nodes into two distinct SCC + using the barbell graph. + + >>> G = nx.barbell_graph(4, 0) + >>> G.remove_edge(3, 4) + >>> G = nx.DiGraph(G) + >>> H = nx.condensation(G) + >>> H.nodes.data() + NodeDataView({0: {'members': {0, 1, 2, 3}}, 1: {'members': {4, 5, 6, 7}}}) + >>> H.graph["mapping"] + {0: 0, 1: 0, 2: 0, 3: 0, 4: 1, 5: 1, 6: 1, 7: 1} + + Contracting a complete graph into one single SCC. + + >>> G = nx.complete_graph(7, create_using=nx.DiGraph) + >>> H = nx.condensation(G) + >>> H.nodes + NodeView((0,)) + >>> H.nodes.data() + NodeDataView({0: {'members': {0, 1, 2, 3, 4, 5, 6}}}) + + Notes + ----- + After contracting all strongly connected components to a single node, + the resulting graph is a directed acyclic graph. + + """ + if scc is None: + scc = nx.strongly_connected_components(G) + mapping = {} + members = {} + C = nx.DiGraph() + # Add mapping dict as graph attribute + C.graph["mapping"] = mapping + if len(G) == 0: + return C + for i, component in enumerate(scc): + members[i] = component + mapping.update((n, i) for n in component) + number_of_components = i + 1 + C.add_nodes_from(range(number_of_components)) + C.add_edges_from( + (mapping[u], mapping[v]) for u, v in G.edges() if mapping[u] != mapping[v] + ) + # Add a list of members (ie original nodes) to each node (ie scc) in C. + nx.set_node_attributes(C, members, "members") + return C diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/__pycache__/test_connected.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/__pycache__/test_connected.cpython-310.pyc new file mode 100644 index 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nx.DiGraph() + cls.G1.add_edges_from( + [ + (5, 11), + (11, 2), + (11, 9), + (11, 10), + (7, 11), + (7, 8), + (8, 9), + (3, 8), + (3, 10), + ] + ) + cls.G2 = nx.DiGraph() + cls.G2.add_edges_from([(0, 1), (0, 2), (1, 1), (1, 2), (2, 1)]) + + cls.G3 = nx.DiGraph() + cls.G3.add_edges_from([(0, 1), (1, 2), (2, 1), (0, 3), (3, 4), (4, 3)]) + + cls.G4 = nx.DiGraph() + + def test_attracting_components(self): + ac = list(nx.attracting_components(self.G1)) + assert {2} in ac + assert {9} in ac + assert {10} in ac + + ac = list(nx.attracting_components(self.G2)) + ac = [tuple(sorted(x)) for x in ac] + assert ac == [(1, 2)] + + ac = list(nx.attracting_components(self.G3)) + ac = [tuple(sorted(x)) for x in ac] + assert (1, 2) in ac + assert (3, 4) in ac + assert len(ac) == 2 + + ac = list(nx.attracting_components(self.G4)) + assert ac == [] + + def test_number_attacting_components(self): + assert nx.number_attracting_components(self.G1) == 3 + assert nx.number_attracting_components(self.G2) == 1 + assert nx.number_attracting_components(self.G3) == 2 + assert nx.number_attracting_components(self.G4) == 0 + + def test_is_attracting_component(self): + assert not nx.is_attracting_component(self.G1) + assert not nx.is_attracting_component(self.G2) + assert not nx.is_attracting_component(self.G3) + g2 = self.G3.subgraph([1, 2]) + assert nx.is_attracting_component(g2) + assert not nx.is_attracting_component(self.G4) + + def test_connected_raise(self): + G = nx.Graph() + with pytest.raises(NetworkXNotImplemented): + next(nx.attracting_components(G)) + pytest.raises(NetworkXNotImplemented, nx.number_attracting_components, G) + pytest.raises(NetworkXNotImplemented, nx.is_attracting_component, G) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_semiconnected.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_semiconnected.py new file mode 100644 index 0000000000000000000000000000000000000000..6376bbfb12a061e1724b0c74d2614e116149d8bf --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_semiconnected.py @@ -0,0 +1,55 @@ +from itertools import chain + +import pytest + +import networkx as nx + + +class TestIsSemiconnected: + def test_undirected(self): + pytest.raises(nx.NetworkXNotImplemented, nx.is_semiconnected, nx.Graph()) + pytest.raises(nx.NetworkXNotImplemented, nx.is_semiconnected, nx.MultiGraph()) + + def test_empty(self): + pytest.raises(nx.NetworkXPointlessConcept, nx.is_semiconnected, nx.DiGraph()) + pytest.raises( + nx.NetworkXPointlessConcept, nx.is_semiconnected, nx.MultiDiGraph() + ) + + def test_single_node_graph(self): + G = nx.DiGraph() + G.add_node(0) + assert nx.is_semiconnected(G) + + def test_path(self): + G = nx.path_graph(100, create_using=nx.DiGraph()) + assert nx.is_semiconnected(G) + G.add_edge(100, 99) + assert not nx.is_semiconnected(G) + + def test_cycle(self): + G = nx.cycle_graph(100, create_using=nx.DiGraph()) + assert nx.is_semiconnected(G) + G = nx.path_graph(100, create_using=nx.DiGraph()) + G.add_edge(0, 99) + assert nx.is_semiconnected(G) + + def test_tree(self): + G = nx.DiGraph() + G.add_edges_from( + chain.from_iterable([(i, 2 * i + 1), (i, 2 * i + 2)] for i in range(100)) + ) + assert not nx.is_semiconnected(G) + + def test_dumbbell(self): + G = nx.cycle_graph(100, create_using=nx.DiGraph()) + G.add_edges_from((i + 100, (i + 1) % 100 + 100) for i in range(100)) + assert not nx.is_semiconnected(G) # G is disconnected. + G.add_edge(100, 99) + assert nx.is_semiconnected(G) + + def test_alternating_path(self): + G = nx.DiGraph( + chain.from_iterable([(i, i - 1), (i, i + 1)] for i in range(0, 100, 2)) + ) + assert not nx.is_semiconnected(G) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_strongly_connected.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_strongly_connected.py new file mode 100644 index 0000000000000000000000000000000000000000..27f40988265b61eec9edb2bde64433f7396022f0 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_strongly_connected.py @@ -0,0 +1,193 @@ +import pytest + +import networkx as nx +from networkx import NetworkXNotImplemented + + +class TestStronglyConnected: + @classmethod + def setup_class(cls): + cls.gc = [] + G = nx.DiGraph() + G.add_edges_from( + [ + (1, 2), + (2, 3), + (2, 8), + (3, 4), + (3, 7), + (4, 5), + (5, 3), + (5, 6), + (7, 4), + (7, 6), + (8, 1), + (8, 7), + ] + ) + C = {frozenset([3, 4, 5, 7]), frozenset([1, 2, 8]), frozenset([6])} + cls.gc.append((G, C)) + + G = nx.DiGraph() + G.add_edges_from([(1, 2), (1, 3), (1, 4), (4, 2), (3, 4), (2, 3)]) + C = {frozenset([2, 3, 4]), frozenset([1])} + cls.gc.append((G, C)) + + G = nx.DiGraph() + G.add_edges_from([(1, 2), (2, 3), (3, 2), (2, 1)]) + C = {frozenset([1, 2, 3])} + cls.gc.append((G, C)) + + # Eppstein's tests + G = nx.DiGraph({0: [1], 1: [2, 3], 2: [4, 5], 3: [4, 5], 4: [6], 5: [], 6: []}) + C = { + frozenset([0]), + frozenset([1]), + frozenset([2]), + frozenset([3]), + frozenset([4]), + frozenset([5]), + frozenset([6]), + } + cls.gc.append((G, C)) + + G = nx.DiGraph({0: [1], 1: [2, 3, 4], 2: [0, 3], 3: [4], 4: [3]}) + C = {frozenset([0, 1, 2]), frozenset([3, 4])} + cls.gc.append((G, C)) + + def test_tarjan(self): + scc = nx.strongly_connected_components + for G, C in self.gc: + assert {frozenset(g) for g in scc(G)} == C + + def test_kosaraju(self): + scc = nx.kosaraju_strongly_connected_components + for G, C in self.gc: + assert {frozenset(g) for g in scc(G)} == C + + def test_number_strongly_connected_components(self): + ncc = nx.number_strongly_connected_components + for G, C in self.gc: + assert ncc(G) == len(C) + + def test_is_strongly_connected(self): + for G, C in self.gc: + if len(C) == 1: + assert nx.is_strongly_connected(G) + else: + assert not nx.is_strongly_connected(G) + + def test_contract_scc1(self): + G = nx.DiGraph() + G.add_edges_from( + [ + (1, 2), + (2, 3), + (2, 11), + (2, 12), + (3, 4), + (4, 3), + (4, 5), + (5, 6), + (6, 5), + (6, 7), + (7, 8), + (7, 9), + (7, 10), + (8, 9), + (9, 7), + (10, 6), + (11, 2), + (11, 4), + (11, 6), + (12, 6), + (12, 11), + ] + ) + scc = list(nx.strongly_connected_components(G)) + cG = nx.condensation(G, scc) + # DAG + assert nx.is_directed_acyclic_graph(cG) + # nodes + assert sorted(cG.nodes()) == [0, 1, 2, 3] + # edges + mapping = {} + for i, component in enumerate(scc): + for n in component: + mapping[n] = i + edge = (mapping[2], mapping[3]) + assert cG.has_edge(*edge) + edge = (mapping[2], mapping[5]) + assert cG.has_edge(*edge) + edge = (mapping[3], mapping[5]) + assert cG.has_edge(*edge) + + def test_contract_scc_isolate(self): + # Bug found and fixed in [1687]. + G = nx.DiGraph() + G.add_edge(1, 2) + G.add_edge(2, 1) + scc = list(nx.strongly_connected_components(G)) + cG = nx.condensation(G, scc) + assert list(cG.nodes()) == [0] + assert list(cG.edges()) == [] + + def test_contract_scc_edge(self): + G = nx.DiGraph() + G.add_edge(1, 2) + G.add_edge(2, 1) + G.add_edge(2, 3) + G.add_edge(3, 4) + G.add_edge(4, 3) + scc = list(nx.strongly_connected_components(G)) + cG = nx.condensation(G, scc) + assert sorted(cG.nodes()) == [0, 1] + if 1 in scc[0]: + edge = (0, 1) + else: + edge = (1, 0) + assert list(cG.edges()) == [edge] + + def test_condensation_mapping_and_members(self): + G, C = self.gc[1] + C = sorted(C, key=len, reverse=True) + cG = nx.condensation(G) + mapping = cG.graph["mapping"] + assert all(n in G for n in mapping) + assert all(0 == cN for n, cN in mapping.items() if n in C[0]) + assert all(1 == cN for n, cN in mapping.items() if n in C[1]) + for n, d in cG.nodes(data=True): + assert set(C[n]) == cG.nodes[n]["members"] + + def test_null_graph(self): + G = nx.DiGraph() + assert list(nx.strongly_connected_components(G)) == [] + assert list(nx.kosaraju_strongly_connected_components(G)) == [] + assert len(nx.condensation(G)) == 0 + pytest.raises( + nx.NetworkXPointlessConcept, nx.is_strongly_connected, nx.DiGraph() + ) + + def test_connected_raise(self): + G = nx.Graph() + with pytest.raises(NetworkXNotImplemented): + next(nx.strongly_connected_components(G)) + with pytest.raises(NetworkXNotImplemented): + next(nx.kosaraju_strongly_connected_components(G)) + pytest.raises(NetworkXNotImplemented, nx.is_strongly_connected, G) + pytest.raises(NetworkXNotImplemented, nx.condensation, G) + + strong_cc_methods = ( + nx.strongly_connected_components, + nx.kosaraju_strongly_connected_components, + ) + + @pytest.mark.parametrize("get_components", strong_cc_methods) + def test_connected_mutability(self, get_components): + DG = nx.path_graph(5, create_using=nx.DiGraph) + G = nx.disjoint_union(DG, DG) + seen = set() + for component in get_components(G): + assert len(seen & component) == 0 + seen.update(component) + component.clear() diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/components/weakly_connected.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/weakly_connected.py new file mode 100644 index 0000000000000000000000000000000000000000..ecfac50a75177a7a87e41430953276e29778d6e0 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/components/weakly_connected.py @@ -0,0 +1,197 @@ +"""Weakly connected components.""" + +import networkx as nx +from networkx.utils.decorators import not_implemented_for + +__all__ = [ + "number_weakly_connected_components", + "weakly_connected_components", + "is_weakly_connected", +] + + +@not_implemented_for("undirected") +@nx._dispatchable +def weakly_connected_components(G): + """Generate weakly connected components of G. + + Parameters + ---------- + G : NetworkX graph + A directed graph + + Returns + ------- + comp : generator of sets + A generator of sets of nodes, one for each weakly connected + component of G. + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + Examples + -------- + Generate a sorted list of weakly connected components, largest first. + + >>> G = nx.path_graph(4, create_using=nx.DiGraph()) + >>> nx.add_path(G, [10, 11, 12]) + >>> [ + ... len(c) + ... for c in sorted(nx.weakly_connected_components(G), key=len, reverse=True) + ... ] + [4, 3] + + If you only want the largest component, it's more efficient to + use max instead of sort: + + >>> largest_cc = max(nx.weakly_connected_components(G), key=len) + + See Also + -------- + connected_components + strongly_connected_components + + Notes + ----- + For directed graphs only. + + """ + seen = set() + n = len(G) # must be outside the loop to avoid performance hit with graph views + for v in G: + if v not in seen: + c = set(_plain_bfs(G, n, v)) + seen.update(c) + yield c + + +@not_implemented_for("undirected") +@nx._dispatchable +def number_weakly_connected_components(G): + """Returns the number of weakly connected components in G. + + Parameters + ---------- + G : NetworkX graph + A directed graph. + + Returns + ------- + n : integer + Number of weakly connected components + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + Examples + -------- + >>> G = nx.DiGraph([(0, 1), (2, 1), (3, 4)]) + >>> nx.number_weakly_connected_components(G) + 2 + + See Also + -------- + weakly_connected_components + number_connected_components + number_strongly_connected_components + + Notes + ----- + For directed graphs only. + + """ + return sum(1 for wcc in weakly_connected_components(G)) + + +@not_implemented_for("undirected") +@nx._dispatchable +def is_weakly_connected(G): + """Test directed graph for weak connectivity. + + A directed graph is weakly connected if and only if the graph + is connected when the direction of the edge between nodes is ignored. + + Note that if a graph is strongly connected (i.e. the graph is connected + even when we account for directionality), it is by definition weakly + connected as well. + + Parameters + ---------- + G : NetworkX Graph + A directed graph. + + Returns + ------- + connected : bool + True if the graph is weakly connected, False otherwise. + + Raises + ------ + NetworkXNotImplemented + If G is undirected. + + Examples + -------- + >>> G = nx.DiGraph([(0, 1), (2, 1)]) + >>> G.add_node(3) + >>> nx.is_weakly_connected(G) # node 3 is not connected to the graph + False + >>> G.add_edge(2, 3) + >>> nx.is_weakly_connected(G) + True + + See Also + -------- + is_strongly_connected + is_semiconnected + is_connected + is_biconnected + weakly_connected_components + + Notes + ----- + For directed graphs only. + + """ + if len(G) == 0: + raise nx.NetworkXPointlessConcept( + """Connectivity is undefined for the null graph.""" + ) + + return len(next(weakly_connected_components(G))) == len(G) + + +def _plain_bfs(G, n, source): + """A fast BFS node generator + + The direction of the edge between nodes is ignored. + + For directed graphs only. + + """ + Gsucc = G._succ + Gpred = G._pred + seen = {source} + nextlevel = [source] + + yield source + while nextlevel: + thislevel = nextlevel + nextlevel = [] + for v in thislevel: + for w in Gsucc[v]: + if w not in seen: + seen.add(w) + nextlevel.append(w) + yield w + for w in Gpred[v]: + if w not in seen: + seen.add(w) + nextlevel.append(w) + yield w + if len(seen) == n: + return diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/__init__.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..d08a360628d4604bb37d350746e5c9796fe31d06 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/__init__.py @@ -0,0 +1,11 @@ +"""Connectivity and cut algorithms""" + +from .connectivity import * +from .cuts import * +from .edge_augmentation import * +from .edge_kcomponents import * +from .disjoint_paths import * +from .kcomponents import * +from .kcutsets import * +from .stoerwagner import * +from .utils import * diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/__pycache__/utils.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/__pycache__/utils.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..77ebcf6be6e8fb06324bdd49fc54eb52a9a359b9 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/__pycache__/utils.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/cuts.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/cuts.py new file mode 100644 index 0000000000000000000000000000000000000000..27124e1bdd6fece3a1b4fad13cbf6529f1cc8d71 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/cuts.py @@ -0,0 +1,612 @@ +""" +Flow based cut algorithms +""" + +import itertools + +import networkx as nx + +# Define the default maximum flow function to use in all flow based +# cut algorithms. +from networkx.algorithms.flow import build_residual_network, edmonds_karp + +default_flow_func = edmonds_karp + +from .utils import build_auxiliary_edge_connectivity, build_auxiliary_node_connectivity + +__all__ = [ + "minimum_st_node_cut", + "minimum_node_cut", + "minimum_st_edge_cut", + "minimum_edge_cut", +] + + +@nx._dispatchable( + graphs={"G": 0, "auxiliary?": 4}, + preserve_edge_attrs={"auxiliary": {"capacity": float("inf")}}, + preserve_graph_attrs={"auxiliary"}, +) +def minimum_st_edge_cut(G, s, t, flow_func=None, auxiliary=None, residual=None): + """Returns the edges of the cut-set of a minimum (s, t)-cut. + + This function returns the set of edges of minimum cardinality that, + if removed, would destroy all paths among source and target in G. + Edge weights are not considered. See :meth:`minimum_cut` for + computing minimum cuts considering edge weights. + + Parameters + ---------- + G : NetworkX graph + + s : node + Source node for the flow. + + t : node + Sink node for the flow. + + auxiliary : NetworkX DiGraph + Auxiliary digraph to compute flow based node connectivity. It has + to have a graph attribute called mapping with a dictionary mapping + node names in G and in the auxiliary digraph. If provided + it will be reused instead of recreated. Default value: None. + + flow_func : function + A function for computing the maximum flow among a pair of nodes. + The function has to accept at least three parameters: a Digraph, + a source node, and a target node. And return a residual network + that follows NetworkX conventions (see :meth:`maximum_flow` for + details). If flow_func is None, the default maximum flow function + (:meth:`edmonds_karp`) is used. See :meth:`node_connectivity` for + details. The choice of the default function may change from version + to version and should not be relied on. Default value: None. + + residual : NetworkX DiGraph + Residual network to compute maximum flow. If provided it will be + reused instead of recreated. Default value: None. + + Returns + ------- + cutset : set + Set of edges that, if removed from the graph, will disconnect it. + + See also + -------- + :meth:`minimum_cut` + :meth:`minimum_node_cut` + :meth:`minimum_edge_cut` + :meth:`stoer_wagner` + :meth:`node_connectivity` + :meth:`edge_connectivity` + :meth:`maximum_flow` + :meth:`edmonds_karp` + :meth:`preflow_push` + :meth:`shortest_augmenting_path` + + Examples + -------- + This function is not imported in the base NetworkX namespace, so you + have to explicitly import it from the connectivity package: + + >>> from networkx.algorithms.connectivity import minimum_st_edge_cut + + We use in this example the platonic icosahedral graph, which has edge + connectivity 5. + + >>> G = nx.icosahedral_graph() + >>> len(minimum_st_edge_cut(G, 0, 6)) + 5 + + If you need to compute local edge cuts on several pairs of + nodes in the same graph, it is recommended that you reuse the + data structures that NetworkX uses in the computation: the + auxiliary digraph for edge connectivity, and the residual + network for the underlying maximum flow computation. + + Example of how to compute local edge cuts among all pairs of + nodes of the platonic icosahedral graph reusing the data + structures. + + >>> import itertools + >>> # You also have to explicitly import the function for + >>> # building the auxiliary digraph from the connectivity package + >>> from networkx.algorithms.connectivity import build_auxiliary_edge_connectivity + >>> H = build_auxiliary_edge_connectivity(G) + >>> # And the function for building the residual network from the + >>> # flow package + >>> from networkx.algorithms.flow import build_residual_network + >>> # Note that the auxiliary digraph has an edge attribute named capacity + >>> R = build_residual_network(H, "capacity") + >>> result = dict.fromkeys(G, dict()) + >>> # Reuse the auxiliary digraph and the residual network by passing them + >>> # as parameters + >>> for u, v in itertools.combinations(G, 2): + ... k = len(minimum_st_edge_cut(G, u, v, auxiliary=H, residual=R)) + ... result[u][v] = k + >>> all(result[u][v] == 5 for u, v in itertools.combinations(G, 2)) + True + + You can also use alternative flow algorithms for computing edge + cuts. For instance, in dense networks the algorithm + :meth:`shortest_augmenting_path` will usually perform better than + the default :meth:`edmonds_karp` which is faster for sparse + networks with highly skewed degree distributions. Alternative flow + functions have to be explicitly imported from the flow package. + + >>> from networkx.algorithms.flow import shortest_augmenting_path + >>> len(minimum_st_edge_cut(G, 0, 6, flow_func=shortest_augmenting_path)) + 5 + + """ + if flow_func is None: + flow_func = default_flow_func + + if auxiliary is None: + H = build_auxiliary_edge_connectivity(G) + else: + H = auxiliary + + kwargs = {"capacity": "capacity", "flow_func": flow_func, "residual": residual} + + cut_value, partition = nx.minimum_cut(H, s, t, **kwargs) + reachable, non_reachable = partition + # Any edge in the original graph linking the two sets in the + # partition is part of the edge cutset + cutset = set() + for u, nbrs in ((n, G[n]) for n in reachable): + cutset.update((u, v) for v in nbrs if v in non_reachable) + + return cutset + + +@nx._dispatchable( + graphs={"G": 0, "auxiliary?": 4}, + preserve_node_attrs={"auxiliary": {"id": None}}, + preserve_graph_attrs={"auxiliary"}, +) +def minimum_st_node_cut(G, s, t, flow_func=None, auxiliary=None, residual=None): + r"""Returns a set of nodes of minimum cardinality that disconnect source + from target in G. + + This function returns the set of nodes of minimum cardinality that, + if removed, would destroy all paths among source and target in G. + + Parameters + ---------- + G : NetworkX graph + + s : node + Source node. + + t : node + Target node. + + flow_func : function + A function for computing the maximum flow among a pair of nodes. + The function has to accept at least three parameters: a Digraph, + a source node, and a target node. And return a residual network + that follows NetworkX conventions (see :meth:`maximum_flow` for + details). If flow_func is None, the default maximum flow function + (:meth:`edmonds_karp`) is used. See below for details. The choice + of the default function may change from version to version and + should not be relied on. Default value: None. + + auxiliary : NetworkX DiGraph + Auxiliary digraph to compute flow based node connectivity. It has + to have a graph attribute called mapping with a dictionary mapping + node names in G and in the auxiliary digraph. If provided + it will be reused instead of recreated. Default value: None. + + residual : NetworkX DiGraph + Residual network to compute maximum flow. If provided it will be + reused instead of recreated. Default value: None. + + Returns + ------- + cutset : set + Set of nodes that, if removed, would destroy all paths between + source and target in G. + + Examples + -------- + This function is not imported in the base NetworkX namespace, so you + have to explicitly import it from the connectivity package: + + >>> from networkx.algorithms.connectivity import minimum_st_node_cut + + We use in this example the platonic icosahedral graph, which has node + connectivity 5. + + >>> G = nx.icosahedral_graph() + >>> len(minimum_st_node_cut(G, 0, 6)) + 5 + + If you need to compute local st cuts between several pairs of + nodes in the same graph, it is recommended that you reuse the + data structures that NetworkX uses in the computation: the + auxiliary digraph for node connectivity and node cuts, and the + residual network for the underlying maximum flow computation. + + Example of how to compute local st node cuts reusing the data + structures: + + >>> # You also have to explicitly import the function for + >>> # building the auxiliary digraph from the connectivity package + >>> from networkx.algorithms.connectivity import build_auxiliary_node_connectivity + >>> H = build_auxiliary_node_connectivity(G) + >>> # And the function for building the residual network from the + >>> # flow package + >>> from networkx.algorithms.flow import build_residual_network + >>> # Note that the auxiliary digraph has an edge attribute named capacity + >>> R = build_residual_network(H, "capacity") + >>> # Reuse the auxiliary digraph and the residual network by passing them + >>> # as parameters + >>> len(minimum_st_node_cut(G, 0, 6, auxiliary=H, residual=R)) + 5 + + You can also use alternative flow algorithms for computing minimum st + node cuts. For instance, in dense networks the algorithm + :meth:`shortest_augmenting_path` will usually perform better than + the default :meth:`edmonds_karp` which is faster for sparse + networks with highly skewed degree distributions. Alternative flow + functions have to be explicitly imported from the flow package. + + >>> from networkx.algorithms.flow import shortest_augmenting_path + >>> len(minimum_st_node_cut(G, 0, 6, flow_func=shortest_augmenting_path)) + 5 + + Notes + ----- + This is a flow based implementation of minimum node cut. The algorithm + is based in solving a number of maximum flow computations to determine + the capacity of the minimum cut on an auxiliary directed network that + corresponds to the minimum node cut of G. It handles both directed + and undirected graphs. This implementation is based on algorithm 11 + in [1]_. + + See also + -------- + :meth:`minimum_node_cut` + :meth:`minimum_edge_cut` + :meth:`stoer_wagner` + :meth:`node_connectivity` + :meth:`edge_connectivity` + :meth:`maximum_flow` + :meth:`edmonds_karp` + :meth:`preflow_push` + :meth:`shortest_augmenting_path` + + References + ---------- + .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms. + http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf + + """ + if auxiliary is None: + H = build_auxiliary_node_connectivity(G) + else: + H = auxiliary + + mapping = H.graph.get("mapping", None) + if mapping is None: + raise nx.NetworkXError("Invalid auxiliary digraph.") + if G.has_edge(s, t) or G.has_edge(t, s): + return {} + kwargs = {"flow_func": flow_func, "residual": residual, "auxiliary": H} + + # The edge cut in the auxiliary digraph corresponds to the node cut in the + # original graph. + edge_cut = minimum_st_edge_cut(H, f"{mapping[s]}B", f"{mapping[t]}A", **kwargs) + # Each node in the original graph maps to two nodes of the auxiliary graph + node_cut = {H.nodes[node]["id"] for edge in edge_cut for node in edge} + return node_cut - {s, t} + + +@nx._dispatchable +def minimum_node_cut(G, s=None, t=None, flow_func=None): + r"""Returns a set of nodes of minimum cardinality that disconnects G. + + If source and target nodes are provided, this function returns the + set of nodes of minimum cardinality that, if removed, would destroy + all paths among source and target in G. If not, it returns a set + of nodes of minimum cardinality that disconnects G. + + Parameters + ---------- + G : NetworkX graph + + s : node + Source node. Optional. Default value: None. + + t : node + Target node. Optional. Default value: None. + + flow_func : function + A function for computing the maximum flow among a pair of nodes. + The function has to accept at least three parameters: a Digraph, + a source node, and a target node. And return a residual network + that follows NetworkX conventions (see :meth:`maximum_flow` for + details). If flow_func is None, the default maximum flow function + (:meth:`edmonds_karp`) is used. See below for details. The + choice of the default function may change from version + to version and should not be relied on. Default value: None. + + Returns + ------- + cutset : set + Set of nodes that, if removed, would disconnect G. If source + and target nodes are provided, the set contains the nodes that + if removed, would destroy all paths between source and target. + + Examples + -------- + >>> # Platonic icosahedral graph has node connectivity 5 + >>> G = nx.icosahedral_graph() + >>> node_cut = nx.minimum_node_cut(G) + >>> len(node_cut) + 5 + + You can use alternative flow algorithms for the underlying maximum + flow computation. In dense networks the algorithm + :meth:`shortest_augmenting_path` will usually perform better + than the default :meth:`edmonds_karp`, which is faster for + sparse networks with highly skewed degree distributions. Alternative + flow functions have to be explicitly imported from the flow package. + + >>> from networkx.algorithms.flow import shortest_augmenting_path + >>> node_cut == nx.minimum_node_cut(G, flow_func=shortest_augmenting_path) + True + + If you specify a pair of nodes (source and target) as parameters, + this function returns a local st node cut. + + >>> len(nx.minimum_node_cut(G, 3, 7)) + 5 + + If you need to perform several local st cuts among different + pairs of nodes on the same graph, it is recommended that you reuse + the data structures used in the maximum flow computations. See + :meth:`minimum_st_node_cut` for details. + + Notes + ----- + This is a flow based implementation of minimum node cut. The algorithm + is based in solving a number of maximum flow computations to determine + the capacity of the minimum cut on an auxiliary directed network that + corresponds to the minimum node cut of G. It handles both directed + and undirected graphs. This implementation is based on algorithm 11 + in [1]_. + + See also + -------- + :meth:`minimum_st_node_cut` + :meth:`minimum_cut` + :meth:`minimum_edge_cut` + :meth:`stoer_wagner` + :meth:`node_connectivity` + :meth:`edge_connectivity` + :meth:`maximum_flow` + :meth:`edmonds_karp` + :meth:`preflow_push` + :meth:`shortest_augmenting_path` + + References + ---------- + .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms. + http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf + + """ + if (s is not None and t is None) or (s is None and t is not None): + raise nx.NetworkXError("Both source and target must be specified.") + + # Local minimum node cut. + if s is not None and t is not None: + if s not in G: + raise nx.NetworkXError(f"node {s} not in graph") + if t not in G: + raise nx.NetworkXError(f"node {t} not in graph") + return minimum_st_node_cut(G, s, t, flow_func=flow_func) + + # Global minimum node cut. + # Analog to the algorithm 11 for global node connectivity in [1]. + if G.is_directed(): + if not nx.is_weakly_connected(G): + raise nx.NetworkXError("Input graph is not connected") + iter_func = itertools.permutations + + def neighbors(v): + return itertools.chain.from_iterable([G.predecessors(v), G.successors(v)]) + + else: + if not nx.is_connected(G): + raise nx.NetworkXError("Input graph is not connected") + iter_func = itertools.combinations + neighbors = G.neighbors + + # Reuse the auxiliary digraph and the residual network. + H = build_auxiliary_node_connectivity(G) + R = build_residual_network(H, "capacity") + kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R} + + # Choose a node with minimum degree. + v = min(G, key=G.degree) + # Initial node cutset is all neighbors of the node with minimum degree. + min_cut = set(G[v]) + # Compute st node cuts between v and all its non-neighbors nodes in G. + for w in set(G) - set(neighbors(v)) - {v}: + this_cut = minimum_st_node_cut(G, v, w, **kwargs) + if len(min_cut) >= len(this_cut): + min_cut = this_cut + # Also for non adjacent pairs of neighbors of v. + for x, y in iter_func(neighbors(v), 2): + if y in G[x]: + continue + this_cut = minimum_st_node_cut(G, x, y, **kwargs) + if len(min_cut) >= len(this_cut): + min_cut = this_cut + + return min_cut + + +@nx._dispatchable +def minimum_edge_cut(G, s=None, t=None, flow_func=None): + r"""Returns a set of edges of minimum cardinality that disconnects G. + + If source and target nodes are provided, this function returns the + set of edges of minimum cardinality that, if removed, would break + all paths among source and target in G. If not, it returns a set of + edges of minimum cardinality that disconnects G. + + Parameters + ---------- + G : NetworkX graph + + s : node + Source node. Optional. Default value: None. + + t : node + Target node. Optional. Default value: None. + + flow_func : function + A function for computing the maximum flow among a pair of nodes. + The function has to accept at least three parameters: a Digraph, + a source node, and a target node. And return a residual network + that follows NetworkX conventions (see :meth:`maximum_flow` for + details). If flow_func is None, the default maximum flow function + (:meth:`edmonds_karp`) is used. See below for details. The + choice of the default function may change from version + to version and should not be relied on. Default value: None. + + Returns + ------- + cutset : set + Set of edges that, if removed, would disconnect G. If source + and target nodes are provided, the set contains the edges that + if removed, would destroy all paths between source and target. + + Examples + -------- + >>> # Platonic icosahedral graph has edge connectivity 5 + >>> G = nx.icosahedral_graph() + >>> len(nx.minimum_edge_cut(G)) + 5 + + You can use alternative flow algorithms for the underlying + maximum flow computation. In dense networks the algorithm + :meth:`shortest_augmenting_path` will usually perform better + than the default :meth:`edmonds_karp`, which is faster for + sparse networks with highly skewed degree distributions. + Alternative flow functions have to be explicitly imported + from the flow package. + + >>> from networkx.algorithms.flow import shortest_augmenting_path + >>> len(nx.minimum_edge_cut(G, flow_func=shortest_augmenting_path)) + 5 + + If you specify a pair of nodes (source and target) as parameters, + this function returns the value of local edge connectivity. + + >>> nx.edge_connectivity(G, 3, 7) + 5 + + If you need to perform several local computations among different + pairs of nodes on the same graph, it is recommended that you reuse + the data structures used in the maximum flow computations. See + :meth:`local_edge_connectivity` for details. + + Notes + ----- + This is a flow based implementation of minimum edge cut. For + undirected graphs the algorithm works by finding a 'small' dominating + set of nodes of G (see algorithm 7 in [1]_) and computing the maximum + flow between an arbitrary node in the dominating set and the rest of + nodes in it. This is an implementation of algorithm 6 in [1]_. For + directed graphs, the algorithm does n calls to the max flow function. + The function raises an error if the directed graph is not weakly + connected and returns an empty set if it is weakly connected. + It is an implementation of algorithm 8 in [1]_. + + See also + -------- + :meth:`minimum_st_edge_cut` + :meth:`minimum_node_cut` + :meth:`stoer_wagner` + :meth:`node_connectivity` + :meth:`edge_connectivity` + :meth:`maximum_flow` + :meth:`edmonds_karp` + :meth:`preflow_push` + :meth:`shortest_augmenting_path` + + References + ---------- + .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms. + http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf + + """ + if (s is not None and t is None) or (s is None and t is not None): + raise nx.NetworkXError("Both source and target must be specified.") + + # reuse auxiliary digraph and residual network + H = build_auxiliary_edge_connectivity(G) + R = build_residual_network(H, "capacity") + kwargs = {"flow_func": flow_func, "residual": R, "auxiliary": H} + + # Local minimum edge cut if s and t are not None + if s is not None and t is not None: + if s not in G: + raise nx.NetworkXError(f"node {s} not in graph") + if t not in G: + raise nx.NetworkXError(f"node {t} not in graph") + return minimum_st_edge_cut(H, s, t, **kwargs) + + # Global minimum edge cut + # Analog to the algorithm for global edge connectivity + if G.is_directed(): + # Based on algorithm 8 in [1] + if not nx.is_weakly_connected(G): + raise nx.NetworkXError("Input graph is not connected") + + # Initial cutset is all edges of a node with minimum degree + node = min(G, key=G.degree) + min_cut = set(G.edges(node)) + nodes = list(G) + n = len(nodes) + for i in range(n): + try: + this_cut = minimum_st_edge_cut(H, nodes[i], nodes[i + 1], **kwargs) + if len(this_cut) <= len(min_cut): + min_cut = this_cut + except IndexError: # Last node! + this_cut = minimum_st_edge_cut(H, nodes[i], nodes[0], **kwargs) + if len(this_cut) <= len(min_cut): + min_cut = this_cut + + return min_cut + + else: # undirected + # Based on algorithm 6 in [1] + if not nx.is_connected(G): + raise nx.NetworkXError("Input graph is not connected") + + # Initial cutset is all edges of a node with minimum degree + node = min(G, key=G.degree) + min_cut = set(G.edges(node)) + # A dominating set is \lambda-covering + # We need a dominating set with at least two nodes + for node in G: + D = nx.dominating_set(G, start_with=node) + v = D.pop() + if D: + break + else: + # in complete graphs the dominating set will always be of one node + # thus we return min_cut, which now contains the edges of a node + # with minimum degree + return min_cut + for w in D: + this_cut = minimum_st_edge_cut(H, v, w, **kwargs) + if len(this_cut) <= len(min_cut): + min_cut = this_cut + + return min_cut diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/kcomponents.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/kcomponents.py new file mode 100644 index 0000000000000000000000000000000000000000..e2f1ba289fb14a705ab6b80883d36f9cdcbed7f1 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/kcomponents.py @@ -0,0 +1,223 @@ +""" +Moody and White algorithm for k-components +""" + +from collections import defaultdict +from itertools import combinations +from operator import itemgetter + +import networkx as nx + +# Define the default maximum flow function. +from networkx.algorithms.flow import edmonds_karp +from networkx.utils import not_implemented_for + +default_flow_func = edmonds_karp + +__all__ = ["k_components"] + + +@not_implemented_for("directed") +@nx._dispatchable +def k_components(G, flow_func=None): + r"""Returns the k-component structure of a graph G. + + A `k`-component is a maximal subgraph of a graph G that has, at least, + node connectivity `k`: we need to remove at least `k` nodes to break it + into more components. `k`-components have an inherent hierarchical + structure because they are nested in terms of connectivity: a connected + graph can contain several 2-components, each of which can contain + one or more 3-components, and so forth. + + Parameters + ---------- + G : NetworkX graph + + flow_func : function + Function to perform the underlying flow computations. Default value + :meth:`edmonds_karp`. This function performs better in sparse graphs with + right tailed degree distributions. :meth:`shortest_augmenting_path` will + perform better in denser graphs. + + Returns + ------- + k_components : dict + Dictionary with all connectivity levels `k` in the input Graph as keys + and a list of sets of nodes that form a k-component of level `k` as + values. + + Raises + ------ + NetworkXNotImplemented + If the input graph is directed. + + Examples + -------- + >>> # Petersen graph has 10 nodes and it is triconnected, thus all + >>> # nodes are in a single component on all three connectivity levels + >>> G = nx.petersen_graph() + >>> k_components = nx.k_components(G) + + Notes + ----- + Moody and White [1]_ (appendix A) provide an algorithm for identifying + k-components in a graph, which is based on Kanevsky's algorithm [2]_ + for finding all minimum-size node cut-sets of a graph (implemented in + :meth:`all_node_cuts` function): + + 1. Compute node connectivity, k, of the input graph G. + + 2. Identify all k-cutsets at the current level of connectivity using + Kanevsky's algorithm. + + 3. Generate new graph components based on the removal of + these cutsets. Nodes in a cutset belong to both sides + of the induced cut. + + 4. If the graph is neither complete nor trivial, return to 1; + else end. + + This implementation also uses some heuristics (see [3]_ for details) + to speed up the computation. + + See also + -------- + node_connectivity + all_node_cuts + biconnected_components : special case of this function when k=2 + k_edge_components : similar to this function, but uses edge-connectivity + instead of node-connectivity + + References + ---------- + .. [1] Moody, J. and D. White (2003). Social cohesion and embeddedness: + A hierarchical conception of social groups. + American Sociological Review 68(1), 103--28. + http://www2.asanet.org/journals/ASRFeb03MoodyWhite.pdf + + .. [2] Kanevsky, A. (1993). Finding all minimum-size separating vertex + sets in a graph. Networks 23(6), 533--541. + http://onlinelibrary.wiley.com/doi/10.1002/net.3230230604/abstract + + .. [3] Torrents, J. and F. Ferraro (2015). Structural Cohesion: + Visualization and Heuristics for Fast Computation. + https://arxiv.org/pdf/1503.04476v1 + + """ + # Dictionary with connectivity level (k) as keys and a list of + # sets of nodes that form a k-component as values. Note that + # k-components can overlap (but only k - 1 nodes). + k_components = defaultdict(list) + # Define default flow function + if flow_func is None: + flow_func = default_flow_func + # Bicomponents as a base to check for higher order k-components + for component in nx.connected_components(G): + # isolated nodes have connectivity 0 + comp = set(component) + if len(comp) > 1: + k_components[1].append(comp) + bicomponents = [G.subgraph(c) for c in nx.biconnected_components(G)] + for bicomponent in bicomponents: + bicomp = set(bicomponent) + # avoid considering dyads as bicomponents + if len(bicomp) > 2: + k_components[2].append(bicomp) + for B in bicomponents: + if len(B) <= 2: + continue + k = nx.node_connectivity(B, flow_func=flow_func) + if k > 2: + k_components[k].append(set(B)) + # Perform cuts in a DFS like order. + cuts = list(nx.all_node_cuts(B, k=k, flow_func=flow_func)) + stack = [(k, _generate_partition(B, cuts, k))] + while stack: + (parent_k, partition) = stack[-1] + try: + nodes = next(partition) + C = B.subgraph(nodes) + this_k = nx.node_connectivity(C, flow_func=flow_func) + if this_k > parent_k and this_k > 2: + k_components[this_k].append(set(C)) + cuts = list(nx.all_node_cuts(C, k=this_k, flow_func=flow_func)) + if cuts: + stack.append((this_k, _generate_partition(C, cuts, this_k))) + except StopIteration: + stack.pop() + + # This is necessary because k-components may only be reported at their + # maximum k level. But we want to return a dictionary in which keys are + # connectivity levels and values list of sets of components, without + # skipping any connectivity level. Also, it's possible that subsets of + # an already detected k-component appear at a level k. Checking for this + # in the while loop above penalizes the common case. Thus we also have to + # _consolidate all connectivity levels in _reconstruct_k_components. + return _reconstruct_k_components(k_components) + + +def _consolidate(sets, k): + """Merge sets that share k or more elements. + + See: http://rosettacode.org/wiki/Set_consolidation + + The iterative python implementation posted there is + faster than this because of the overhead of building a + Graph and calling nx.connected_components, but it's not + clear for us if we can use it in NetworkX because there + is no licence for the code. + + """ + G = nx.Graph() + nodes = dict(enumerate(sets)) + G.add_nodes_from(nodes) + G.add_edges_from( + (u, v) for u, v in combinations(nodes, 2) if len(nodes[u] & nodes[v]) >= k + ) + for component in nx.connected_components(G): + yield set.union(*[nodes[n] for n in component]) + + +def _generate_partition(G, cuts, k): + def has_nbrs_in_partition(G, node, partition): + return any(n in partition for n in G[node]) + + components = [] + nodes = {n for n, d in G.degree() if d > k} - {n for cut in cuts for n in cut} + H = G.subgraph(nodes) + for cc in nx.connected_components(H): + component = set(cc) + for cut in cuts: + for node in cut: + if has_nbrs_in_partition(G, node, cc): + component.add(node) + if len(component) < G.order(): + components.append(component) + yield from _consolidate(components, k + 1) + + +def _reconstruct_k_components(k_comps): + result = {} + max_k = max(k_comps) + for k in reversed(range(1, max_k + 1)): + if k == max_k: + result[k] = list(_consolidate(k_comps[k], k)) + elif k not in k_comps: + result[k] = list(_consolidate(result[k + 1], k)) + else: + nodes_at_k = set.union(*k_comps[k]) + to_add = [c for c in result[k + 1] if any(n not in nodes_at_k for n in c)] + if to_add: + result[k] = list(_consolidate(k_comps[k] + to_add, k)) + else: + result[k] = list(_consolidate(k_comps[k], k)) + return result + + +def build_k_number_dict(kcomps): + result = {} + for k, comps in sorted(kcomps.items(), key=itemgetter(0)): + for comp in comps: + for node in comp: + result[node] = k + return result diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/kcutsets.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/kcutsets.py new file mode 100644 index 0000000000000000000000000000000000000000..de26f4c5d85f42312a811509b7a9b92cd5db952c --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/kcutsets.py @@ -0,0 +1,235 @@ +""" +Kanevsky all minimum node k cutsets algorithm. +""" + +import copy +from collections import defaultdict +from itertools import combinations +from operator import itemgetter + +import networkx as nx +from networkx.algorithms.flow import ( + build_residual_network, + edmonds_karp, + shortest_augmenting_path, +) + +from .utils import build_auxiliary_node_connectivity + +default_flow_func = edmonds_karp + + +__all__ = ["all_node_cuts"] + + +@nx._dispatchable +def all_node_cuts(G, k=None, flow_func=None): + r"""Returns all minimum k cutsets of an undirected graph G. + + This implementation is based on Kanevsky's algorithm [1]_ for finding all + minimum-size node cut-sets of an undirected graph G; ie the set (or sets) + of nodes of cardinality equal to the node connectivity of G. Thus if + removed, would break G into two or more connected components. + + Parameters + ---------- + G : NetworkX graph + Undirected graph + + k : Integer + Node connectivity of the input graph. If k is None, then it is + computed. Default value: None. + + flow_func : function + Function to perform the underlying flow computations. Default value is + :func:`~networkx.algorithms.flow.edmonds_karp`. This function performs + better in sparse graphs with right tailed degree distributions. + :func:`~networkx.algorithms.flow.shortest_augmenting_path` will + perform better in denser graphs. + + + Returns + ------- + cuts : a generator of node cutsets + Each node cutset has cardinality equal to the node connectivity of + the input graph. + + Examples + -------- + >>> # A two-dimensional grid graph has 4 cutsets of cardinality 2 + >>> G = nx.grid_2d_graph(5, 5) + >>> cutsets = list(nx.all_node_cuts(G)) + >>> len(cutsets) + 4 + >>> all(2 == len(cutset) for cutset in cutsets) + True + >>> nx.node_connectivity(G) + 2 + + Notes + ----- + This implementation is based on the sequential algorithm for finding all + minimum-size separating vertex sets in a graph [1]_. The main idea is to + compute minimum cuts using local maximum flow computations among a set + of nodes of highest degree and all other non-adjacent nodes in the Graph. + Once we find a minimum cut, we add an edge between the high degree + node and the target node of the local maximum flow computation to make + sure that we will not find that minimum cut again. + + See also + -------- + node_connectivity + edmonds_karp + shortest_augmenting_path + + References + ---------- + .. [1] Kanevsky, A. (1993). Finding all minimum-size separating vertex + sets in a graph. Networks 23(6), 533--541. + http://onlinelibrary.wiley.com/doi/10.1002/net.3230230604/abstract + + """ + if not nx.is_connected(G): + raise nx.NetworkXError("Input graph is disconnected.") + + # Address some corner cases first. + # For complete Graphs + + if nx.density(G) == 1: + yield from () + return + + # Initialize data structures. + # Keep track of the cuts already computed so we do not repeat them. + seen = [] + # Even-Tarjan reduction is what we call auxiliary digraph + # for node connectivity. + H = build_auxiliary_node_connectivity(G) + H_nodes = H.nodes # for speed + mapping = H.graph["mapping"] + # Keep a copy of original predecessors, H will be modified later. + # Shallow copy is enough. + original_H_pred = copy.copy(H._pred) + R = build_residual_network(H, "capacity") + kwargs = {"capacity": "capacity", "residual": R} + # Define default flow function + if flow_func is None: + flow_func = default_flow_func + if flow_func is shortest_augmenting_path: + kwargs["two_phase"] = True + # Begin the actual algorithm + # step 1: Find node connectivity k of G + if k is None: + k = nx.node_connectivity(G, flow_func=flow_func) + # step 2: + # Find k nodes with top degree, call it X: + X = {n for n, d in sorted(G.degree(), key=itemgetter(1), reverse=True)[:k]} + # Check if X is a k-node-cutset + if _is_separating_set(G, X): + seen.append(X) + yield X + + for x in X: + # step 3: Compute local connectivity flow of x with all other + # non adjacent nodes in G + non_adjacent = set(G) - {x} - set(G[x]) + for v in non_adjacent: + # step 4: compute maximum flow in an Even-Tarjan reduction H of G + # and step 5: build the associated residual network R + R = flow_func(H, f"{mapping[x]}B", f"{mapping[v]}A", **kwargs) + flow_value = R.graph["flow_value"] + + if flow_value == k: + # Find the nodes incident to the flow. + E1 = flowed_edges = [ + (u, w) for (u, w, d) in R.edges(data=True) if d["flow"] != 0 + ] + VE1 = incident_nodes = {n for edge in E1 for n in edge} + # Remove saturated edges form the residual network. + # Note that reversed edges are introduced with capacity 0 + # in the residual graph and they need to be removed too. + saturated_edges = [ + (u, w, d) + for (u, w, d) in R.edges(data=True) + if d["capacity"] == d["flow"] or d["capacity"] == 0 + ] + R.remove_edges_from(saturated_edges) + R_closure = nx.transitive_closure(R) + # step 6: shrink the strongly connected components of + # residual flow network R and call it L. + L = nx.condensation(R) + cmap = L.graph["mapping"] + inv_cmap = defaultdict(list) + for n, scc in cmap.items(): + inv_cmap[scc].append(n) + # Find the incident nodes in the condensed graph. + VE1 = {cmap[n] for n in VE1} + # step 7: Compute all antichains of L; + # they map to closed sets in H. + # Any edge in H that links a closed set is part of a cutset. + for antichain in nx.antichains(L): + # Only antichains that are subsets of incident nodes counts. + # Lemma 8 in reference. + if not set(antichain).issubset(VE1): + continue + # Nodes in an antichain of the condensation graph of + # the residual network map to a closed set of nodes that + # define a node partition of the auxiliary digraph H + # through taking all of antichain's predecessors in the + # transitive closure. + S = set() + for scc in antichain: + S.update(inv_cmap[scc]) + S_ancestors = set() + for n in S: + S_ancestors.update(R_closure._pred[n]) + S.update(S_ancestors) + if f"{mapping[x]}B" not in S or f"{mapping[v]}A" in S: + continue + # Find the cutset that links the node partition (S,~S) in H + cutset = set() + for u in S: + cutset.update((u, w) for w in original_H_pred[u] if w not in S) + # The edges in H that form the cutset are internal edges + # (ie edges that represent a node of the original graph G) + if any(H_nodes[u]["id"] != H_nodes[w]["id"] for u, w in cutset): + continue + node_cut = {H_nodes[u]["id"] for u, _ in cutset} + + if len(node_cut) == k: + # The cut is invalid if it includes internal edges of + # end nodes. The other half of Lemma 8 in ref. + if x in node_cut or v in node_cut: + continue + if node_cut not in seen: + yield node_cut + seen.append(node_cut) + + # Add an edge (x, v) to make sure that we do not + # find this cutset again. This is equivalent + # of adding the edge in the input graph + # G.add_edge(x, v) and then regenerate H and R: + # Add edges to the auxiliary digraph. + # See build_residual_network for convention we used + # in residual graphs. + H.add_edge(f"{mapping[x]}B", f"{mapping[v]}A", capacity=1) + H.add_edge(f"{mapping[v]}B", f"{mapping[x]}A", capacity=1) + # Add edges to the residual network. + R.add_edge(f"{mapping[x]}B", f"{mapping[v]}A", capacity=1) + R.add_edge(f"{mapping[v]}A", f"{mapping[x]}B", capacity=0) + R.add_edge(f"{mapping[v]}B", f"{mapping[x]}A", capacity=1) + R.add_edge(f"{mapping[x]}A", f"{mapping[v]}B", capacity=0) + + # Add again the saturated edges to reuse the residual network + R.add_edges_from(saturated_edges) + + +def _is_separating_set(G, cut): + """Assumes that the input graph is connected""" + if len(cut) == len(G) - 1: + return True + + H = nx.restricted_view(G, cut, []) + if nx.is_connected(H): + return False + return True diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/tests/test_kcomponents.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/tests/test_kcomponents.py new file mode 100644 index 0000000000000000000000000000000000000000..f4436acd07fe57cb510fee138b36f10923a9688a --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/connectivity/tests/test_kcomponents.py @@ -0,0 +1,296 @@ +# Test for Moody and White k-components algorithm +import pytest + +import networkx as nx +from networkx.algorithms.connectivity.kcomponents import ( + _consolidate, + build_k_number_dict, +) + +## +# A nice synthetic graph +## + + +def torrents_and_ferraro_graph(): + # Graph from https://arxiv.org/pdf/1503.04476v1 p.26 + G = nx.convert_node_labels_to_integers( + nx.grid_graph([5, 5]), label_attribute="labels" + ) + rlabels = nx.get_node_attributes(G, "labels") + labels = {v: k for k, v in rlabels.items()} + + for nodes in [(labels[(0, 4)], labels[(1, 4)]), (labels[(3, 4)], labels[(4, 4)])]: + new_node = G.order() + 1 + # Petersen graph is triconnected + P = nx.petersen_graph() + G = nx.disjoint_union(G, P) + # Add two edges between the grid and P + G.add_edge(new_node + 1, nodes[0]) + G.add_edge(new_node, nodes[1]) + # K5 is 4-connected + K = nx.complete_graph(5) + G = nx.disjoint_union(G, K) + # Add three edges between P and K5 + G.add_edge(new_node + 2, new_node + 11) + G.add_edge(new_node + 3, new_node + 12) + G.add_edge(new_node + 4, new_node + 13) + # Add another K5 sharing a node + G = nx.disjoint_union(G, K) + nbrs = G[new_node + 10] + G.remove_node(new_node + 10) + for nbr in nbrs: + G.add_edge(new_node + 17, nbr) + # This edge makes the graph biconnected; it's + # needed because K5s share only one node. + G.add_edge(new_node + 16, new_node + 8) + + for nodes in [(labels[(0, 0)], labels[(1, 0)]), (labels[(3, 0)], labels[(4, 0)])]: + new_node = G.order() + 1 + # Petersen graph is triconnected + P = nx.petersen_graph() + G = nx.disjoint_union(G, P) + # Add two edges between the grid and P + G.add_edge(new_node + 1, nodes[0]) + G.add_edge(new_node, nodes[1]) + # K5 is 4-connected + K = nx.complete_graph(5) + G = nx.disjoint_union(G, K) + # Add three edges between P and K5 + G.add_edge(new_node + 2, new_node + 11) + G.add_edge(new_node + 3, new_node + 12) + G.add_edge(new_node + 4, new_node + 13) + # Add another K5 sharing two nodes + G = nx.disjoint_union(G, K) + nbrs = G[new_node + 10] + G.remove_node(new_node + 10) + for nbr in nbrs: + G.add_edge(new_node + 17, nbr) + nbrs2 = G[new_node + 9] + G.remove_node(new_node + 9) + for nbr in nbrs2: + G.add_edge(new_node + 18, nbr) + return G + + +def test_directed(): + with pytest.raises(nx.NetworkXNotImplemented): + G = nx.gnp_random_graph(10, 0.2, directed=True, seed=42) + nx.k_components(G) + + +# Helper function +def _check_connectivity(G, k_components): + for k, components in k_components.items(): + if k < 3: + continue + # check that k-components have node connectivity >= k. + for component in components: + C = G.subgraph(component) + K = nx.node_connectivity(C) + assert K >= k + + +@pytest.mark.slow +def test_torrents_and_ferraro_graph(): + G = torrents_and_ferraro_graph() + result = nx.k_components(G) + _check_connectivity(G, result) + + # In this example graph there are 8 3-components, 4 with 15 nodes + # and 4 with 5 nodes. + assert len(result[3]) == 8 + assert len([c for c in result[3] if len(c) == 15]) == 4 + assert len([c for c in result[3] if len(c) == 5]) == 4 + # There are also 8 4-components all with 5 nodes. + assert len(result[4]) == 8 + assert all(len(c) == 5 for c in result[4]) + + +@pytest.mark.slow +def test_random_gnp(): + G = nx.gnp_random_graph(50, 0.2, seed=42) + result = nx.k_components(G) + _check_connectivity(G, result) + + +@pytest.mark.slow +def test_shell(): + constructor = [(20, 80, 0.8), (80, 180, 0.6)] + G = nx.random_shell_graph(constructor, seed=42) + result = nx.k_components(G) + _check_connectivity(G, result) + + +def test_configuration(): + deg_seq = nx.random_powerlaw_tree_sequence(100, tries=5, seed=72) + G = nx.Graph(nx.configuration_model(deg_seq)) + G.remove_edges_from(nx.selfloop_edges(G)) + result = nx.k_components(G) + _check_connectivity(G, result) + + +def test_karate(): + G = nx.karate_club_graph() + result = nx.k_components(G) + _check_connectivity(G, result) + + +def test_karate_component_number(): + karate_k_num = { + 0: 4, + 1: 4, + 2: 4, + 3: 4, + 4: 3, + 5: 3, + 6: 3, + 7: 4, + 8: 4, + 9: 2, + 10: 3, + 11: 1, + 12: 2, + 13: 4, + 14: 2, + 15: 2, + 16: 2, + 17: 2, + 18: 2, + 19: 3, + 20: 2, + 21: 2, + 22: 2, + 23: 3, + 24: 3, + 25: 3, + 26: 2, + 27: 3, + 28: 3, + 29: 3, + 30: 4, + 31: 3, + 32: 4, + 33: 4, + } + G = nx.karate_club_graph() + k_components = nx.k_components(G) + k_num = build_k_number_dict(k_components) + assert karate_k_num == k_num + + +def test_davis_southern_women(): + G = nx.davis_southern_women_graph() + result = nx.k_components(G) + _check_connectivity(G, result) + + +def test_davis_southern_women_detail_3_and_4(): + solution = { + 3: [ + { + "Nora Fayette", + "E10", + "Myra Liddel", + "E12", + "E14", + "Frances Anderson", + "Evelyn Jefferson", + "Ruth DeSand", + "Helen Lloyd", + "Eleanor Nye", + "E9", + "E8", + "E5", + "E4", + "E7", + "E6", + "E1", + "Verne Sanderson", + "E3", + "E2", + "Theresa Anderson", + "Pearl Oglethorpe", + "Katherina Rogers", + "Brenda Rogers", + "E13", + "Charlotte McDowd", + "Sylvia Avondale", + "Laura Mandeville", + } + ], + 4: [ + { + "Nora Fayette", + "E10", + "Verne Sanderson", + "E12", + "Frances Anderson", + "Evelyn Jefferson", + "Ruth DeSand", + "Helen Lloyd", + "Eleanor Nye", + "E9", + "E8", + "E5", + "E4", + "E7", + "E6", + "Myra Liddel", + "E3", + "Theresa Anderson", + "Katherina Rogers", + "Brenda Rogers", + "Charlotte McDowd", + "Sylvia Avondale", + "Laura Mandeville", + } + ], + } + G = nx.davis_southern_women_graph() + result = nx.k_components(G) + for k, components in result.items(): + if k < 3: + continue + assert len(components) == len(solution[k]) + for component in components: + assert component in solution[k] + + +def test_set_consolidation_rosettacode(): + # Tests from http://rosettacode.org/wiki/Set_consolidation + def list_of_sets_equal(result, solution): + assert {frozenset(s) for s in result} == {frozenset(s) for s in solution} + + question = [{"A", "B"}, {"C", "D"}] + solution = [{"A", "B"}, {"C", "D"}] + list_of_sets_equal(_consolidate(question, 1), solution) + question = [{"A", "B"}, {"B", "C"}] + solution = [{"A", "B", "C"}] + list_of_sets_equal(_consolidate(question, 1), solution) + question = [{"A", "B"}, {"C", "D"}, {"D", "B"}] + solution = [{"A", "C", "B", "D"}] + list_of_sets_equal(_consolidate(question, 1), solution) + question = [{"H", "I", "K"}, {"A", "B"}, {"C", "D"}, {"D", "B"}, {"F", "G", "H"}] + solution = [{"A", "C", "B", "D"}, {"G", "F", "I", "H", "K"}] + list_of_sets_equal(_consolidate(question, 1), solution) + question = [ + {"A", "H"}, + {"H", "I", "K"}, + {"A", "B"}, + {"C", "D"}, + {"D", "B"}, + {"F", "G", "H"}, + ] + solution = [{"A", "C", "B", "D", "G", "F", "I", "H", "K"}] + list_of_sets_equal(_consolidate(question, 1), solution) + question = [ + {"H", "I", "K"}, + {"A", "B"}, + {"C", "D"}, + {"D", "B"}, + {"F", "G", "H"}, + {"A", "H"}, + ] + solution = [{"A", "C", "B", "D", "G", "F", "I", "H", "K"}] + list_of_sets_equal(_consolidate(question, 1), solution) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/operators/tests/test_unary.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/operators/tests/test_unary.py new file mode 100644 index 0000000000000000000000000000000000000000..d68e55cd9c9fa37459b497c32a7a095576c306c3 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/operators/tests/test_unary.py @@ -0,0 +1,55 @@ +import pytest + +import networkx as nx + + +def test_complement(): + null = nx.null_graph() + empty1 = nx.empty_graph(1) + empty10 = nx.empty_graph(10) + K3 = nx.complete_graph(3) + K5 = nx.complete_graph(5) + K10 = nx.complete_graph(10) + P2 = nx.path_graph(2) + P3 = nx.path_graph(3) + P5 = nx.path_graph(5) + P10 = nx.path_graph(10) + # complement of the complete graph is empty + + G = nx.complement(K3) + assert nx.is_isomorphic(G, nx.empty_graph(3)) + G = nx.complement(K5) + assert nx.is_isomorphic(G, nx.empty_graph(5)) + # for any G, G=complement(complement(G)) + P3cc = nx.complement(nx.complement(P3)) + assert nx.is_isomorphic(P3, P3cc) + nullcc = nx.complement(nx.complement(null)) + assert nx.is_isomorphic(null, nullcc) + b = nx.bull_graph() + bcc = nx.complement(nx.complement(b)) + assert nx.is_isomorphic(b, bcc) + + +def test_complement_2(): + G1 = nx.DiGraph() + G1.add_edge("A", "B") + G1.add_edge("A", "C") + G1.add_edge("A", "D") + G1C = nx.complement(G1) + assert sorted(G1C.edges()) == [ + ("B", "A"), + ("B", "C"), + ("B", "D"), + ("C", "A"), + ("C", "B"), + ("C", "D"), + ("D", "A"), + ("D", "B"), + ("D", "C"), + ] + + +def test_reverse1(): + # Other tests for reverse are done by the DiGraph and MultiDigraph. + G1 = nx.Graph() + pytest.raises(nx.NetworkXError, nx.reverse, G1) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/tests/__pycache__/test_planarity.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/tests/__pycache__/test_planarity.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..837fde7f7a696e11d1882c4a234ce36f91835d9b Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/tests/__pycache__/test_planarity.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/tests/__pycache__/test_similarity.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/tests/__pycache__/test_similarity.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..4988ebced691014ca8a33061d7631ffacd33d36c Binary files /dev/null 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breadth-first search begins at `source` and enqueues the + neighbors of newly visited nodes specified by the `neighbors` + function. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node for the breadth-first search; this function + iterates over only those edges in the component reachable from + this node. + + neighbors : function + A function that takes a newly visited node of the graph as input + and returns an *iterator* (not just a list) of nodes that are + neighbors of that node with custom ordering. If not specified, this is + just the ``G.neighbors`` method, but in general it can be any function + that returns an iterator over some or all of the neighbors of a + given node, in any order. + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth. + + Yields + ------ + edge + Edges in the breadth-first search starting from `source`. + + Examples + -------- + >>> G = nx.path_graph(7) + >>> list(nx.generic_bfs_edges(G, source=0)) + [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6)] + >>> list(nx.generic_bfs_edges(G, source=2)) + [(2, 1), (2, 3), (1, 0), (3, 4), (4, 5), (5, 6)] + >>> list(nx.generic_bfs_edges(G, source=2, depth_limit=2)) + [(2, 1), (2, 3), (1, 0), (3, 4)] + + The `neighbors` param can be used to specify the visitation order of each + node's neighbors generically. In the following example, we modify the default + neighbor to return *odd* nodes first: + + >>> def odd_first(n): + ... return sorted(G.neighbors(n), key=lambda x: x % 2, reverse=True) + + >>> G = nx.star_graph(5) + >>> list(nx.generic_bfs_edges(G, source=0)) # Default neighbor ordering + [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)] + >>> list(nx.generic_bfs_edges(G, source=0, neighbors=odd_first)) + [(0, 1), (0, 3), (0, 5), (0, 2), (0, 4)] + + Notes + ----- + This implementation is from `PADS`_, which was in the public domain + when it was first accessed in July, 2004. The modifications + to allow depth limits are based on the Wikipedia article + "`Depth-limited-search`_". + + .. _PADS: http://www.ics.uci.edu/~eppstein/PADS/BFS.py + .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search + """ + if neighbors is None: + neighbors = G.neighbors + if depth_limit is None: + depth_limit = len(G) + + seen = {source} + n = len(G) + depth = 0 + next_parents_children = [(source, neighbors(source))] + while next_parents_children and depth < depth_limit: + this_parents_children = next_parents_children + next_parents_children = [] + for parent, children in this_parents_children: + for child in children: + if child not in seen: + seen.add(child) + next_parents_children.append((child, neighbors(child))) + yield parent, child + if len(seen) == n: + return + depth += 1 + + +@nx._dispatchable +def bfs_edges(G, source, reverse=False, depth_limit=None, sort_neighbors=None): + """Iterate over edges in a breadth-first-search starting at source. + + Parameters + ---------- + G : NetworkX graph + + source : node + Specify starting node for breadth-first search; this function + iterates over only those edges in the component reachable from + this node. + + reverse : bool, optional + If True traverse a directed graph in the reverse direction + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Yields + ------ + edge: 2-tuple of nodes + Yields edges resulting from the breadth-first search. + + Examples + -------- + To get the edges in a breadth-first search:: + + >>> G = nx.path_graph(3) + >>> list(nx.bfs_edges(G, 0)) + [(0, 1), (1, 2)] + >>> list(nx.bfs_edges(G, source=0, depth_limit=1)) + [(0, 1)] + + To get the nodes in a breadth-first search order:: + + >>> G = nx.path_graph(3) + >>> root = 2 + >>> edges = nx.bfs_edges(G, root) + >>> nodes = [root] + [v for u, v in edges] + >>> nodes + [2, 1, 0] + + Notes + ----- + The naming of this function is very similar to + :func:`~networkx.algorithms.traversal.edgebfs.edge_bfs`. The difference + is that ``edge_bfs`` yields edges even if they extend back to an already + explored node while this generator yields the edges of the tree that results + from a breadth-first-search (BFS) so no edges are reported if they extend + to already explored nodes. That means ``edge_bfs`` reports all edges while + ``bfs_edges`` only reports those traversed by a node-based BFS. Yet another + description is that ``bfs_edges`` reports the edges traversed during BFS + while ``edge_bfs`` reports all edges in the order they are explored. + + Based on the breadth-first search implementation in PADS [1]_ + by D. Eppstein, July 2004; with modifications to allow depth limits + as described in [2]_. + + References + ---------- + .. [1] http://www.ics.uci.edu/~eppstein/PADS/BFS.py. + .. [2] https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + bfs_tree + :func:`~networkx.algorithms.traversal.depth_first_search.dfs_edges` + :func:`~networkx.algorithms.traversal.edgebfs.edge_bfs` + + """ + if reverse and G.is_directed(): + successors = G.predecessors + else: + successors = G.neighbors + + if sort_neighbors is not None: + yield from generic_bfs_edges( + G, source, lambda node: iter(sort_neighbors(successors(node))), depth_limit + ) + else: + yield from generic_bfs_edges(G, source, successors, depth_limit) + + +@nx._dispatchable(returns_graph=True) +def bfs_tree(G, source, reverse=False, depth_limit=None, sort_neighbors=None): + """Returns an oriented tree constructed from of a breadth-first-search + starting at source. + + Parameters + ---------- + G : NetworkX graph + + source : node + Specify starting node for breadth-first search + + reverse : bool, optional + If True traverse a directed graph in the reverse direction + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + T: NetworkX DiGraph + An oriented tree + + Examples + -------- + >>> G = nx.path_graph(3) + >>> list(nx.bfs_tree(G, 1).edges()) + [(1, 0), (1, 2)] + >>> H = nx.Graph() + >>> nx.add_path(H, [0, 1, 2, 3, 4, 5, 6]) + >>> nx.add_path(H, [2, 7, 8, 9, 10]) + >>> sorted(list(nx.bfs_tree(H, source=3, depth_limit=3).edges())) + [(1, 0), (2, 1), (2, 7), (3, 2), (3, 4), (4, 5), (5, 6), (7, 8)] + + + Notes + ----- + Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py + by D. Eppstein, July 2004. The modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited-search`_". + + .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + dfs_tree + bfs_edges + edge_bfs + """ + T = nx.DiGraph() + T.add_node(source) + edges_gen = bfs_edges( + G, + source, + reverse=reverse, + depth_limit=depth_limit, + sort_neighbors=sort_neighbors, + ) + T.add_edges_from(edges_gen) + return T + + +@nx._dispatchable +def bfs_predecessors(G, source, depth_limit=None, sort_neighbors=None): + """Returns an iterator of predecessors in breadth-first-search from source. + + Parameters + ---------- + G : NetworkX graph + + source : node + Specify starting node for breadth-first search + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + pred: iterator + (node, predecessor) iterator where `predecessor` is the predecessor of + `node` in a breadth first search starting from `source`. + + Examples + -------- + >>> G = nx.path_graph(3) + >>> dict(nx.bfs_predecessors(G, 0)) + {1: 0, 2: 1} + >>> H = nx.Graph() + >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) + >>> dict(nx.bfs_predecessors(H, 0)) + {1: 0, 2: 0, 3: 1, 4: 1, 5: 2, 6: 2} + >>> M = nx.Graph() + >>> nx.add_path(M, [0, 1, 2, 3, 4, 5, 6]) + >>> nx.add_path(M, [2, 7, 8, 9, 10]) + >>> sorted(nx.bfs_predecessors(M, source=1, depth_limit=3)) + [(0, 1), (2, 1), (3, 2), (4, 3), (7, 2), (8, 7)] + >>> N = nx.DiGraph() + >>> nx.add_path(N, [0, 1, 2, 3, 4, 7]) + >>> nx.add_path(N, [3, 5, 6, 7]) + >>> sorted(nx.bfs_predecessors(N, source=2)) + [(3, 2), (4, 3), (5, 3), (6, 5), (7, 4)] + + Notes + ----- + Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py + by D. Eppstein, July 2004. The modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited-search`_". + + .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + bfs_tree + bfs_edges + edge_bfs + """ + for s, t in bfs_edges( + G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors + ): + yield (t, s) + + +@nx._dispatchable +def bfs_successors(G, source, depth_limit=None, sort_neighbors=None): + """Returns an iterator of successors in breadth-first-search from source. + + Parameters + ---------- + G : NetworkX graph + + source : node + Specify starting node for breadth-first search + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + succ: iterator + (node, successors) iterator where `successors` is the non-empty list of + successors of `node` in a breadth first search from `source`. + To appear in the iterator, `node` must have successors. + + Examples + -------- + >>> G = nx.path_graph(3) + >>> dict(nx.bfs_successors(G, 0)) + {0: [1], 1: [2]} + >>> H = nx.Graph() + >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) + >>> dict(nx.bfs_successors(H, 0)) + {0: [1, 2], 1: [3, 4], 2: [5, 6]} + >>> G = nx.Graph() + >>> nx.add_path(G, [0, 1, 2, 3, 4, 5, 6]) + >>> nx.add_path(G, [2, 7, 8, 9, 10]) + >>> dict(nx.bfs_successors(G, source=1, depth_limit=3)) + {1: [0, 2], 2: [3, 7], 3: [4], 7: [8]} + >>> G = nx.DiGraph() + >>> nx.add_path(G, [0, 1, 2, 3, 4, 5]) + >>> dict(nx.bfs_successors(G, source=3)) + {3: [4], 4: [5]} + + Notes + ----- + Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py + by D. Eppstein, July 2004.The modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited-search`_". + + .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + bfs_tree + bfs_edges + edge_bfs + """ + parent = source + children = [] + for p, c in bfs_edges( + G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors + ): + if p == parent: + children.append(c) + continue + yield (parent, children) + children = [c] + parent = p + yield (parent, children) + + +@nx._dispatchable +def bfs_layers(G, sources): + """Returns an iterator of all the layers in breadth-first search traversal. + + Parameters + ---------- + G : NetworkX graph + A graph over which to find the layers using breadth-first search. + + sources : node in `G` or list of nodes in `G` + Specify starting nodes for single source or multiple sources breadth-first search + + Yields + ------ + layer: list of nodes + Yields list of nodes at the same distance from sources + + Examples + -------- + >>> G = nx.path_graph(5) + >>> dict(enumerate(nx.bfs_layers(G, [0, 4]))) + {0: [0, 4], 1: [1, 3], 2: [2]} + >>> H = nx.Graph() + >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) + >>> dict(enumerate(nx.bfs_layers(H, [1]))) + {0: [1], 1: [0, 3, 4], 2: [2], 3: [5, 6]} + >>> dict(enumerate(nx.bfs_layers(H, [1, 6]))) + {0: [1, 6], 1: [0, 3, 4, 2], 2: [5]} + """ + if sources in G: + sources = [sources] + + current_layer = list(sources) + visited = set(sources) + + for source in current_layer: + if source not in G: + raise nx.NetworkXError(f"The node {source} is not in the graph.") + + # this is basically BFS, except that the current layer only stores the nodes at + # same distance from sources at each iteration + while current_layer: + yield current_layer + next_layer = [] + for node in current_layer: + for child in G[node]: + if child not in visited: + visited.add(child) + next_layer.append(child) + current_layer = next_layer + + +REVERSE_EDGE = "reverse" +TREE_EDGE = "tree" +FORWARD_EDGE = "forward" +LEVEL_EDGE = "level" + + +@nx._dispatchable +def bfs_labeled_edges(G, sources): + """Iterate over edges in a breadth-first search (BFS) labeled by type. + + We generate triple of the form (*u*, *v*, *d*), where (*u*, *v*) is the + edge being explored in the breadth-first search and *d* is one of the + strings 'tree', 'forward', 'level', or 'reverse'. A 'tree' edge is one in + which *v* is first discovered and placed into the layer below *u*. A + 'forward' edge is one in which *u* is on the layer above *v* and *v* has + already been discovered. A 'level' edge is one in which both *u* and *v* + occur on the same layer. A 'reverse' edge is one in which *u* is on a layer + below *v*. + + We emit each edge exactly once. In an undirected graph, 'reverse' edges do + not occur, because each is discovered either as a 'tree' or 'forward' edge. + + Parameters + ---------- + G : NetworkX graph + A graph over which to find the layers using breadth-first search. + + sources : node in `G` or list of nodes in `G` + Starting nodes for single source or multiple sources breadth-first search + + Yields + ------ + edges: generator + A generator of triples (*u*, *v*, *d*) where (*u*, *v*) is the edge being + explored and *d* is described above. + + Examples + -------- + >>> G = nx.cycle_graph(4, create_using=nx.DiGraph) + >>> list(nx.bfs_labeled_edges(G, 0)) + [(0, 1, 'tree'), (1, 2, 'tree'), (2, 3, 'tree'), (3, 0, 'reverse')] + >>> G = nx.complete_graph(3) + >>> list(nx.bfs_labeled_edges(G, 0)) + [(0, 1, 'tree'), (0, 2, 'tree'), (1, 2, 'level')] + >>> list(nx.bfs_labeled_edges(G, [0, 1])) + [(0, 1, 'level'), (0, 2, 'tree'), (1, 2, 'forward')] + """ + if sources in G: + sources = [sources] + + neighbors = G._adj + directed = G.is_directed() + visited = set() + visit = visited.discard if directed else visited.add + # We use visited in a negative sense, so the visited set stays empty for the + # directed case and level edges are reported on their first occurrence in + # the undirected case. Note our use of visited.discard -- this is built-in + # thus somewhat faster than a python-defined def nop(x): pass + depth = {s: 0 for s in sources} + queue = deque(depth.items()) + push = queue.append + pop = queue.popleft + while queue: + u, du = pop() + for v in neighbors[u]: + if v not in depth: + depth[v] = dv = du + 1 + push((v, dv)) + yield u, v, TREE_EDGE + else: + dv = depth[v] + if du == dv: + if v not in visited: + yield u, v, LEVEL_EDGE + elif du < dv: + yield u, v, FORWARD_EDGE + elif directed: + yield u, v, REVERSE_EDGE + visit(u) + + +@nx._dispatchable +def descendants_at_distance(G, source, distance): + """Returns all nodes at a fixed `distance` from `source` in `G`. + + Parameters + ---------- + G : NetworkX graph + A graph + source : node in `G` + distance : the distance of the wanted nodes from `source` + + Returns + ------- + set() + The descendants of `source` in `G` at the given `distance` from `source` + + Examples + -------- + >>> G = nx.path_graph(5) + >>> nx.descendants_at_distance(G, 2, 2) + {0, 4} + >>> H = nx.DiGraph() + >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) + >>> nx.descendants_at_distance(H, 0, 2) + {3, 4, 5, 6} + >>> nx.descendants_at_distance(H, 5, 0) + {5} + >>> nx.descendants_at_distance(H, 5, 1) + set() + """ + if source not in G: + raise nx.NetworkXError(f"The node {source} is not in the graph.") + + bfs_generator = nx.bfs_layers(G, source) + for i, layer in enumerate(bfs_generator): + if i == distance: + return set(layer) + return set() diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/tree/operations.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/tree/operations.py new file mode 100644 index 0000000000000000000000000000000000000000..6c3e839453e686c80d33c94a66defa87698a066f --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/tree/operations.py @@ -0,0 +1,105 @@ +"""Operations on trees.""" + +from functools import partial +from itertools import accumulate, chain + +import networkx as nx + +__all__ = ["join_trees"] + + +# Argument types don't match dispatching, but allow manual selection of backend +@nx._dispatchable(graphs=None, returns_graph=True) +def join_trees(rooted_trees, *, label_attribute=None, first_label=0): + """Returns a new rooted tree made by joining `rooted_trees` + + Constructs a new tree by joining each tree in `rooted_trees`. + A new root node is added and connected to each of the roots + of the input trees. While copying the nodes from the trees, + relabeling to integers occurs. If the `label_attribute` is provided, + the old node labels will be stored in the new tree under this attribute. + + Parameters + ---------- + rooted_trees : list + A list of pairs in which each left element is a NetworkX graph + object representing a tree and each right element is the root + node of that tree. The nodes of these trees will be relabeled to + integers. + + label_attribute : str + If provided, the old node labels will be stored in the new tree + under this node attribute. If not provided, the original labels + of the nodes in the input trees are not stored. + + first_label : int, optional (default=0) + Specifies the label for the new root node. If provided, the root node of the joined tree + will have this label. If not provided, the root node will default to a label of 0. + + Returns + ------- + NetworkX graph + The rooted tree resulting from joining the provided `rooted_trees`. The new tree has a root node + labeled as specified by `first_label` (defaulting to 0 if not provided). Subtrees from the input + `rooted_trees` are attached to this new root node. Each non-root node, if the `label_attribute` + is provided, has an attribute that indicates the original label of the node in the input tree. + + Notes + ----- + Trees are stored in NetworkX as NetworkX Graphs. There is no specific + enforcement of the fact that these are trees. Testing for each tree + can be done using :func:`networkx.is_tree`. + + Graph, edge, and node attributes are propagated from the given + rooted trees to the created tree. If there are any overlapping graph + attributes, those from later trees will overwrite those from earlier + trees in the tuple of positional arguments. + + Examples + -------- + Join two full balanced binary trees of height *h* to get a full + balanced binary tree of depth *h* + 1:: + + >>> h = 4 + >>> left = nx.balanced_tree(2, h) + >>> right = nx.balanced_tree(2, h) + >>> joined_tree = nx.join_trees([(left, 0), (right, 0)]) + >>> nx.is_isomorphic(joined_tree, nx.balanced_tree(2, h + 1)) + True + + """ + if not rooted_trees: + return nx.empty_graph(1) + + # Unzip the zipped list of (tree, root) pairs. + trees, roots = zip(*rooted_trees) + + # The join of the trees has the same type as the type of the first tree. + R = type(trees[0])() + + lengths = (len(tree) for tree in trees[:-1]) + first_labels = list(accumulate(lengths, initial=first_label + 1)) + + new_roots = [] + for tree, root, first_node in zip(trees, roots, first_labels): + new_root = first_node + list(tree.nodes()).index(root) + new_roots.append(new_root) + + # Relabel the nodes so that their union is the integers starting at first_label. + relabel = partial( + nx.convert_node_labels_to_integers, label_attribute=label_attribute + ) + new_trees = [ + relabel(tree, first_label=first_label) + for tree, first_label in zip(trees, first_labels) + ] + + # Add all sets of nodes and edges, attributes + for tree in new_trees: + R.update(tree) + + # Finally, join the subtrees at the root. We know first_label is unused by the way we relabeled the subtrees. + R.add_node(first_label) + R.add_edges_from((first_label, root) for root in new_roots) + + return R diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/tree/tests/__init__.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/tree/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/tree/tests/test_operations.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/tree/tests/test_operations.py new file mode 100644 index 0000000000000000000000000000000000000000..284d94e2e5059de267b5ea47f6012a42c6ac4639 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/tree/tests/test_operations.py @@ -0,0 +1,53 @@ +from itertools import chain + +import networkx as nx +from networkx.utils import edges_equal, nodes_equal + + +def _check_custom_label_attribute(input_trees, res_tree, label_attribute): + res_attr_dict = nx.get_node_attributes(res_tree, label_attribute) + res_attr_set = set(res_attr_dict.values()) + input_label = (tree for tree, root in input_trees) + input_label_set = set(chain.from_iterable(input_label)) + return res_attr_set == input_label_set + + +def test_empty_sequence(): + """Joining the empty sequence results in the tree with one node.""" + T = nx.join_trees([]) + assert len(T) == 1 + assert T.number_of_edges() == 0 + + +def test_single(): + """Joining just one tree yields a tree with one more node.""" + T = nx.empty_graph(1) + trees = [(T, 0)] + actual_with_label = nx.join_trees(trees, label_attribute="custom_label") + expected = nx.path_graph(2) + assert nodes_equal(list(expected), list(actual_with_label)) + assert edges_equal(list(expected.edges()), list(actual_with_label.edges())) + + +def test_basic(): + """Joining multiple subtrees at a root node.""" + trees = [(nx.full_rary_tree(2, 2**2 - 1), 0) for i in range(2)] + expected = nx.full_rary_tree(2, 2**3 - 1) + actual = nx.join_trees(trees, label_attribute="old_labels") + assert nx.is_isomorphic(actual, expected) + assert _check_custom_label_attribute(trees, actual, "old_labels") + + actual_without_label = nx.join_trees(trees) + assert nx.is_isomorphic(actual_without_label, expected) + # check that no labels were stored + assert all(not data for _, data in actual_without_label.nodes(data=True)) + + +def test_first_label(): + """Test the functionality of the first_label argument.""" + T1 = nx.path_graph(3) + T2 = nx.path_graph(2) + actual = nx.join_trees([(T1, 0), (T2, 0)], first_label=10) + expected_nodes = set(range(10, 16)) + assert set(actual.nodes()) == expected_nodes + assert set(actual.neighbors(10)) == {11, 14} diff --git a/wemm/lib/python3.10/site-packages/networkx/tests/__pycache__/test_import.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/tests/__pycache__/test_import.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..eea62729faf92e83489c111de5ce436bae5bbaf9 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/tests/__pycache__/test_import.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/tests/__pycache__/test_lazy_imports.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/tests/__pycache__/test_lazy_imports.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..accc862d78b307402c6e6b40a6abb32d2639eea5 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/tests/__pycache__/test_lazy_imports.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/tests/test_convert.py b/wemm/lib/python3.10/site-packages/networkx/tests/test_convert.py new file mode 100644 index 0000000000000000000000000000000000000000..44bed9438945a39bb5eb85477301f58cfcd70cf0 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/tests/test_convert.py @@ -0,0 +1,321 @@ +import pytest + +import networkx as nx +from networkx.convert import ( + from_dict_of_dicts, + from_dict_of_lists, + to_dict_of_dicts, + to_dict_of_lists, + to_networkx_graph, +) +from networkx.generators.classic import barbell_graph, cycle_graph +from networkx.utils import edges_equal, graphs_equal, nodes_equal + + +class TestConvert: + def edgelists_equal(self, e1, e2): + return sorted(sorted(e) for e in e1) == sorted(sorted(e) for e in e2) + + def test_simple_graphs(self): + for dest, source in [ + (to_dict_of_dicts, from_dict_of_dicts), + (to_dict_of_lists, from_dict_of_lists), + ]: + G = barbell_graph(10, 3) + G.graph = {} + dod = dest(G) + + # Dict of [dicts, lists] + GG = source(dod) + assert graphs_equal(G, GG) + GW = to_networkx_graph(dod) + assert graphs_equal(G, GW) + GI = nx.Graph(dod) + assert graphs_equal(G, GI) + + # With nodelist keyword + P4 = nx.path_graph(4) + P3 = nx.path_graph(3) + P4.graph = {} + P3.graph = {} + dod = dest(P4, nodelist=[0, 1, 2]) + Gdod = nx.Graph(dod) + assert graphs_equal(Gdod, P3) + + def test_exceptions(self): + # NX graph + class G: + adj = None + + pytest.raises(nx.NetworkXError, to_networkx_graph, G) + + # pygraphviz agraph + class G: + is_strict = None + + pytest.raises(nx.NetworkXError, to_networkx_graph, G) + + # Dict of [dicts, lists] + G = {"a": 0} + pytest.raises(TypeError, to_networkx_graph, G) + + # list or generator of edges + class G: + next = None + + pytest.raises(nx.NetworkXError, to_networkx_graph, G) + + # no match + pytest.raises(nx.NetworkXError, to_networkx_graph, "a") + + def test_digraphs(self): + for dest, source in [ + (to_dict_of_dicts, from_dict_of_dicts), + (to_dict_of_lists, from_dict_of_lists), + ]: + G = cycle_graph(10) + + # Dict of [dicts, lists] + dod = dest(G) + GG = source(dod) + assert nodes_equal(sorted(G.nodes()), sorted(GG.nodes())) + assert edges_equal(sorted(G.edges()), sorted(GG.edges())) + GW = to_networkx_graph(dod) + assert nodes_equal(sorted(G.nodes()), sorted(GW.nodes())) + assert edges_equal(sorted(G.edges()), sorted(GW.edges())) + GI = nx.Graph(dod) + assert nodes_equal(sorted(G.nodes()), sorted(GI.nodes())) + assert edges_equal(sorted(G.edges()), sorted(GI.edges())) + + G = cycle_graph(10, create_using=nx.DiGraph) + dod = dest(G) + GG = source(dod, create_using=nx.DiGraph) + assert sorted(G.nodes()) == sorted(GG.nodes()) + assert sorted(G.edges()) == sorted(GG.edges()) + GW = to_networkx_graph(dod, create_using=nx.DiGraph) + assert sorted(G.nodes()) == sorted(GW.nodes()) + assert sorted(G.edges()) == sorted(GW.edges()) + GI = nx.DiGraph(dod) + assert sorted(G.nodes()) == sorted(GI.nodes()) + assert sorted(G.edges()) == sorted(GI.edges()) + + def test_graph(self): + g = nx.cycle_graph(10) + G = nx.Graph() + G.add_nodes_from(g) + G.add_weighted_edges_from((u, v, u) for u, v in g.edges()) + + # Dict of dicts + dod = to_dict_of_dicts(G) + GG = from_dict_of_dicts(dod, create_using=nx.Graph) + assert nodes_equal(sorted(G.nodes()), sorted(GG.nodes())) + assert edges_equal(sorted(G.edges()), sorted(GG.edges())) + GW = to_networkx_graph(dod, create_using=nx.Graph) + assert nodes_equal(sorted(G.nodes()), sorted(GW.nodes())) + assert edges_equal(sorted(G.edges()), sorted(GW.edges())) + GI = nx.Graph(dod) + assert sorted(G.nodes()) == sorted(GI.nodes()) + assert sorted(G.edges()) == sorted(GI.edges()) + + # Dict of lists + dol = to_dict_of_lists(G) + GG = from_dict_of_lists(dol, create_using=nx.Graph) + # dict of lists throws away edge data so set it to none + enone = [(u, v, {}) for (u, v, d) in G.edges(data=True)] + assert nodes_equal(sorted(G.nodes()), sorted(GG.nodes())) + assert edges_equal(enone, sorted(GG.edges(data=True))) + GW = to_networkx_graph(dol, create_using=nx.Graph) + assert nodes_equal(sorted(G.nodes()), sorted(GW.nodes())) + assert edges_equal(enone, sorted(GW.edges(data=True))) + GI = nx.Graph(dol) + assert nodes_equal(sorted(G.nodes()), sorted(GI.nodes())) + assert edges_equal(enone, sorted(GI.edges(data=True))) + + def test_with_multiedges_self_loops(self): + G = cycle_graph(10) + XG = nx.Graph() + XG.add_nodes_from(G) + XG.add_weighted_edges_from((u, v, u) for u, v in G.edges()) + XGM = nx.MultiGraph() + XGM.add_nodes_from(G) + XGM.add_weighted_edges_from((u, v, u) for u, v in G.edges()) + XGM.add_edge(0, 1, weight=2) # multiedge + XGS = nx.Graph() + XGS.add_nodes_from(G) + XGS.add_weighted_edges_from((u, v, u) for u, v in G.edges()) + XGS.add_edge(0, 0, weight=100) # self loop + + # Dict of dicts + # with self loops, OK + dod = to_dict_of_dicts(XGS) + GG = from_dict_of_dicts(dod, create_using=nx.Graph) + assert nodes_equal(XGS.nodes(), GG.nodes()) + assert edges_equal(XGS.edges(), GG.edges()) + GW = to_networkx_graph(dod, create_using=nx.Graph) + assert nodes_equal(XGS.nodes(), GW.nodes()) + assert edges_equal(XGS.edges(), GW.edges()) + GI = nx.Graph(dod) + assert nodes_equal(XGS.nodes(), GI.nodes()) + assert edges_equal(XGS.edges(), GI.edges()) + + # Dict of lists + # with self loops, OK + dol = to_dict_of_lists(XGS) + GG = from_dict_of_lists(dol, create_using=nx.Graph) + # dict of lists throws away edge data so set it to none + enone = [(u, v, {}) for (u, v, d) in XGS.edges(data=True)] + assert nodes_equal(sorted(XGS.nodes()), sorted(GG.nodes())) + assert edges_equal(enone, sorted(GG.edges(data=True))) + GW = to_networkx_graph(dol, create_using=nx.Graph) + assert nodes_equal(sorted(XGS.nodes()), sorted(GW.nodes())) + assert edges_equal(enone, sorted(GW.edges(data=True))) + GI = nx.Graph(dol) + assert nodes_equal(sorted(XGS.nodes()), sorted(GI.nodes())) + assert edges_equal(enone, sorted(GI.edges(data=True))) + + # Dict of dicts + # with multiedges, OK + dod = to_dict_of_dicts(XGM) + GG = from_dict_of_dicts(dod, create_using=nx.MultiGraph, multigraph_input=True) + assert nodes_equal(sorted(XGM.nodes()), sorted(GG.nodes())) + assert edges_equal(sorted(XGM.edges()), sorted(GG.edges())) + GW = to_networkx_graph(dod, create_using=nx.MultiGraph, multigraph_input=True) + assert nodes_equal(sorted(XGM.nodes()), sorted(GW.nodes())) + assert edges_equal(sorted(XGM.edges()), sorted(GW.edges())) + GI = nx.MultiGraph(dod) + assert nodes_equal(sorted(XGM.nodes()), sorted(GI.nodes())) + assert sorted(XGM.edges()) == sorted(GI.edges()) + GE = from_dict_of_dicts(dod, create_using=nx.MultiGraph, multigraph_input=False) + assert nodes_equal(sorted(XGM.nodes()), sorted(GE.nodes())) + assert sorted(XGM.edges()) != sorted(GE.edges()) + GI = nx.MultiGraph(XGM) + assert nodes_equal(sorted(XGM.nodes()), sorted(GI.nodes())) + assert edges_equal(sorted(XGM.edges()), sorted(GI.edges())) + GM = nx.MultiGraph(G) + assert nodes_equal(sorted(GM.nodes()), sorted(G.nodes())) + assert edges_equal(sorted(GM.edges()), sorted(G.edges())) + + # Dict of lists + # with multiedges, OK, but better write as DiGraph else you'll + # get double edges + dol = to_dict_of_lists(G) + GG = from_dict_of_lists(dol, create_using=nx.MultiGraph) + assert nodes_equal(sorted(G.nodes()), sorted(GG.nodes())) + assert edges_equal(sorted(G.edges()), sorted(GG.edges())) + GW = to_networkx_graph(dol, create_using=nx.MultiGraph) + assert nodes_equal(sorted(G.nodes()), sorted(GW.nodes())) + assert edges_equal(sorted(G.edges()), sorted(GW.edges())) + GI = nx.MultiGraph(dol) + assert nodes_equal(sorted(G.nodes()), sorted(GI.nodes())) + assert edges_equal(sorted(G.edges()), sorted(GI.edges())) + + def test_edgelists(self): + P = nx.path_graph(4) + e = [(0, 1), (1, 2), (2, 3)] + G = nx.Graph(e) + assert nodes_equal(sorted(G.nodes()), sorted(P.nodes())) + assert edges_equal(sorted(G.edges()), sorted(P.edges())) + assert edges_equal(sorted(G.edges(data=True)), sorted(P.edges(data=True))) + + e = [(0, 1, {}), (1, 2, {}), (2, 3, {})] + G = nx.Graph(e) + assert nodes_equal(sorted(G.nodes()), sorted(P.nodes())) + assert edges_equal(sorted(G.edges()), sorted(P.edges())) + assert edges_equal(sorted(G.edges(data=True)), sorted(P.edges(data=True))) + + e = ((n, n + 1) for n in range(3)) + G = nx.Graph(e) + assert nodes_equal(sorted(G.nodes()), sorted(P.nodes())) + assert edges_equal(sorted(G.edges()), sorted(P.edges())) + assert edges_equal(sorted(G.edges(data=True)), sorted(P.edges(data=True))) + + def test_directed_to_undirected(self): + edges1 = [(0, 1), (1, 2), (2, 0)] + edges2 = [(0, 1), (1, 2), (0, 2)] + assert self.edgelists_equal(nx.Graph(nx.DiGraph(edges1)).edges(), edges1) + assert self.edgelists_equal(nx.Graph(nx.DiGraph(edges2)).edges(), edges1) + assert self.edgelists_equal(nx.MultiGraph(nx.DiGraph(edges1)).edges(), edges1) + assert self.edgelists_equal(nx.MultiGraph(nx.DiGraph(edges2)).edges(), edges1) + + assert self.edgelists_equal( + nx.MultiGraph(nx.MultiDiGraph(edges1)).edges(), edges1 + ) + assert self.edgelists_equal( + nx.MultiGraph(nx.MultiDiGraph(edges2)).edges(), edges1 + ) + + assert self.edgelists_equal(nx.Graph(nx.MultiDiGraph(edges1)).edges(), edges1) + assert self.edgelists_equal(nx.Graph(nx.MultiDiGraph(edges2)).edges(), edges1) + + def test_attribute_dict_integrity(self): + # we must not replace dict-like graph data structures with dicts + G = nx.Graph() + G.add_nodes_from("abc") + H = to_networkx_graph(G, create_using=nx.Graph) + assert list(H.nodes) == list(G.nodes) + H = nx.DiGraph(G) + assert list(H.nodes) == list(G.nodes) + + def test_to_edgelist(self): + G = nx.Graph([(1, 1)]) + elist = nx.to_edgelist(G, nodelist=list(G)) + assert edges_equal(G.edges(data=True), elist) + + def test_custom_node_attr_dict_safekeeping(self): + class custom_dict(dict): + pass + + class Custom(nx.Graph): + node_attr_dict_factory = custom_dict + + g = nx.Graph() + g.add_node(1, weight=1) + + h = Custom(g) + assert isinstance(g._node[1], dict) + assert isinstance(h._node[1], custom_dict) + + # this raise exception + # h._node.update((n, dd.copy()) for n, dd in g.nodes.items()) + # assert isinstance(h._node[1], custom_dict) + + +@pytest.mark.parametrize( + "edgelist", + ( + # Graph with no edge data + [(0, 1), (1, 2)], + # Graph with edge data + [(0, 1, {"weight": 1.0}), (1, 2, {"weight": 2.0})], + ), +) +def test_to_dict_of_dicts_with_edgedata_param(edgelist): + G = nx.Graph() + G.add_edges_from(edgelist) + # Innermost dict value == edge_data when edge_data != None. + # In the case when G has edge data, it is overwritten + expected = {0: {1: 10}, 1: {0: 10, 2: 10}, 2: {1: 10}} + assert nx.to_dict_of_dicts(G, edge_data=10) == expected + + +def test_to_dict_of_dicts_with_edgedata_and_nodelist(): + G = nx.path_graph(5) + nodelist = [2, 3, 4] + expected = {2: {3: 10}, 3: {2: 10, 4: 10}, 4: {3: 10}} + assert nx.to_dict_of_dicts(G, nodelist=nodelist, edge_data=10) == expected + + +def test_to_dict_of_dicts_with_edgedata_multigraph(): + """Multi edge data overwritten when edge_data != None""" + G = nx.MultiGraph() + G.add_edge(0, 1, key="a") + G.add_edge(0, 1, key="b") + # Multi edge data lost when edge_data is not None + expected = {0: {1: 10}, 1: {0: 10}} + assert nx.to_dict_of_dicts(G, edge_data=10) == expected + + +def test_to_networkx_graph_non_edgelist(): + invalid_edgelist = [1, 2, 3] + with pytest.raises(nx.NetworkXError, match="Input is not a valid edge list"): + nx.to_networkx_graph(invalid_edgelist) diff --git a/wemm/lib/python3.10/site-packages/networkx/utils/heaps.py b/wemm/lib/python3.10/site-packages/networkx/utils/heaps.py new file mode 100644 index 0000000000000000000000000000000000000000..3db27906314924380a8a87f2dfd3a81292ffbb9f --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/utils/heaps.py @@ -0,0 +1,340 @@ +""" +Min-heaps. +""" + +from heapq import heappop, heappush +from itertools import count + +import networkx as nx + +__all__ = ["MinHeap", "PairingHeap", "BinaryHeap"] + + +class MinHeap: + """Base class for min-heaps. + + A MinHeap stores a collection of key-value pairs ordered by their values. + It supports querying the minimum pair, inserting a new pair, decreasing the + value in an existing pair and deleting the minimum pair. + """ + + class _Item: + """Used by subclassess to represent a key-value pair.""" + + __slots__ = ("key", "value") + + def __init__(self, key, value): + self.key = key + self.value = value + + def __repr__(self): + return repr((self.key, self.value)) + + def __init__(self): + """Initialize a new min-heap.""" + self._dict = {} + + def min(self): + """Query the minimum key-value pair. + + Returns + ------- + key, value : tuple + The key-value pair with the minimum value in the heap. + + Raises + ------ + NetworkXError + If the heap is empty. + """ + raise NotImplementedError + + def pop(self): + """Delete the minimum pair in the heap. + + Returns + ------- + key, value : tuple + The key-value pair with the minimum value in the heap. + + Raises + ------ + NetworkXError + If the heap is empty. + """ + raise NotImplementedError + + def get(self, key, default=None): + """Returns the value associated with a key. + + Parameters + ---------- + key : hashable object + The key to be looked up. + + default : object + Default value to return if the key is not present in the heap. + Default value: None. + + Returns + ------- + value : object. + The value associated with the key. + """ + raise NotImplementedError + + def insert(self, key, value, allow_increase=False): + """Insert a new key-value pair or modify the value in an existing + pair. + + Parameters + ---------- + key : hashable object + The key. + + value : object comparable with existing values. + The value. + + allow_increase : bool + Whether the value is allowed to increase. If False, attempts to + increase an existing value have no effect. Default value: False. + + Returns + ------- + decreased : bool + True if a pair is inserted or the existing value is decreased. + """ + raise NotImplementedError + + def __nonzero__(self): + """Returns whether the heap if empty.""" + return bool(self._dict) + + def __bool__(self): + """Returns whether the heap if empty.""" + return bool(self._dict) + + def __len__(self): + """Returns the number of key-value pairs in the heap.""" + return len(self._dict) + + def __contains__(self, key): + """Returns whether a key exists in the heap. + + Parameters + ---------- + key : any hashable object. + The key to be looked up. + """ + return key in self._dict + + +class PairingHeap(MinHeap): + """A pairing heap.""" + + class _Node(MinHeap._Item): + """A node in a pairing heap. + + A tree in a pairing heap is stored using the left-child, right-sibling + representation. + """ + + __slots__ = ("left", "next", "prev", "parent") + + def __init__(self, key, value): + super().__init__(key, value) + # The leftmost child. + self.left = None + # The next sibling. + self.next = None + # The previous sibling. + self.prev = None + # The parent. + self.parent = None + + def __init__(self): + """Initialize a pairing heap.""" + super().__init__() + self._root = None + + def min(self): + if self._root is None: + raise nx.NetworkXError("heap is empty.") + return (self._root.key, self._root.value) + + def pop(self): + if self._root is None: + raise nx.NetworkXError("heap is empty.") + min_node = self._root + self._root = self._merge_children(self._root) + del self._dict[min_node.key] + return (min_node.key, min_node.value) + + def get(self, key, default=None): + node = self._dict.get(key) + return node.value if node is not None else default + + def insert(self, key, value, allow_increase=False): + node = self._dict.get(key) + root = self._root + if node is not None: + if value < node.value: + node.value = value + if node is not root and value < node.parent.value: + self._cut(node) + self._root = self._link(root, node) + return True + elif allow_increase and value > node.value: + node.value = value + child = self._merge_children(node) + # Nonstandard step: Link the merged subtree with the root. See + # below for the standard step. + if child is not None: + self._root = self._link(self._root, child) + # Standard step: Perform a decrease followed by a pop as if the + # value were the smallest in the heap. Then insert the new + # value into the heap. + # if node is not root: + # self._cut(node) + # if child is not None: + # root = self._link(root, child) + # self._root = self._link(root, node) + # else: + # self._root = (self._link(node, child) + # if child is not None else node) + return False + else: + # Insert a new key. + node = self._Node(key, value) + self._dict[key] = node + self._root = self._link(root, node) if root is not None else node + return True + + def _link(self, root, other): + """Link two nodes, making the one with the smaller value the parent of + the other. + """ + if other.value < root.value: + root, other = other, root + next = root.left + other.next = next + if next is not None: + next.prev = other + other.prev = None + root.left = other + other.parent = root + return root + + def _merge_children(self, root): + """Merge the subtrees of the root using the standard two-pass method. + The resulting subtree is detached from the root. + """ + node = root.left + root.left = None + if node is not None: + link = self._link + # Pass 1: Merge pairs of consecutive subtrees from left to right. + # At the end of the pass, only the prev pointers of the resulting + # subtrees have meaningful values. The other pointers will be fixed + # in pass 2. + prev = None + while True: + next = node.next + if next is None: + node.prev = prev + break + next_next = next.next + node = link(node, next) + node.prev = prev + prev = node + if next_next is None: + break + node = next_next + # Pass 2: Successively merge the subtrees produced by pass 1 from + # right to left with the rightmost one. + prev = node.prev + while prev is not None: + prev_prev = prev.prev + node = link(prev, node) + prev = prev_prev + # Now node can become the new root. Its has no parent nor siblings. + node.prev = None + node.next = None + node.parent = None + return node + + def _cut(self, node): + """Cut a node from its parent.""" + prev = node.prev + next = node.next + if prev is not None: + prev.next = next + else: + node.parent.left = next + node.prev = None + if next is not None: + next.prev = prev + node.next = None + node.parent = None + + +class BinaryHeap(MinHeap): + """A binary heap.""" + + def __init__(self): + """Initialize a binary heap.""" + super().__init__() + self._heap = [] + self._count = count() + + def min(self): + dict = self._dict + if not dict: + raise nx.NetworkXError("heap is empty") + heap = self._heap + pop = heappop + # Repeatedly remove stale key-value pairs until a up-to-date one is + # met. + while True: + value, _, key = heap[0] + if key in dict and value == dict[key]: + break + pop(heap) + return (key, value) + + def pop(self): + dict = self._dict + if not dict: + raise nx.NetworkXError("heap is empty") + heap = self._heap + pop = heappop + # Repeatedly remove stale key-value pairs until a up-to-date one is + # met. + while True: + value, _, key = heap[0] + pop(heap) + if key in dict and value == dict[key]: + break + del dict[key] + return (key, value) + + def get(self, key, default=None): + return self._dict.get(key, default) + + def insert(self, key, value, allow_increase=False): + dict = self._dict + if key in dict: + old_value = dict[key] + if value < old_value or (allow_increase and value > old_value): + # Since there is no way to efficiently obtain the location of a + # key-value pair in the heap, insert a new pair even if ones + # with the same key may already be present. Deem the old ones + # as stale and skip them when the minimum pair is queried. + dict[key] = value + heappush(self._heap, (value, next(self._count), key)) + return value < old_value + return False + else: + dict[key] = value + heappush(self._heap, (value, next(self._count), key)) + return True diff --git a/wemm/lib/python3.10/site-packages/networkx/utils/mapped_queue.py b/wemm/lib/python3.10/site-packages/networkx/utils/mapped_queue.py new file mode 100644 index 0000000000000000000000000000000000000000..0dcea368a93873fd72195fc8d388891c129942e0 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/utils/mapped_queue.py @@ -0,0 +1,297 @@ +"""Priority queue class with updatable priorities.""" + +import heapq + +__all__ = ["MappedQueue"] + + +class _HeapElement: + """This proxy class separates the heap element from its priority. + + The idea is that using a 2-tuple (priority, element) works + for sorting, but not for dict lookup because priorities are + often floating point values so round-off can mess up equality. + + So, we need inequalities to look at the priority (for sorting) + and equality (and hash) to look at the element to enable + updates to the priority. + + Unfortunately, this class can be tricky to work with if you forget that + `__lt__` compares the priority while `__eq__` compares the element. + In `greedy_modularity_communities()` the following code is + used to check that two _HeapElements differ in either element or priority: + + if d_oldmax != row_max or d_oldmax.priority != row_max.priority: + + If the priorities are the same, this implementation uses the element + as a tiebreaker. This provides compatibility with older systems that + use tuples to combine priority and elements. + """ + + __slots__ = ["priority", "element", "_hash"] + + def __init__(self, priority, element): + self.priority = priority + self.element = element + self._hash = hash(element) + + def __lt__(self, other): + try: + other_priority = other.priority + except AttributeError: + return self.priority < other + # assume comparing to another _HeapElement + if self.priority == other_priority: + try: + return self.element < other.element + except TypeError as err: + raise TypeError( + "Consider using a tuple, with a priority value that can be compared." + ) + return self.priority < other_priority + + def __gt__(self, other): + try: + other_priority = other.priority + except AttributeError: + return self.priority > other + # assume comparing to another _HeapElement + if self.priority == other_priority: + try: + return self.element > other.element + except TypeError as err: + raise TypeError( + "Consider using a tuple, with a priority value that can be compared." + ) + return self.priority > other_priority + + def __eq__(self, other): + try: + return self.element == other.element + except AttributeError: + return self.element == other + + def __hash__(self): + return self._hash + + def __getitem__(self, indx): + return self.priority if indx == 0 else self.element[indx - 1] + + def __iter__(self): + yield self.priority + try: + yield from self.element + except TypeError: + yield self.element + + def __repr__(self): + return f"_HeapElement({self.priority}, {self.element})" + + +class MappedQueue: + """The MappedQueue class implements a min-heap with removal and update-priority. + + The min heap uses heapq as well as custom written _siftup and _siftdown + methods to allow the heap positions to be tracked by an additional dict + keyed by element to position. The smallest element can be popped in O(1) time, + new elements can be pushed in O(log n) time, and any element can be removed + or updated in O(log n) time. The queue cannot contain duplicate elements + and an attempt to push an element already in the queue will have no effect. + + MappedQueue complements the heapq package from the python standard + library. While MappedQueue is designed for maximum compatibility with + heapq, it adds element removal, lookup, and priority update. + + Parameters + ---------- + data : dict or iterable + + Examples + -------- + + A `MappedQueue` can be created empty, or optionally, given a dictionary + of initial elements and priorities. The methods `push`, `pop`, + `remove`, and `update` operate on the queue. + + >>> colors_nm = {"red": 665, "blue": 470, "green": 550} + >>> q = MappedQueue(colors_nm) + >>> q.remove("red") + >>> q.update("green", "violet", 400) + >>> q.push("indigo", 425) + True + >>> [q.pop().element for i in range(len(q.heap))] + ['violet', 'indigo', 'blue'] + + A `MappedQueue` can also be initialized with a list or other iterable. The priority is assumed + to be the sort order of the items in the list. + + >>> q = MappedQueue([916, 50, 4609, 493, 237]) + >>> q.remove(493) + >>> q.update(237, 1117) + >>> [q.pop() for i in range(len(q.heap))] + [50, 916, 1117, 4609] + + An exception is raised if the elements are not comparable. + + >>> q = MappedQueue([100, "a"]) + Traceback (most recent call last): + ... + TypeError: '<' not supported between instances of 'int' and 'str' + + To avoid the exception, use a dictionary to assign priorities to the elements. + + >>> q = MappedQueue({100: 0, "a": 1}) + + References + ---------- + .. [1] Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2001). + Introduction to algorithms second edition. + .. [2] Knuth, D. E. (1997). The art of computer programming (Vol. 3). + Pearson Education. + """ + + def __init__(self, data=None): + """Priority queue class with updatable priorities.""" + if data is None: + self.heap = [] + elif isinstance(data, dict): + self.heap = [_HeapElement(v, k) for k, v in data.items()] + else: + self.heap = list(data) + self.position = {} + self._heapify() + + def _heapify(self): + """Restore heap invariant and recalculate map.""" + heapq.heapify(self.heap) + self.position = {elt: pos for pos, elt in enumerate(self.heap)} + if len(self.heap) != len(self.position): + raise AssertionError("Heap contains duplicate elements") + + def __len__(self): + return len(self.heap) + + def push(self, elt, priority=None): + """Add an element to the queue.""" + if priority is not None: + elt = _HeapElement(priority, elt) + # If element is already in queue, do nothing + if elt in self.position: + return False + # Add element to heap and dict + pos = len(self.heap) + self.heap.append(elt) + self.position[elt] = pos + # Restore invariant by sifting down + self._siftdown(0, pos) + return True + + def pop(self): + """Remove and return the smallest element in the queue.""" + # Remove smallest element + elt = self.heap[0] + del self.position[elt] + # If elt is last item, remove and return + if len(self.heap) == 1: + self.heap.pop() + return elt + # Replace root with last element + last = self.heap.pop() + self.heap[0] = last + self.position[last] = 0 + # Restore invariant by sifting up + self._siftup(0) + # Return smallest element + return elt + + def update(self, elt, new, priority=None): + """Replace an element in the queue with a new one.""" + if priority is not None: + new = _HeapElement(priority, new) + # Replace + pos = self.position[elt] + self.heap[pos] = new + del self.position[elt] + self.position[new] = pos + # Restore invariant by sifting up + self._siftup(pos) + + def remove(self, elt): + """Remove an element from the queue.""" + # Find and remove element + try: + pos = self.position[elt] + del self.position[elt] + except KeyError: + # Not in queue + raise + # If elt is last item, remove and return + if pos == len(self.heap) - 1: + self.heap.pop() + return + # Replace elt with last element + last = self.heap.pop() + self.heap[pos] = last + self.position[last] = pos + # Restore invariant by sifting up + self._siftup(pos) + + def _siftup(self, pos): + """Move smaller child up until hitting a leaf. + + Built to mimic code for heapq._siftup + only updating position dict too. + """ + heap, position = self.heap, self.position + end_pos = len(heap) + startpos = pos + newitem = heap[pos] + # Shift up the smaller child until hitting a leaf + child_pos = (pos << 1) + 1 # start with leftmost child position + while child_pos < end_pos: + # Set child_pos to index of smaller child. + child = heap[child_pos] + right_pos = child_pos + 1 + if right_pos < end_pos: + right = heap[right_pos] + if not child < right: + child = right + child_pos = right_pos + # Move the smaller child up. + heap[pos] = child + position[child] = pos + pos = child_pos + child_pos = (pos << 1) + 1 + # pos is a leaf position. Put newitem there, and bubble it up + # to its final resting place (by sifting its parents down). + while pos > 0: + parent_pos = (pos - 1) >> 1 + parent = heap[parent_pos] + if not newitem < parent: + break + heap[pos] = parent + position[parent] = pos + pos = parent_pos + heap[pos] = newitem + position[newitem] = pos + + def _siftdown(self, start_pos, pos): + """Restore invariant. keep swapping with parent until smaller. + + Built to mimic code for heapq._siftdown + only updating position dict too. + """ + heap, position = self.heap, self.position + newitem = heap[pos] + # Follow the path to the root, moving parents down until finding a place + # newitem fits. + while pos > start_pos: + parent_pos = (pos - 1) >> 1 + parent = heap[parent_pos] + if not newitem < parent: + break + heap[pos] = parent + position[parent] = pos + pos = parent_pos + heap[pos] = newitem + position[newitem] = pos diff --git a/wemm/lib/python3.10/site-packages/networkx/utils/tests/__init__.py b/wemm/lib/python3.10/site-packages/networkx/utils/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/wemm/lib/python3.10/site-packages/networkx/utils/tests/test_decorators.py b/wemm/lib/python3.10/site-packages/networkx/utils/tests/test_decorators.py new file mode 100644 index 0000000000000000000000000000000000000000..0a4aeabfe0b016bec362eac628489f6f4244cc59 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/utils/tests/test_decorators.py @@ -0,0 +1,510 @@ +import os +import pathlib +import random +import tempfile + +import pytest + +import networkx as nx +from networkx.utils.decorators import ( + argmap, + not_implemented_for, + np_random_state, + open_file, + py_random_state, +) +from networkx.utils.misc import PythonRandomInterface, PythonRandomViaNumpyBits + + +def test_not_implemented_decorator(): + @not_implemented_for("directed") + def test_d(G): + pass + + test_d(nx.Graph()) + with pytest.raises(nx.NetworkXNotImplemented): + test_d(nx.DiGraph()) + + @not_implemented_for("undirected") + def test_u(G): + pass + + test_u(nx.DiGraph()) + with pytest.raises(nx.NetworkXNotImplemented): + test_u(nx.Graph()) + + @not_implemented_for("multigraph") + def test_m(G): + pass + + test_m(nx.Graph()) + with pytest.raises(nx.NetworkXNotImplemented): + test_m(nx.MultiGraph()) + + @not_implemented_for("graph") + def test_g(G): + pass + + test_g(nx.MultiGraph()) + with pytest.raises(nx.NetworkXNotImplemented): + test_g(nx.Graph()) + + # not MultiDiGraph (multiple arguments => AND) + @not_implemented_for("directed", "multigraph") + def test_not_md(G): + pass + + test_not_md(nx.Graph()) + test_not_md(nx.DiGraph()) + test_not_md(nx.MultiGraph()) + with pytest.raises(nx.NetworkXNotImplemented): + test_not_md(nx.MultiDiGraph()) + + # Graph only (multiple decorators => OR) + @not_implemented_for("directed") + @not_implemented_for("multigraph") + def test_graph_only(G): + pass + + test_graph_only(nx.Graph()) + with pytest.raises(nx.NetworkXNotImplemented): + test_graph_only(nx.DiGraph()) + with pytest.raises(nx.NetworkXNotImplemented): + test_graph_only(nx.MultiGraph()) + with pytest.raises(nx.NetworkXNotImplemented): + test_graph_only(nx.MultiDiGraph()) + + with pytest.raises(ValueError): + not_implemented_for("directed", "undirected") + + with pytest.raises(ValueError): + not_implemented_for("multigraph", "graph") + + +def test_not_implemented_decorator_key(): + with pytest.raises(KeyError): + + @not_implemented_for("foo") + def test1(G): + pass + + test1(nx.Graph()) + + +def test_not_implemented_decorator_raise(): + with pytest.raises(nx.NetworkXNotImplemented): + + @not_implemented_for("graph") + def test1(G): + pass + + test1(nx.Graph()) + + +class TestOpenFileDecorator: + def setup_method(self): + self.text = ["Blah... ", "BLAH ", "BLAH!!!!"] + self.fobj = tempfile.NamedTemporaryFile("wb+", delete=False) + self.name = self.fobj.name + + def teardown_method(self): + self.fobj.close() + os.unlink(self.name) + + def write(self, path): + for text in self.text: + path.write(text.encode("ascii")) + + @open_file(1, "r") + def read(self, path): + return path.readlines()[0] + + @staticmethod + @open_file(0, "wb") + def writer_arg0(path): + path.write(b"demo") + + @open_file(1, "wb+") + def writer_arg1(self, path): + self.write(path) + + @open_file(2, "wb") + def writer_arg2default(self, x, path=None): + if path is None: + with tempfile.NamedTemporaryFile("wb+") as fh: + self.write(fh) + else: + self.write(path) + + @open_file(4, "wb") + def writer_arg4default(self, x, y, other="hello", path=None, **kwargs): + if path is None: + with tempfile.NamedTemporaryFile("wb+") as fh: + self.write(fh) + else: + self.write(path) + + @open_file("path", "wb") + def writer_kwarg(self, **kwargs): + path = kwargs.get("path", None) + if path is None: + with tempfile.NamedTemporaryFile("wb+") as fh: + self.write(fh) + else: + self.write(path) + + def test_writer_arg0_str(self): + self.writer_arg0(self.name) + + def test_writer_arg0_fobj(self): + self.writer_arg0(self.fobj) + + def test_writer_arg0_pathlib(self): + self.writer_arg0(pathlib.Path(self.name)) + + def test_writer_arg1_str(self): + self.writer_arg1(self.name) + assert self.read(self.name) == "".join(self.text) + + def test_writer_arg1_fobj(self): + self.writer_arg1(self.fobj) + assert not self.fobj.closed + self.fobj.close() + assert self.read(self.name) == "".join(self.text) + + def test_writer_arg2default_str(self): + self.writer_arg2default(0, path=None) + self.writer_arg2default(0, path=self.name) + assert self.read(self.name) == "".join(self.text) + + def test_writer_arg2default_fobj(self): + self.writer_arg2default(0, path=self.fobj) + assert not self.fobj.closed + self.fobj.close() + assert self.read(self.name) == "".join(self.text) + + def test_writer_arg2default_fobj_path_none(self): + self.writer_arg2default(0, path=None) + + def test_writer_arg4default_fobj(self): + self.writer_arg4default(0, 1, dog="dog", other="other") + self.writer_arg4default(0, 1, dog="dog", other="other", path=self.name) + assert self.read(self.name) == "".join(self.text) + + def test_writer_kwarg_str(self): + self.writer_kwarg(path=self.name) + assert self.read(self.name) == "".join(self.text) + + def test_writer_kwarg_fobj(self): + self.writer_kwarg(path=self.fobj) + self.fobj.close() + assert self.read(self.name) == "".join(self.text) + + def test_writer_kwarg_path_none(self): + self.writer_kwarg(path=None) + + +class TestRandomState: + @classmethod + def setup_class(cls): + global np + np = pytest.importorskip("numpy") + + @np_random_state(1) + def instantiate_np_random_state(self, random_state): + allowed = (np.random.RandomState, np.random.Generator) + assert isinstance(random_state, allowed) + return random_state.random() + + @py_random_state(1) + def instantiate_py_random_state(self, random_state): + allowed = (random.Random, PythonRandomInterface, PythonRandomViaNumpyBits) + assert isinstance(random_state, allowed) + return random_state.random() + + def test_random_state_None(self): + np.random.seed(42) + rv = np.random.random() + np.random.seed(42) + assert rv == self.instantiate_np_random_state(None) + + random.seed(42) + rv = random.random() + random.seed(42) + assert rv == self.instantiate_py_random_state(None) + + def test_random_state_np_random(self): + np.random.seed(42) + rv = np.random.random() + np.random.seed(42) + assert rv == self.instantiate_np_random_state(np.random) + np.random.seed(42) + assert rv == self.instantiate_py_random_state(np.random) + + def test_random_state_int(self): + np.random.seed(42) + np_rv = np.random.random() + random.seed(42) + py_rv = random.random() + + np.random.seed(42) + seed = 1 + rval = self.instantiate_np_random_state(seed) + rval_expected = np.random.RandomState(seed).rand() + assert rval == rval_expected + # test that global seed wasn't changed in function + assert np_rv == np.random.random() + + random.seed(42) + rval = self.instantiate_py_random_state(seed) + rval_expected = random.Random(seed).random() + assert rval == rval_expected + # test that global seed wasn't changed in function + assert py_rv == random.random() + + def test_random_state_np_random_Generator(self): + np.random.seed(42) + np_rv = np.random.random() + np.random.seed(42) + seed = 1 + + rng = np.random.default_rng(seed) + rval = self.instantiate_np_random_state(rng) + rval_expected = np.random.default_rng(seed).random() + assert rval == rval_expected + + rval = self.instantiate_py_random_state(rng) + rval_expected = np.random.default_rng(seed).random(size=2)[1] + assert rval == rval_expected + # test that global seed wasn't changed in function + assert np_rv == np.random.random() + + def test_random_state_np_random_RandomState(self): + np.random.seed(42) + np_rv = np.random.random() + np.random.seed(42) + seed = 1 + + rng = np.random.RandomState(seed) + rval = self.instantiate_np_random_state(rng) + rval_expected = np.random.RandomState(seed).random() + assert rval == rval_expected + + rval = self.instantiate_py_random_state(rng) + rval_expected = np.random.RandomState(seed).random(size=2)[1] + assert rval == rval_expected + # test that global seed wasn't changed in function + assert np_rv == np.random.random() + + def test_random_state_py_random(self): + seed = 1 + rng = random.Random(seed) + rv = self.instantiate_py_random_state(rng) + assert rv == random.Random(seed).random() + + pytest.raises(ValueError, self.instantiate_np_random_state, rng) + + +def test_random_state_string_arg_index(): + with pytest.raises(nx.NetworkXError): + + @np_random_state("a") + def make_random_state(rs): + pass + + rstate = make_random_state(1) + + +def test_py_random_state_string_arg_index(): + with pytest.raises(nx.NetworkXError): + + @py_random_state("a") + def make_random_state(rs): + pass + + rstate = make_random_state(1) + + +def test_random_state_invalid_arg_index(): + with pytest.raises(nx.NetworkXError): + + @np_random_state(2) + def make_random_state(rs): + pass + + rstate = make_random_state(1) + + +def test_py_random_state_invalid_arg_index(): + with pytest.raises(nx.NetworkXError): + + @py_random_state(2) + def make_random_state(rs): + pass + + rstate = make_random_state(1) + + +class TestArgmap: + class ArgmapError(RuntimeError): + pass + + def test_trivial_function(self): + def do_not_call(x): + raise ArgmapError("do not call this function") + + @argmap(do_not_call) + def trivial_argmap(): + return 1 + + assert trivial_argmap() == 1 + + def test_trivial_iterator(self): + def do_not_call(x): + raise ArgmapError("do not call this function") + + @argmap(do_not_call) + def trivial_argmap(): + yield from (1, 2, 3) + + assert tuple(trivial_argmap()) == (1, 2, 3) + + def test_contextmanager(self): + container = [] + + def contextmanager(x): + nonlocal container + return x, lambda: container.append(x) + + @argmap(contextmanager, 0, 1, 2, try_finally=True) + def foo(x, y, z): + return x, y, z + + x, y, z = foo("a", "b", "c") + + # context exits are called in reverse + assert container == ["c", "b", "a"] + + def test_tryfinally_generator(self): + container = [] + + def singleton(x): + return (x,) + + with pytest.raises(nx.NetworkXError): + + @argmap(singleton, 0, 1, 2, try_finally=True) + def foo(x, y, z): + yield from (x, y, z) + + @argmap(singleton, 0, 1, 2) + def foo(x, y, z): + return x + y + z + + q = foo("a", "b", "c") + + assert q == ("a", "b", "c") + + def test_actual_vararg(self): + @argmap(lambda x: -x, 4) + def foo(x, y, *args): + return (x, y) + tuple(args) + + assert foo(1, 2, 3, 4, 5, 6) == (1, 2, 3, 4, -5, 6) + + def test_signature_destroying_intermediate_decorator(self): + def add_one_to_first_bad_decorator(f): + """Bad because it doesn't wrap the f signature (clobbers it)""" + + def decorated(a, *args, **kwargs): + return f(a + 1, *args, **kwargs) + + return decorated + + add_two_to_second = argmap(lambda b: b + 2, 1) + + @add_two_to_second + @add_one_to_first_bad_decorator + def add_one_and_two(a, b): + return a, b + + assert add_one_and_two(5, 5) == (6, 7) + + def test_actual_kwarg(self): + @argmap(lambda x: -x, "arg") + def foo(*, arg): + return arg + + assert foo(arg=3) == -3 + + def test_nested_tuple(self): + def xform(x, y): + u, v = y + return x + u + v, (x + u, x + v) + + # we're testing args and kwargs here, too + @argmap(xform, (0, ("t", 2))) + def foo(a, *args, **kwargs): + return a, args, kwargs + + a, args, kwargs = foo(1, 2, 3, t=4) + + assert a == 1 + 4 + 3 + assert args == (2, 1 + 3) + assert kwargs == {"t": 1 + 4} + + def test_flatten(self): + assert tuple(argmap._flatten([[[[[], []], [], []], [], [], []]], set())) == () + + rlist = ["a", ["b", "c"], [["d"], "e"], "f"] + assert "".join(argmap._flatten(rlist, set())) == "abcdef" + + def test_indent(self): + code = "\n".join( + argmap._indent( + *[ + "try:", + "try:", + "pass#", + "finally:", + "pass#", + "#", + "finally:", + "pass#", + ] + ) + ) + assert ( + code + == """try: + try: + pass# + finally: + pass# + # +finally: + pass#""" + ) + + def test_immediate_raise(self): + @not_implemented_for("directed") + def yield_nodes(G): + yield from G + + G = nx.Graph([(1, 2)]) + D = nx.DiGraph() + + # test first call (argmap is compiled and executed) + with pytest.raises(nx.NetworkXNotImplemented): + node_iter = yield_nodes(D) + + # test second call (argmap is only executed) + with pytest.raises(nx.NetworkXNotImplemented): + node_iter = yield_nodes(D) + + # ensure that generators still make generators + node_iter = yield_nodes(G) + next(node_iter) + next(node_iter) + with pytest.raises(StopIteration): + next(node_iter) diff --git a/wemm/lib/python3.10/site-packages/networkx/utils/tests/test_mapped_queue.py b/wemm/lib/python3.10/site-packages/networkx/utils/tests/test_mapped_queue.py new file mode 100644 index 0000000000000000000000000000000000000000..ca9b7e42072f5aebbf4b794302d06f21f5d8e17c --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/utils/tests/test_mapped_queue.py @@ -0,0 +1,268 @@ +import pytest + +from networkx.utils.mapped_queue import MappedQueue, _HeapElement + + +def test_HeapElement_gtlt(): + bar = _HeapElement(1.1, "a") + foo = _HeapElement(1, "b") + assert foo < bar + assert bar > foo + assert foo < 1.1 + assert 1 < bar + + +def test_HeapElement_gtlt_tied_priority(): + bar = _HeapElement(1, "a") + foo = _HeapElement(1, "b") + assert foo > bar + assert bar < foo + + +def test_HeapElement_eq(): + bar = _HeapElement(1.1, "a") + foo = _HeapElement(1, "a") + assert foo == bar + assert bar == foo + assert foo == "a" + + +def test_HeapElement_iter(): + foo = _HeapElement(1, "a") + bar = _HeapElement(1.1, (3, 2, 1)) + assert list(foo) == [1, "a"] + assert list(bar) == [1.1, 3, 2, 1] + + +def test_HeapElement_getitem(): + foo = _HeapElement(1, "a") + bar = _HeapElement(1.1, (3, 2, 1)) + assert foo[1] == "a" + assert foo[0] == 1 + assert bar[0] == 1.1 + assert bar[2] == 2 + assert bar[3] == 1 + pytest.raises(IndexError, bar.__getitem__, 4) + pytest.raises(IndexError, foo.__getitem__, 2) + + +class TestMappedQueue: + def setup_method(self): + pass + + def _check_map(self, q): + assert q.position == {elt: pos for pos, elt in enumerate(q.heap)} + + def _make_mapped_queue(self, h): + q = MappedQueue() + q.heap = h + q.position = {elt: pos for pos, elt in enumerate(h)} + return q + + def test_heapify(self): + h = [5, 4, 3, 2, 1, 0] + q = self._make_mapped_queue(h) + q._heapify() + self._check_map(q) + + def test_init(self): + h = [5, 4, 3, 2, 1, 0] + q = MappedQueue(h) + self._check_map(q) + + def test_incomparable(self): + h = [5, 4, "a", 2, 1, 0] + pytest.raises(TypeError, MappedQueue, h) + + def test_len(self): + h = [5, 4, 3, 2, 1, 0] + q = MappedQueue(h) + self._check_map(q) + assert len(q) == 6 + + def test_siftup_leaf(self): + h = [2] + h_sifted = [2] + q = self._make_mapped_queue(h) + q._siftup(0) + assert q.heap == h_sifted + self._check_map(q) + + def test_siftup_one_child(self): + h = [2, 0] + h_sifted = [0, 2] + q = self._make_mapped_queue(h) + q._siftup(0) + assert q.heap == h_sifted + self._check_map(q) + + def test_siftup_left_child(self): + h = [2, 0, 1] + h_sifted = [0, 2, 1] + q = self._make_mapped_queue(h) + q._siftup(0) + assert q.heap == h_sifted + self._check_map(q) + + def test_siftup_right_child(self): + h = [2, 1, 0] + h_sifted = [0, 1, 2] + q = self._make_mapped_queue(h) + q._siftup(0) + assert q.heap == h_sifted + self._check_map(q) + + def test_siftup_multiple(self): + h = [0, 1, 2, 4, 3, 5, 6] + h_sifted = [0, 1, 2, 4, 3, 5, 6] + q = self._make_mapped_queue(h) + q._siftup(0) + assert q.heap == h_sifted + self._check_map(q) + + def test_siftdown_leaf(self): + h = [2] + h_sifted = [2] + q = self._make_mapped_queue(h) + q._siftdown(0, 0) + assert q.heap == h_sifted + self._check_map(q) + + def test_siftdown_single(self): + h = [1, 0] + h_sifted = [0, 1] + q = self._make_mapped_queue(h) + q._siftdown(0, len(h) - 1) + assert q.heap == h_sifted + self._check_map(q) + + def test_siftdown_multiple(self): + h = [1, 2, 3, 4, 5, 6, 7, 0] + h_sifted = [0, 1, 3, 2, 5, 6, 7, 4] + q = self._make_mapped_queue(h) + q._siftdown(0, len(h) - 1) + assert q.heap == h_sifted + self._check_map(q) + + def test_push(self): + to_push = [6, 1, 4, 3, 2, 5, 0] + h_sifted = [0, 2, 1, 6, 3, 5, 4] + q = MappedQueue() + for elt in to_push: + q.push(elt) + assert q.heap == h_sifted + self._check_map(q) + + def test_push_duplicate(self): + to_push = [2, 1, 0] + h_sifted = [0, 2, 1] + q = MappedQueue() + for elt in to_push: + inserted = q.push(elt) + assert inserted + assert q.heap == h_sifted + self._check_map(q) + inserted = q.push(1) + assert not inserted + + def test_pop(self): + h = [3, 4, 6, 0, 1, 2, 5] + h_sorted = sorted(h) + q = self._make_mapped_queue(h) + q._heapify() + popped = [q.pop() for _ in range(len(h))] + assert popped == h_sorted + self._check_map(q) + + def test_remove_leaf(self): + h = [0, 2, 1, 6, 3, 5, 4] + h_removed = [0, 2, 1, 6, 4, 5] + q = self._make_mapped_queue(h) + removed = q.remove(3) + assert q.heap == h_removed + + def test_remove_root(self): + h = [0, 2, 1, 6, 3, 5, 4] + h_removed = [1, 2, 4, 6, 3, 5] + q = self._make_mapped_queue(h) + removed = q.remove(0) + assert q.heap == h_removed + + def test_update_leaf(self): + h = [0, 20, 10, 60, 30, 50, 40] + h_updated = [0, 15, 10, 60, 20, 50, 40] + q = self._make_mapped_queue(h) + removed = q.update(30, 15) + assert q.heap == h_updated + + def test_update_root(self): + h = [0, 20, 10, 60, 30, 50, 40] + h_updated = [10, 20, 35, 60, 30, 50, 40] + q = self._make_mapped_queue(h) + removed = q.update(0, 35) + assert q.heap == h_updated + + +class TestMappedDict(TestMappedQueue): + def _make_mapped_queue(self, h): + priority_dict = {elt: elt for elt in h} + return MappedQueue(priority_dict) + + def test_init(self): + d = {5: 0, 4: 1, "a": 2, 2: 3, 1: 4} + q = MappedQueue(d) + assert q.position == d + + def test_ties(self): + d = {5: 0, 4: 1, 3: 2, 2: 3, 1: 4} + q = MappedQueue(d) + assert q.position == {elt: pos for pos, elt in enumerate(q.heap)} + + def test_pop(self): + d = {5: 0, 4: 1, 3: 2, 2: 3, 1: 4} + q = MappedQueue(d) + assert q.pop() == _HeapElement(0, 5) + assert q.position == {elt: pos for pos, elt in enumerate(q.heap)} + + def test_empty_pop(self): + q = MappedQueue() + pytest.raises(IndexError, q.pop) + + def test_incomparable_ties(self): + d = {5: 0, 4: 0, "a": 0, 2: 0, 1: 0} + pytest.raises(TypeError, MappedQueue, d) + + def test_push(self): + to_push = [6, 1, 4, 3, 2, 5, 0] + h_sifted = [0, 2, 1, 6, 3, 5, 4] + q = MappedQueue() + for elt in to_push: + q.push(elt, priority=elt) + assert q.heap == h_sifted + self._check_map(q) + + def test_push_duplicate(self): + to_push = [2, 1, 0] + h_sifted = [0, 2, 1] + q = MappedQueue() + for elt in to_push: + inserted = q.push(elt, priority=elt) + assert inserted + assert q.heap == h_sifted + self._check_map(q) + inserted = q.push(1, priority=1) + assert not inserted + + def test_update_leaf(self): + h = [0, 20, 10, 60, 30, 50, 40] + h_updated = [0, 15, 10, 60, 20, 50, 40] + q = self._make_mapped_queue(h) + removed = q.update(30, 15, priority=15) + assert q.heap == h_updated + + def test_update_root(self): + h = [0, 20, 10, 60, 30, 50, 40] + h_updated = [10, 20, 35, 60, 30, 50, 40] + q = self._make_mapped_queue(h) + removed = q.update(0, 35, priority=35) + assert q.heap == h_updated