rm CondaPkg environment

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/README.txt

@@ -0,0 +1,2 @@
+Algorithms
+----------

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/hartford_drug.edgelist

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+# source target
+1 2
+1 10
+2 1
+2 10
+3 7
+4 7
+4 209
+5 132
+6 150
+7 3
+7 4
+7 9
+8 106
+8 115
+9 1
+9 2
+9 7
+10 1
+10 2
+11 133
+11 218
+12 88
+13 214
+14 24
+14 52
+16 10
+16 19
+17 64
+17 78
+18 55
+18 103
+18 163
+19 18
+20 64
+20 180
+21 16
+21 22
+22 21
+22 64
+22 106
+23 20
+23 22
+23 64
+24 14
+24 31
+24 122
+27 115
+28 29
+29 28
+30 19
+31 24
+31 32
+31 122
+31 147
+31 233
+32 31
+32 86
+34 35
+34 37
+35 34
+35 43
+36 132
+36 187
+37 38
+37 90
+37 282
+38 42
+38 43
+38 210
+40 20
+42 15
+42 38
+43 34
+43 35
+43 38
+45 107
+46 61
+46 72
+48 23
+49 30
+49 64
+49 108
+49 115
+49 243
+50 30
+50 47
+50 55
+50 125
+50 163
+52 218
+52 224
+54 111
+54 210
+55 65
+55 67
+55 105
+55 108
+55 222
+56 18
+56 64
+57 65
+57 125
+58 20
+58 30
+58 50
+58 103
+58 180
+59 164
+63 125
+64 8
+64 50
+64 70
+64 256
+66 20
+66 84
+66 106
+66 125
+67 22
+67 50
+67 113
+68 50
+70 50
+70 64
+71 72
+74 29
+74 75
+74 215
+75 74
+75 215
+76 58
+76 104
+77 103
+78 64
+78 68
+80 207
+80 210
+82 8
+82 77
+82 83
+82 97
+82 163
+83 82
+83 226
+83 243
+84 29
+84 154
+87 101
+87 189
+89 90
+90 89
+90 94
+91 86
+92 19
+92 30
+92 106
+94 72
+94 89
+94 90
+95 30
+96 75
+96 256
+97 80
+97 128
+98 86
+100 86
+101 87
+103 77
+103 104
+104 58
+104 77
+104 103
+106 22
+107 38
+107 114
+107 122
+108 49
+108 55
+111 121
+111 128
+111 210
+113 253
+114 107
+116 30
+116 140
+118 129
+118 138
+120 88
+121 128
+122 31
+123 32
+124 244
+125 132
+126 163
+126 180
+128 38
+128 111
+129 118
+132 29
+132 30
+133 30
+134 135
+134 150
+135 134
+137 144
+138 118
+138 129
+139 142
+141 157
+141 163
+142 139
+143 2
+144 137
+145 151
+146 137
+146 165
+146 169
+146 171
+147 31
+147 128
+148 146
+148 169
+148 171
+148 282
+149 128
+149 148
+149 172
+150 86
+151 145
+152 4
+153 134
+154 155
+156 161
+157 141
+161 156
+165 144
+165 148
+167 149
+169 15
+169 148
+169 171
+170 115
+170 173
+170 183
+170 202
+171 72
+171 148
+171 169
+173 170
+175 100
+176 10
+178 181
+181 178
+182 38
+182 171
+183 96
+185 50
+186 127
+187 50
+187 65
+188 30
+188 50
+189 87
+189 89
+190 35
+190 38
+190 122
+190 182
+191 54
+191 118
+191 129
+191 172
+192 149
+192 167
+195 75
+197 50
+197 188
+198 218
+198 221
+198 222
+200 65
+200 220
+201 113
+202 156
+203 232
+204 194
+207 38
+207 122
+207 124
+208 30
+208 50
+210 38
+210 207
+211 37
+213 35
+213 38
+214 13
+214 14
+214 171
+214 213
+215 75
+217 39
+218 68
+218 222
+221 198
+222 198
+222 218
+223 39
+225 3
+226 22
+229 65
+230 68
+231 43
+232 95
+232 203
+233 99
+234 68
+234 230
+237 244
+238 145
+242 3
+242 113
+244 237
+249 96
+250 156
+252 65
+254 65
+258 113
+268 4
+270 183
+272 6
+275 96
+280 183
+280 206
+282 37
+285 75
+290 285
+293 290

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_beam_search.py

@@ -0,0 +1,112 @@
+"""
+===========
+Beam Search
+===========
+
+Beam search with dynamic beam width.
+
+The progressive widening beam search repeatedly executes a beam search
+with increasing beam width until the target node is found.
+"""
+import math
+
+import matplotlib.pyplot as plt
+import networkx as nx
+
+
+def progressive_widening_search(G, source, value, condition, initial_width=1):
+    """Progressive widening beam search to find a node.
+
+    The progressive widening beam search involves a repeated beam
+    search, starting with a small beam width then extending to
+    progressively larger beam widths if the target node is not
+    found. This implementation simply returns the first node found that
+    matches the termination condition.
+
+    `G` is a NetworkX graph.
+
+    `source` is a node in the graph. The search for the node of interest
+    begins here and extends only to those nodes in the (weakly)
+    connected component of this node.
+
+    `value` is a function that returns a real number indicating how good
+    a potential neighbor node is when deciding which neighbor nodes to
+    enqueue in the breadth-first search. Only the best nodes within the
+    current beam width will be enqueued at each step.
+
+    `condition` is the termination condition for the search. This is a
+    function that takes a node as input and return a Boolean indicating
+    whether the node is the target. If no node matches the termination
+    condition, this function raises :exc:`NodeNotFound`.
+
+    `initial_width` is the starting beam width for the beam search (the
+    default is one). If no node matching the `condition` is found with
+    this beam width, the beam search is restarted from the `source` node
+    with a beam width that is twice as large (so the beam width
+    increases exponentially). The search terminates after the beam width
+    exceeds the number of nodes in the graph.
+
+    """
+    # Check for the special case in which the source node satisfies the
+    # termination condition.
+    if condition(source):
+        return source
+    # The largest possible value of `i` in this range yields a width at
+    # least the number of nodes in the graph, so the final invocation of
+    # `bfs_beam_edges` is equivalent to a plain old breadth-first
+    # search. Therefore, all nodes will eventually be visited.
+    log_m = math.ceil(math.log2(len(G)))
+    for i in range(log_m):
+        width = initial_width * pow(2, i)
+        # Since we are always starting from the same source node, this
+        # search may visit the same nodes many times (depending on the
+        # implementation of the `value` function).
+        for u, v in nx.bfs_beam_edges(G, source, value, width):
+            if condition(v):
+                return v
+    # At this point, since all nodes have been visited, we know that
+    # none of the nodes satisfied the termination condition.
+    raise nx.NodeNotFound("no node satisfied the termination condition")
+
+
+###############################################################################
+# Search for a node with high centrality.
+# ---------------------------------------
+#
+# We generate a random graph, compute the centrality of each node, then perform
+# the progressive widening search in order to find a node of high centrality.
+
+# Set a seed for random number generation so the example is reproducible
+seed = 89
+
+G = nx.gnp_random_graph(100, 0.5, seed=seed)
+centrality = nx.eigenvector_centrality(G)
+avg_centrality = sum(centrality.values()) / len(G)
+
+
+def has_high_centrality(v):
+    return centrality[v] >= avg_centrality
+
+
+source = 0
+value = centrality.get
+condition = has_high_centrality
+
+found_node = progressive_widening_search(G, source, value, condition)
+c = centrality[found_node]
+print(f"found node {found_node} with centrality {c}")
+
+
+# Draw graph
+pos = nx.spring_layout(G, seed=seed)
+options = {
+    "node_color": "blue",
+    "node_size": 20,
+    "edge_color": "grey",
+    "linewidths": 0,
+    "width": 0.1,
+}
+nx.draw(G, pos, **options)
+# Draw node with high centrality as large and red
+nx.draw_networkx_nodes(G, pos, nodelist=[found_node], node_size=100, node_color="r")
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_betweenness_centrality.py

@@ -0,0 +1,83 @@
+"""
+======================
+Betweenness Centrality
+======================
+
+Betweenness centrality measures of positive gene functional associations
+using WormNet v.3-GS.
+
+Data from: https://www.inetbio.org/wormnet/downloadnetwork.php
+"""
+
+from random import sample
+import networkx as nx
+import matplotlib.pyplot as plt
+
+# Gold standard data of positive gene functional associations
+# from https://www.inetbio.org/wormnet/downloadnetwork.php
+G = nx.read_edgelist("WormNet.v3.benchmark.txt")
+
+# remove randomly selected nodes (to make example fast)
+num_to_remove = int(len(G) / 1.5)
+nodes = sample(list(G.nodes), num_to_remove)
+G.remove_nodes_from(nodes)
+
+# remove low-degree nodes
+low_degree = [n for n, d in G.degree() if d < 10]
+G.remove_nodes_from(low_degree)
+
+# largest connected component
+components = nx.connected_components(G)
+largest_component = max(components, key=len)
+H = G.subgraph(largest_component)
+
+# compute centrality
+centrality = nx.betweenness_centrality(H, k=10, endpoints=True)
+
+# compute community structure
+lpc = nx.community.label_propagation_communities(H)
+community_index = {n: i for i, com in enumerate(lpc) for n in com}
+
+#### draw graph ####
+fig, ax = plt.subplots(figsize=(20, 15))
+pos = nx.spring_layout(H, k=0.15, seed=4572321)
+node_color = [community_index[n] for n in H]
+node_size = [v * 20000 for v in centrality.values()]
+nx.draw_networkx(
+    H,
+    pos=pos,
+    with_labels=False,
+    node_color=node_color,
+    node_size=node_size,
+    edge_color="gainsboro",
+    alpha=0.4,
+)
+
+# Title/legend
+font = {"color": "k", "fontweight": "bold", "fontsize": 20}
+ax.set_title("Gene functional association network (C. elegans)", font)
+# Change font color for legend
+font["color"] = "r"
+
+ax.text(
+    0.80,
+    0.10,
+    "node color = community structure",
+    horizontalalignment="center",
+    transform=ax.transAxes,
+    fontdict=font,
+)
+ax.text(
+    0.80,
+    0.06,
+    "node size = betweenness centrality",
+    horizontalalignment="center",
+    transform=ax.transAxes,
+    fontdict=font,
+)
+
+# Resize figure for label readability
+ax.margins(0.1, 0.05)
+fig.tight_layout()
+plt.axis("off")
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_blockmodel.py

@@ -0,0 +1,79 @@
+"""
+==========
+Blockmodel
+==========
+
+Example of creating a block model using the quotient_graph function in NX.  Data
+used is the Hartford, CT drug users network::
+
+    @article{weeks2002social,
+      title={Social networks of drug users in high-risk sites: Finding the connections},
+      url = {https://doi.org/10.1023/A:1015457400897},
+      doi = {10.1023/A:1015457400897},
+      author={Weeks, Margaret R and Clair, Scott and Borgatti, Stephen P and Radda, Kim and Schensul, Jean J},
+      journal={{AIDS and Behavior}},
+      volume={6},
+      number={2},
+      pages={193--206},
+      year={2002},
+      publisher={Springer}
+    }
+
+"""
+
+from collections import defaultdict
+
+import matplotlib.pyplot as plt
+import networkx as nx
+import numpy as np
+from scipy.cluster import hierarchy
+from scipy.spatial import distance
+
+
+def create_hc(G):
+    """Creates hierarchical cluster of graph G from distance matrix"""
+    path_length = nx.all_pairs_shortest_path_length(G)
+    distances = np.zeros((len(G), len(G)))
+    for u, p in path_length:
+        for v, d in p.items():
+            distances[u][v] = d
+    # Create hierarchical cluster
+    Y = distance.squareform(distances)
+    Z = hierarchy.complete(Y)  # Creates HC using farthest point linkage
+    # This partition selection is arbitrary, for illustrive purposes
+    membership = list(hierarchy.fcluster(Z, t=1.15))
+    # Create collection of lists for blockmodel
+    partition = defaultdict(list)
+    for n, p in zip(list(range(len(G))), membership):
+        partition[p].append(n)
+    return list(partition.values())
+
+
+G = nx.read_edgelist("hartford_drug.edgelist")
+
+# Extract largest connected component into graph H
+H = G.subgraph(next(nx.connected_components(G)))
+# Makes life easier to have consecutively labeled integer nodes
+H = nx.convert_node_labels_to_integers(H)
+# Create partitions with hierarchical clustering
+partitions = create_hc(H)
+# Build blockmodel graph
+BM = nx.quotient_graph(H, partitions, relabel=True)
+
+# Draw original graph
+pos = nx.spring_layout(H, iterations=100, seed=83)  # Seed for reproducibility
+plt.subplot(211)
+nx.draw(H, pos, with_labels=False, node_size=10)
+
+# Draw block model with weighted edges and nodes sized by number of internal nodes
+node_size = [BM.nodes[x]["nnodes"] * 10 for x in BM.nodes()]
+edge_width = [(2 * d["weight"]) for (u, v, d) in BM.edges(data=True)]
+# Set positions to mean of positions of internal nodes from original graph
+posBM = {}
+for n in BM:
+    xy = np.array([pos[u] for u in BM.nodes[n]["graph"]])
+    posBM[n] = xy.mean(axis=0)
+plt.subplot(212)
+nx.draw(BM, posBM, node_size=node_size, width=edge_width, with_labels=False)
+plt.axis("off")
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_circuits.py

@@ -0,0 +1,103 @@
+"""
+========
+Circuits
+========
+
+Convert a Boolean circuit to an equivalent Boolean formula.
+
+A Boolean circuit can be exponentially more expressive than an
+equivalent formula in the worst case, since the circuit can reuse
+subcircuits multiple times, whereas a formula cannot reuse subformulas
+more than once. Thus creating a Boolean formula from a Boolean circuit
+in this way may be infeasible if the circuit is large.
+
+"""
+import matplotlib.pyplot as plt
+import networkx as nx
+
+
+def circuit_to_formula(circuit):
+    # Convert the circuit to an equivalent formula.
+    formula = nx.dag_to_branching(circuit)
+    # Transfer the operator or variable labels for each node from the
+    # circuit to the formula.
+    for v in formula:
+        source = formula.nodes[v]["source"]
+        formula.nodes[v]["label"] = circuit.nodes[source]["label"]
+    return formula
+
+
+def formula_to_string(formula):
+    def _to_string(formula, root):
+        # If there are no children, this is a variable node.
+        label = formula.nodes[root]["label"]
+        if not formula[root]:
+            return label
+        # Otherwise, this is an operator.
+        children = formula[root]
+        # If one child, the label must be a NOT operator.
+        if len(children) == 1:
+            child = nx.utils.arbitrary_element(children)
+            return f"{label}({_to_string(formula, child)})"
+        # NB "left" and "right" here are a little misleading: there is
+        # no order on the children of a node. That's okay because the
+        # Boolean AND and OR operators are symmetric. It just means that
+        # the order of the operands cannot be predicted and hence the
+        # function does not necessarily behave the same way on every
+        # invocation.
+        left, right = formula[root]
+        left_subformula = _to_string(formula, left)
+        right_subformula = _to_string(formula, right)
+        return f"({left_subformula} {label} {right_subformula})"
+
+    root = next(v for v, d in formula.in_degree() if d == 0)
+    return _to_string(formula, root)
+
+
+###############################################################################
+# Create an example Boolean circuit.
+# ----------------------------------
+#
+# This circuit has a ∧ at the output and two ∨s at the next layer.
+# The third layer has a variable x that appears in the left ∨, a
+# variable y that appears in both the left and right ∨s, and a
+# negation for the variable z that appears as the sole node in the
+# fourth layer.
+circuit = nx.DiGraph()
+# Layer 0
+circuit.add_node(0, label="∧", layer=0)
+# Layer 1
+circuit.add_node(1, label="∨", layer=1)
+circuit.add_node(2, label="∨", layer=1)
+circuit.add_edge(0, 1)
+circuit.add_edge(0, 2)
+# Layer 2
+circuit.add_node(3, label="x", layer=2)
+circuit.add_node(4, label="y", layer=2)
+circuit.add_node(5, label="¬", layer=2)
+circuit.add_edge(1, 3)
+circuit.add_edge(1, 4)
+circuit.add_edge(2, 4)
+circuit.add_edge(2, 5)
+# Layer 3
+circuit.add_node(6, label="z", layer=3)
+circuit.add_edge(5, 6)
+# Convert the circuit to an equivalent formula.
+formula = circuit_to_formula(circuit)
+print(formula_to_string(formula))
+
+
+labels = nx.get_node_attributes(circuit, "label")
+options = {
+    "node_size": 600,
+    "alpha": 0.5,
+    "node_color": "blue",
+    "labels": labels,
+    "font_size": 22,
+}
+plt.figure(figsize=(8, 8))
+pos = nx.multipartite_layout(circuit, subset_key="layer")
+nx.draw_networkx(circuit, pos, **options)
+plt.title(formula_to_string(formula))
+plt.axis("equal")
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_davis_club.py

@@ -0,0 +1,43 @@
+"""
+==========
+Davis Club
+==========
+
+Davis Southern Club Women
+
+Shows how to make unipartite projections of the graph and compute the
+properties of those graphs.
+
+These data were collected by Davis et al. in the 1930s.
+They represent observed attendance at 14 social events by 18 Southern women.
+The graph is bipartite (clubs, women).
+"""
+import matplotlib.pyplot as plt
+import networkx as nx
+from networkx.algorithms import bipartite
+
+G = nx.davis_southern_women_graph()
+women = G.graph["top"]
+clubs = G.graph["bottom"]
+
+print("Biadjacency matrix")
+print(bipartite.biadjacency_matrix(G, women, clubs))
+
+# project bipartite graph onto women nodes
+W = bipartite.projected_graph(G, women)
+print()
+print("#Friends, Member")
+for w in women:
+    print(f"{W.degree(w)} {w}")
+
+# project bipartite graph onto women nodes keeping number of co-occurrence
+# the degree computed is weighted and counts the total number of shared contacts
+W = bipartite.weighted_projected_graph(G, women)
+print()
+print("#Friend meetings, Member")
+for w in women:
+    print(f"{W.degree(w, weight='weight')} {w}")
+
+pos = nx.spring_layout(G, seed=648)  # Seed layout for reproducible node positions
+nx.draw(G, pos)
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_dedensification.py

@@ -0,0 +1,92 @@
+"""
+===============
+Dedensification
+===============
+
+Examples of dedensification of a graph.  Dedensification retains the structural
+pattern of the original graph and will only add compressor nodes when doing so
+would result in fewer edges in the compressed graph.
+"""
+import matplotlib.pyplot as plt
+import networkx as nx
+
+plt.suptitle("Dedensification")
+
+original_graph = nx.DiGraph()
+white_nodes = ["1", "2", "3", "4", "5", "6"]
+red_nodes = ["A", "B", "C"]
+node_sizes = [250 for node in white_nodes + red_nodes]
+node_colors = ["white" for n in white_nodes] + ["red" for n in red_nodes]
+
+original_graph.add_nodes_from(white_nodes + red_nodes)
+original_graph.add_edges_from(
+    [
+        ("1", "C"),
+        ("1", "B"),
+        ("2", "C"),
+        ("2", "B"),
+        ("2", "A"),
+        ("3", "B"),
+        ("3", "A"),
+        ("3", "6"),
+        ("4", "C"),
+        ("4", "B"),
+        ("4", "A"),
+        ("5", "B"),
+        ("5", "A"),
+        ("6", "5"),
+        ("A", "6"),
+    ]
+)
+base_options = {"with_labels": True, "edgecolors": "black"}
+pos = {
+    "3": (0, 1),
+    "2": (0, 2),
+    "1": (0, 3),
+    "6": (1, 0),
+    "A": (1, 1),
+    "B": (1, 2),
+    "C": (1, 3),
+    "4": (2, 3),
+    "5": (2, 1),
+}
+ax1 = plt.subplot(1, 2, 1)
+plt.title("Original (%s edges)" % original_graph.number_of_edges())
+nx.draw_networkx(original_graph, pos=pos, node_color=node_colors, **base_options)
+
+nonexp_graph, compression_nodes = nx.summarization.dedensify(
+    original_graph, threshold=2, copy=False
+)
+nonexp_node_colors = list(node_colors)
+nonexp_node_sizes = list(node_sizes)
+for node in compression_nodes:
+    nonexp_node_colors.append("yellow")
+    nonexp_node_sizes.append(600)
+plt.subplot(1, 2, 2)
+
+plt.title("Dedensified (%s edges)" % nonexp_graph.number_of_edges())
+nonexp_pos = {
+    "5": (0, 0),
+    "B": (0, 2),
+    "1": (0, 3),
+    "6": (1, 0.75),
+    "3": (1.5, 1.5),
+    "A": (2, 0),
+    "C": (2, 3),
+    "4": (3, 1.5),
+    "2": (3, 2.5),
+}
+c_nodes = list(compression_nodes)
+c_nodes.sort()
+for spot, node in enumerate(c_nodes):
+    nonexp_pos[node] = (2, spot + 2)
+nx.draw_networkx(
+    nonexp_graph,
+    pos=nonexp_pos,
+    node_color=nonexp_node_colors,
+    node_size=nonexp_node_sizes,
+    **base_options,
+)
+
+plt.tight_layout()
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_girvan_newman.py

@@ -0,0 +1,79 @@
+"""
+=======================================
+Community Detection using Girvan-Newman
+=======================================
+
+This example shows the detection of communities in the Zachary Karate
+Club dataset using the Girvan-Newman method.
+
+We plot the change in modularity as important edges are removed. 
+Graph is coloured and plotted based on community detection when number 
+of iterations are 1 and 4 respectively.
+"""
+
+import networkx as nx
+import pandas as pd
+import matplotlib.pyplot as plt
+
+# Load karate graph and find communities using Girvan-Newman
+G = nx.karate_club_graph()
+communities = list(nx.community.girvan_newman(G))
+
+# Modularity -> measures the strength of division of a network into modules
+modularity_df = pd.DataFrame(
+    [
+        [k + 1, nx.community.modularity(G, communities[k])]
+        for k in range(len(communities))
+    ],
+    columns=["k", "modularity"],
+)
+
+
+# function to create node colour list
+def create_community_node_colors(graph, communities):
+    number_of_colors = len(communities[0])
+    colors = ["#D4FCB1", "#CDC5FC", "#FFC2C4", "#F2D140", "#BCC6C8"][:number_of_colors]
+    node_colors = []
+    for node in graph:
+        current_community_index = 0
+        for community in communities:
+            if node in community:
+                node_colors.append(colors[current_community_index])
+                break
+            current_community_index += 1
+    return node_colors
+
+
+# function to plot graph with node colouring based on communities
+def visualize_communities(graph, communities, i):
+    node_colors = create_community_node_colors(graph, communities)
+    modularity = round(nx.community.modularity(graph, communities), 6)
+    title = f"Community Visualization of {len(communities)} communities with modularity of {modularity}"
+    pos = nx.spring_layout(graph, k=0.3, iterations=50, seed=2)
+    plt.subplot(3, 1, i)
+    plt.title(title)
+    nx.draw(
+        graph,
+        pos=pos,
+        node_size=1000,
+        node_color=node_colors,
+        with_labels=True,
+        font_size=20,
+        font_color="black",
+    )
+
+
+fig, ax = plt.subplots(3, figsize=(15, 20))
+
+# Plot graph with colouring based on communities
+visualize_communities(G, communities[0], 1)
+visualize_communities(G, communities[3], 2)
+
+# Plot change in modularity as the important edges are removed
+modularity_df.plot.bar(
+    x="k",
+    ax=ax[2],
+    color="#F2D140",
+    title="Modularity Trend for Girvan-Newman Community Detection",
+)
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_iterated_dynamical_systems.py

@@ -0,0 +1,210 @@
+"""
+==========================
+Iterated Dynamical Systems
+==========================
+
+Digraphs from Integer-valued Iterated Functions
+
+Sums of cubes on 3N
+-------------------
+
+The number 153 has a curious property.
+
+Let 3N={3,6,9,12,...} be the set of positive multiples of 3.  Define an
+iterative process f:3N->3N as follows: for a given n, take each digit
+of n (in base 10), cube it and then sum the cubes to obtain f(n).
+
+When this process is repeated, the resulting series n, f(n), f(f(n)),...
+terminate in 153 after a finite number of iterations (the process ends
+because 153 = 1**3 + 5**3 + 3**3).
+
+In the language of discrete dynamical systems, 153 is the global
+attractor for the iterated map f restricted to the set 3N.
+
+For example: take the number 108
+
+f(108) = 1**3 + 0**3 + 8**3 = 513
+
+and
+
+f(513) = 5**3 + 1**3 + 3**3 = 153
+
+So, starting at 108 we reach 153 in two iterations,
+represented as:
+
+108->513->153
+
+Computing all orbits of 3N up to 10**5 reveals that the attractor
+153 is reached in a maximum of 14 iterations. In this code we
+show that 13 cycles is the maximum required for all integers (in 3N)
+less than 10,000.
+
+The smallest number that requires 13 iterations to reach 153, is 177, i.e.,
+
+177->687->1071->345->216->225->141->66->432->99->1458->702->351->153
+
+The resulting large digraphs are useful for testing network software.
+
+The general problem
+-------------------
+
+Given numbers n, a power p and base b, define F(n; p, b) as the sum of
+the digits of n (in base b) raised to the power p. The above example
+corresponds to f(n)=F(n; 3,10), and below F(n; p, b) is implemented as
+the function powersum(n,p,b). The iterative dynamical system defined by
+the mapping n:->f(n) above (over 3N) converges to a single fixed point;
+153. Applying the map to all positive integers N, leads to a discrete
+dynamical process with 5 fixed points: 1, 153, 370, 371, 407. Modulo 3
+those numbers are 1, 0, 1, 2, 2. The function f above has the added
+property that it maps a multiple of 3 to another multiple of 3; i.e. it
+is invariant on the subset 3N.
+
+
+The squaring of digits (in base 10) result in cycles and the
+single fixed point 1. I.e., from a certain point on, the process
+starts repeating itself.
+
+keywords: "Recurring Digital Invariant", "Narcissistic Number",
+"Happy Number"
+
+The 3n+1 problem
+----------------
+
+There is a rich history of mathematical recreations
+associated with discrete dynamical systems.  The most famous
+is the Collatz 3n+1 problem. See the function
+collatz_problem_digraph below. The Collatz conjecture
+--- that every orbit returns to the fixed point 1 in finite time
+--- is still unproven. Even the great Paul Erdos said "Mathematics
+is not yet ready for such problems", and offered $500
+for its solution.
+
+keywords: "3n+1", "3x+1", "Collatz problem", "Thwaite's conjecture"
+"""
+
+import networkx as nx
+
+nmax = 10000
+p = 3
+
+
+def digitsrep(n, b=10):
+    """Return list of digits comprising n represented in base b.
+    n must be a nonnegative integer"""
+
+    if n <= 0:
+        return [0]
+
+    dlist = []
+    while n > 0:
+        # Prepend next least-significant digit
+        dlist = [n % b] + dlist
+        # Floor-division
+        n = n // b
+    return dlist
+
+
+def powersum(n, p, b=10):
+    """Return sum of digits of n (in base b) raised to the power p."""
+    dlist = digitsrep(n, b)
+    sum = 0
+    for k in dlist:
+        sum += k**p
+    return sum
+
+
+def attractor153_graph(n, p, multiple=3, b=10):
+    """Return digraph of iterations of powersum(n,3,10)."""
+    G = nx.DiGraph()
+    for k in range(1, n + 1):
+        if k % multiple == 0 and k not in G:
+            k1 = k
+            knext = powersum(k1, p, b)
+            while k1 != knext:
+                G.add_edge(k1, knext)
+                k1 = knext
+                knext = powersum(k1, p, b)
+    return G
+
+
+def squaring_cycle_graph_old(n, b=10):
+    """Return digraph of iterations of powersum(n,2,10)."""
+    G = nx.DiGraph()
+    for k in range(1, n + 1):
+        k1 = k
+        G.add_node(k1)  # case k1==knext, at least add node
+        knext = powersum(k1, 2, b)
+        G.add_edge(k1, knext)
+        while k1 != knext:  # stop if fixed point
+            k1 = knext
+            knext = powersum(k1, 2, b)
+            G.add_edge(k1, knext)
+            if G.out_degree(knext) >= 1:
+                # knext has already been iterated in and out
+                break
+    return G
+
+
+def sum_of_digits_graph(nmax, b=10):
+    def f(n):
+        return powersum(n, 1, b)
+
+    return discrete_dynamics_digraph(nmax, f)
+
+
+def squaring_cycle_digraph(nmax, b=10):
+    def f(n):
+        return powersum(n, 2, b)
+
+    return discrete_dynamics_digraph(nmax, f)
+
+
+def cubing_153_digraph(nmax):
+    def f(n):
+        return powersum(n, 3, 10)
+
+    return discrete_dynamics_digraph(nmax, f)
+
+
+def discrete_dynamics_digraph(nmax, f, itermax=50000):
+    G = nx.DiGraph()
+    for k in range(1, nmax + 1):
+        kold = k
+        G.add_node(kold)
+        knew = f(kold)
+        G.add_edge(kold, knew)
+        while kold != knew and kold << itermax:
+            # iterate until fixed point reached or itermax is exceeded
+            kold = knew
+            knew = f(kold)
+            G.add_edge(kold, knew)
+            if G.out_degree(knew) >= 1:
+                # knew has already been iterated in and out
+                break
+    return G
+
+
+def collatz_problem_digraph(nmax):
+    def f(n):
+        if n % 2 == 0:
+            return n // 2
+        else:
+            return 3 * n + 1
+
+    return discrete_dynamics_digraph(nmax, f)
+
+
+def fixed_points(G):
+    """Return a list of fixed points for the discrete dynamical
+    system represented by the digraph G.
+    """
+    return [n for n in G if G.out_degree(n) == 0]
+
+
+nmax = 10000
+print(f"Building cubing_153_digraph({nmax})")
+G = cubing_153_digraph(nmax)
+print("Resulting digraph has", len(G), "nodes and", G.size(), " edges")
+print("Shortest path from 177 to 153 is:")
+print(nx.shortest_path(G, 177, 153))
+print(f"fixed points are {fixed_points(G)}")

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_krackhardt_centrality.py

@@ -0,0 +1,31 @@
+"""
+=====================
+Krackhardt Centrality
+=====================
+
+Centrality measures of Krackhardt social network.
+"""
+
+import matplotlib.pyplot as plt
+import networkx as nx
+
+G = nx.krackhardt_kite_graph()
+
+print("Betweenness")
+b = nx.betweenness_centrality(G)
+for v in G.nodes():
+    print(f"{v:2} {b[v]:.3f}")
+
+print("Degree centrality")
+d = nx.degree_centrality(G)
+for v in G.nodes():
+    print(f"{v:2} {d[v]:.3f}")
+
+print("Closeness centrality")
+c = nx.closeness_centrality(G)
+for v in G.nodes():
+    print(f"{v:2} {c[v]:.3f}")
+
+pos = nx.spring_layout(G, seed=367)  # Seed layout for reproducibility
+nx.draw(G, pos)
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_maximum_independent_set.py

@@ -0,0 +1,44 @@
+"""
+=======================
+Maximum Independent Set
+=======================
+
+An independent set is a set of vertices in a graph where no two vertices in the
+set are adjacent. The maximum independent set is the independent set of largest
+possible size for a given graph.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+import networkx as nx
+from networkx.algorithms import approximation as approx
+
+G = nx.Graph(
+    [
+        (1, 2),
+        (7, 2),
+        (3, 9),
+        (3, 2),
+        (7, 6),
+        (5, 2),
+        (1, 5),
+        (2, 8),
+        (10, 2),
+        (1, 7),
+        (6, 1),
+        (6, 9),
+        (8, 4),
+        (9, 4),
+    ]
+)
+
+I = approx.maximum_independent_set(G)
+print(f"Maximum independent set of G: {I}")
+
+pos = nx.spring_layout(G, seed=39299899)
+nx.draw(
+    G,
+    pos=pos,
+    with_labels=True,
+    node_color=["tab:red" if n in I else "tab:blue" for n in G],
+)

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_parallel_betweenness.py

@@ -0,0 +1,82 @@
+"""
+====================
+Parallel Betweenness
+====================
+
+Example of parallel implementation of betweenness centrality using the
+multiprocessing module from Python Standard Library.
+
+The function betweenness centrality accepts a bunch of nodes and computes
+the contribution of those nodes to the betweenness centrality of the whole
+network. Here we divide the network in chunks of nodes and we compute their
+contribution to the betweenness centrality of the whole network.
+
+Note: The example output below shows that the non-parallel implementation is
+faster. This is a limitation of our CI/CD pipeline running on a single core.
+
+Depending on your setup, you will likely observe a speedup.
+"""
+from multiprocessing import Pool
+import time
+import itertools
+
+import matplotlib.pyplot as plt
+import networkx as nx
+
+
+def chunks(l, n):
+    """Divide a list of nodes `l` in `n` chunks"""
+    l_c = iter(l)
+    while 1:
+        x = tuple(itertools.islice(l_c, n))
+        if not x:
+            return
+        yield x
+
+
+def betweenness_centrality_parallel(G, processes=None):
+    """Parallel betweenness centrality  function"""
+    p = Pool(processes=processes)
+    node_divisor = len(p._pool) * 4
+    node_chunks = list(chunks(G.nodes(), G.order() // node_divisor))
+    num_chunks = len(node_chunks)
+    bt_sc = p.starmap(
+        nx.betweenness_centrality_subset,
+        zip(
+            [G] * num_chunks,
+            node_chunks,
+            [list(G)] * num_chunks,
+            [True] * num_chunks,
+            [None] * num_chunks,
+        ),
+    )
+
+    # Reduce the partial solutions
+    bt_c = bt_sc[0]
+    for bt in bt_sc[1:]:
+        for n in bt:
+            bt_c[n] += bt[n]
+    return bt_c
+
+
+G_ba = nx.barabasi_albert_graph(1000, 3)
+G_er = nx.gnp_random_graph(1000, 0.01)
+G_ws = nx.connected_watts_strogatz_graph(1000, 4, 0.1)
+for G in [G_ba, G_er, G_ws]:
+    print("")
+    print("Computing betweenness centrality for:")
+    print(G)
+    print("\tParallel version")
+    start = time.time()
+    bt = betweenness_centrality_parallel(G)
+    print(f"\t\tTime: {(time.time() - start):.4F} seconds")
+    print(f"\t\tBetweenness centrality for node 0: {bt[0]:.5f}")
+    print("\tNon-Parallel version")
+    start = time.time()
+    bt = nx.betweenness_centrality(G)
+    print(f"\t\tTime: {(time.time() - start):.4F} seconds")
+    print(f"\t\tBetweenness centrality for node 0: {bt[0]:.5f}")
+print("")
+
+nx.draw(G_ba, node_size=100)
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_rcm.py

@@ -0,0 +1,40 @@
+"""
+======================
+Reverse Cuthill--McKee
+======================
+
+Cuthill-McKee ordering of matrices
+
+The reverse Cuthill--McKee algorithm gives a sparse matrix ordering that
+reduces the matrix bandwidth.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+import seaborn as sns
+import networkx as nx
+
+
+# build low-bandwidth matrix
+G = nx.grid_2d_graph(3, 3)
+rcm = list(nx.utils.reverse_cuthill_mckee_ordering(G))
+print("ordering", rcm)
+
+print("unordered Laplacian matrix")
+A = nx.laplacian_matrix(G)
+x, y = np.nonzero(A)
+# print(f"lower bandwidth: {(y - x).max()}")
+# print(f"upper bandwidth: {(x - y).max()}")
+print(f"bandwidth: {(y - x).max() + (x - y).max() + 1}")
+print(A)
+
+B = nx.laplacian_matrix(G, nodelist=rcm)
+print("low-bandwidth Laplacian matrix")
+x, y = np.nonzero(B)
+# print(f"lower bandwidth: {(y - x).max()}")
+# print(f"upper bandwidth: {(x - y).max()}")
+print(f"bandwidth: {(y - x).max() + (x - y).max() + 1}")
+print(B)
+
+sns.heatmap(B.todense(), cbar=False, square=True, linewidths=0.5, annot=True)
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_snap.py

@@ -0,0 +1,108 @@
+"""
+==================
+SNAP Graph Summary
+==================
+An example of summarizing a graph based on node attributes and edge attributes
+using the Summarization by Grouping Nodes on Attributes and Pairwise
+edges (SNAP) algorithm (not to be confused with the Stanford Network
+Analysis Project).  The algorithm groups nodes by their unique
+combinations of node attribute values and edge types with other groups
+of nodes to produce a summary graph.  The summary graph can then be used to
+infer how nodes with different attributes values relate to other nodes in the
+graph.
+"""
+import networkx as nx
+import matplotlib.pyplot as plt
+
+
+nodes = {
+    "A": {"color": "Red"},
+    "B": {"color": "Red"},
+    "C": {"color": "Red"},
+    "D": {"color": "Red"},
+    "E": {"color": "Blue"},
+    "F": {"color": "Blue"},
+    "G": {"color": "Blue"},
+    "H": {"color": "Blue"},
+    "I": {"color": "Yellow"},
+    "J": {"color": "Yellow"},
+    "K": {"color": "Yellow"},
+    "L": {"color": "Yellow"},
+}
+edges = [
+    ("A", "B", "Strong"),
+    ("A", "C", "Weak"),
+    ("A", "E", "Strong"),
+    ("A", "I", "Weak"),
+    ("B", "D", "Weak"),
+    ("B", "J", "Weak"),
+    ("B", "F", "Strong"),
+    ("C", "G", "Weak"),
+    ("D", "H", "Weak"),
+    ("I", "J", "Strong"),
+    ("J", "K", "Strong"),
+    ("I", "L", "Strong"),
+]
+original_graph = nx.Graph()
+original_graph.add_nodes_from(n for n in nodes.items())
+original_graph.add_edges_from((u, v, {"type": label}) for u, v, label in edges)
+
+
+plt.suptitle("SNAP Summarization")
+
+base_options = {"with_labels": True, "edgecolors": "black", "node_size": 500}
+
+ax1 = plt.subplot(1, 2, 1)
+plt.title(
+    "Original (%s nodes, %s edges)"
+    % (original_graph.number_of_nodes(), original_graph.number_of_edges())
+)
+pos = nx.spring_layout(original_graph, seed=7482934)
+node_colors = [d["color"] for _, d in original_graph.nodes(data=True)]
+
+edge_type_visual_weight_lookup = {"Weak": 1.0, "Strong": 3.0}
+edge_weights = [
+    edge_type_visual_weight_lookup[d["type"]]
+    for _, _, d in original_graph.edges(data=True)
+]
+
+nx.draw_networkx(
+    original_graph, pos=pos, node_color=node_colors, width=edge_weights, **base_options
+)
+
+node_attributes = ("color",)
+edge_attributes = ("type",)
+summary_graph = nx.snap_aggregation(
+    original_graph, node_attributes, edge_attributes, prefix="S-"
+)
+
+plt.subplot(1, 2, 2)
+
+plt.title(
+    "SNAP Aggregation (%s nodes, %s edges)"
+    % (summary_graph.number_of_nodes(), summary_graph.number_of_edges())
+)
+summary_pos = nx.spring_layout(summary_graph, seed=8375428)
+node_colors = []
+for node in summary_graph:
+    color = summary_graph.nodes[node]["color"]
+    node_colors.append(color)
+
+edge_weights = []
+for edge in summary_graph.edges():
+    edge_types = summary_graph.get_edge_data(*edge)["types"]
+    edge_weight = 0.0
+    for edge_type in edge_types:
+        edge_weight += edge_type_visual_weight_lookup[edge_type["type"]]
+    edge_weights.append(edge_weight)
+
+nx.draw_networkx(
+    summary_graph,
+    pos=summary_pos,
+    node_color=node_colors,
+    width=edge_weights,
+    **base_options,
+)
+
+plt.tight_layout()
+plt.show()

.CondaPkg/env/share/doc/networkx-3.1/examples/algorithms/plot_subgraphs.py

@@ -0,0 +1,170 @@
+"""
+=========
+Subgraphs
+=========
+Example of partitioning a directed graph with nodes labeled as
+supported and unsupported nodes into a list of subgraphs
+that contain only entirely supported or entirely unsupported nodes.
+Adopted from 
+https://github.com/lobpcg/python_examples/blob/master/networkx_example.py
+"""
+
+import networkx as nx
+import matplotlib.pyplot as plt
+
+
+def graph_partitioning(G, plotting=True):
+    """Partition a directed graph into a list of subgraphs that contain
+    only entirely supported or entirely unsupported nodes.
+    """
+    # Categorize nodes by their node_type attribute
+    supported_nodes = {n for n, d in G.nodes(data="node_type") if d == "supported"}
+    unsupported_nodes = {n for n, d in G.nodes(data="node_type") if d == "unsupported"}
+
+    # Make a copy of the graph.
+    H = G.copy()
+    # Remove all edges connecting supported and unsupported nodes.
+    H.remove_edges_from(
+        (n, nbr, d)
+        for n, nbrs in G.adj.items()
+        if n in supported_nodes
+        for nbr, d in nbrs.items()
+        if nbr in unsupported_nodes
+    )
+    H.remove_edges_from(
+        (n, nbr, d)
+        for n, nbrs in G.adj.items()
+        if n in unsupported_nodes
+        for nbr, d in nbrs.items()
+        if nbr in supported_nodes
+    )
+
+    # Collect all removed edges for reconstruction.
+    G_minus_H = nx.DiGraph()
+    G_minus_H.add_edges_from(set(G.edges) - set(H.edges))
+
+    if plotting:
+        # Plot the stripped graph with the edges removed.
+        _node_colors = [c for _, c in H.nodes(data="node_color")]
+        _pos = nx.spring_layout(H)
+        plt.figure(figsize=(8, 8))
+        nx.draw_networkx_edges(H, _pos, alpha=0.3, edge_color="k")
+        nx.draw_networkx_nodes(H, _pos, node_color=_node_colors)
+        nx.draw_networkx_labels(H, _pos, font_size=14)
+        plt.axis("off")
+        plt.title("The stripped graph with the edges removed.")
+        plt.show()
+        # Plot the the edges removed.
+        _pos = nx.spring_layout(G_minus_H)
+        plt.figure(figsize=(8, 8))
+        ncl = [G.nodes[n]["node_color"] for n in G_minus_H.nodes]
+        nx.draw_networkx_edges(G_minus_H, _pos, alpha=0.3, edge_color="k")
+        nx.draw_networkx_nodes(G_minus_H, _pos, node_color=ncl)
+        nx.draw_networkx_labels(G_minus_H, _pos, font_size=14)
+        plt.axis("off")
+        plt.title("The removed edges.")
+        plt.show()
+
+    # Find the connected components in the stripped undirected graph.
+    # And use the sets, specifying the components, to partition
+    # the original directed graph into a list of directed subgraphs
+    # that contain only entirely supported or entirely unsupported nodes.
+    subgraphs = [
+        H.subgraph(c).copy() for c in nx.connected_components(H.to_undirected())
+    ]
+
+    return subgraphs, G_minus_H
+
+
+###############################################################################
+# Create an example directed graph.
+# ---------------------------------
+#
+# This directed graph has one input node labeled `in` and plotted in blue color
+# and one output node labeled `out` and plotted in magenta color.
+# The other six nodes are classified as four `supported` plotted in green color
+# and two `unsupported` plotted in red color. The goal is computing a list
+# of subgraphs that contain only entirely `supported` or `unsupported` nodes.
+G_ex = nx.DiGraph()
+G_ex.add_nodes_from(["In"], node_type="input", node_color="b")
+G_ex.add_nodes_from(["A", "C", "E", "F"], node_type="supported", node_color="g")
+G_ex.add_nodes_from(["B", "D"], node_type="unsupported", node_color="r")
+G_ex.add_nodes_from(["Out"], node_type="output", node_color="m")
+G_ex.add_edges_from(
+    [
+        ("In", "A"),
+        ("A", "B"),
+        ("B", "C"),
+        ("B", "D"),
+        ("D", "E"),
+        ("C", "F"),
+        ("E", "F"),
+        ("F", "Out"),
+    ]
+)
+
+###############################################################################
+# Plot the original graph.
+# ------------------------
+#
+node_color_list = [nc for _, nc in G_ex.nodes(data="node_color")]
+pos = nx.spectral_layout(G_ex)
+plt.figure(figsize=(8, 8))
+nx.draw_networkx_edges(G_ex, pos, alpha=0.3, edge_color="k")
+nx.draw_networkx_nodes(G_ex, pos, alpha=0.8, node_color=node_color_list)
+nx.draw_networkx_labels(G_ex, pos, font_size=14)
+plt.axis("off")
+plt.title("The original graph.")
+plt.show()
+
+###############################################################################
+# Calculate the subgraphs with plotting all results of intemediate steps.
+# -----------------------------------------------------------------------
+#
+subgraphs_of_G_ex, removed_edges = graph_partitioning(G_ex, plotting=True)
+
+###############################################################################
+# Plot the results: every subgraph in the list.
+# ---------------------------------------------
+#
+for subgraph in subgraphs_of_G_ex:
+    _pos = nx.spring_layout(subgraph)
+    plt.figure(figsize=(8, 8))
+    nx.draw_networkx_edges(subgraph, _pos, alpha=0.3, edge_color="k")
+    node_color_list_c = [nc for _, nc in subgraph.nodes(data="node_color")]
+    nx.draw_networkx_nodes(subgraph, _pos, node_color=node_color_list_c)
+    nx.draw_networkx_labels(subgraph, _pos, font_size=14)
+    plt.axis("off")
+    plt.title("One of the subgraphs.")
+    plt.show()
+
+###############################################################################
+# Put the graph back from the list of subgraphs
+# ---------------------------------------------
+#
+G_ex_r = nx.DiGraph()
+# Composing all subgraphs.
+for subgraph in subgraphs_of_G_ex:
+    G_ex_r = nx.compose(G_ex_r, subgraph)
+# Adding the previously stored edges.
+G_ex_r.add_edges_from(removed_edges.edges())
+
+###############################################################################
+# Check that the original graph and the reconstructed graphs are isomorphic.
+# --------------------------------------------------------------------------
+#
+assert nx.is_isomorphic(G_ex, G_ex_r)
+
+###############################################################################
+# Plot the reconstructed graph.
+# -----------------------------
+#
+node_color_list = [nc for _, nc in G_ex_r.nodes(data="node_color")]
+pos = nx.spectral_layout(G_ex_r)
+plt.figure(figsize=(8, 8))
+nx.draw_networkx_edges(G_ex_r, pos, alpha=0.3, edge_color="k")
+nx.draw_networkx_nodes(G_ex_r, pos, alpha=0.8, node_color=node_color_list)
+nx.draw_networkx_labels(G_ex_r, pos, font_size=14)
+plt.axis("off")
+plt.title("The reconstructed graph.")
+plt.show()