Fixed database typo and removed unnecessary class identifier.

venv/share/doc/networkx-2.5/examples/advanced/README.txt

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+Advanced
+--------

venv/share/doc/networkx-2.5/examples/advanced/plot_eigenvalues.py

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+"""
+===========
+Eigenvalues
+===========
+
+Create an G{n,m} random graph and compute the eigenvalues.
+"""
+import matplotlib.pyplot as plt
+import networkx as nx
+import numpy.linalg
+
+n = 1000  # 1000 nodes
+m = 5000  # 5000 edges
+G = nx.gnm_random_graph(n, m)
+
+L = nx.normalized_laplacian_matrix(G)
+e = numpy.linalg.eigvals(L.A)
+print("Largest eigenvalue:", max(e))
+print("Smallest eigenvalue:", min(e))
+plt.hist(e, bins=100)  # histogram with 100 bins
+plt.xlim(0, 2)  # eigenvalues between 0 and 2
+plt.show()

venv/share/doc/networkx-2.5/examples/advanced/plot_heavy_metal_umlaut.py

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+"""
+==================
+Heavy Metal Umlaut
+==================
+
+Example using unicode strings as graph labels.
+
+Also shows creative use of the Heavy Metal Umlaut:
+https://en.wikipedia.org/wiki/Heavy_metal_umlaut
+"""
+
+import matplotlib.pyplot as plt
+import networkx as nx
+
+hd = "H" + chr(252) + "sker D" + chr(252)
+mh = "Mot" + chr(246) + "rhead"
+mc = "M" + chr(246) + "tley Cr" + chr(252) + "e"
+st = "Sp" + chr(305) + "n" + chr(776) + "al Tap"
+q = "Queensr" + chr(255) + "che"
+boc = "Blue " + chr(214) + "yster Cult"
+dt = "Deatht" + chr(246) + "ngue"
+
+G = nx.Graph()
+G.add_edge(hd, mh)
+G.add_edge(mc, st)
+G.add_edge(boc, mc)
+G.add_edge(boc, dt)
+G.add_edge(st, dt)
+G.add_edge(q, st)
+G.add_edge(dt, mh)
+G.add_edge(st, mh)
+
+# write in UTF-8 encoding
+fh = open("edgelist.utf-8", "wb")
+nx.write_multiline_adjlist(G, fh, delimiter="\t", encoding="utf-8")
+
+# read and store in UTF-8
+fh = open("edgelist.utf-8", "rb")
+H = nx.read_multiline_adjlist(fh, delimiter="\t", encoding="utf-8")
+
+for n in G.nodes():
+    if n not in H:
+        print(False)
+
+print(list(G.nodes()))
+
+pos = nx.spring_layout(G)
+nx.draw(G, pos, font_size=16, with_labels=False)
+for p in pos:  # raise text positions
+    pos[p][1] += 0.07
+nx.draw_networkx_labels(G, pos)
+plt.show()

venv/share/doc/networkx-2.5/examples/advanced/plot_iterated_dynamical_systems.py

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+"""
+==========================
+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)}")

venv/share/doc/networkx-2.5/examples/advanced/plot_parallel_betweenness.py

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+"""
+====================
+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.
+"""
+
+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(), int(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(nx.info(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()