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@@ -16029,7 +16028,7 @@ Wie können wir aus den 7 Fröschen fair einen auswählen?
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-In [6]:
+In [32]:
from numpy import array
@@ -16013,7 +16013,6 @@ Wie können wir aus den 7 Fröschen fair einen auswählen?
])
v = array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ])
v @ M
-# v @ matrix_power(M, 3*1)
-
Out[6]:
+ Out[32]:
@@ -16066,101 +16065,6 @@ Wie können wir aus den 7 Fröschen fair einen auswählen?
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-$$
-\begin{align*}
-X_1 &= X_0 \cdot{} M \\
-X_2 &= X_1 \cdot{} M = (X_0 \cdot M) \cdot{} M = X_0 \cdot M^2 \\
-& \vdots \\
-X_n &= X_0 \cdot \underbrace{M \cdot{} \dots \cdot M}_{\text{$n$ mal}} = X_0 \cdot M^n
-\end{align*}
-$$
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-In [7]:
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-import matplotlib as mpl
-import matplotlib.pyplot as plt
-import networkx as nx
-
-seed = 13649 # Seed random number generators for reproducibility
-G = nx.random_k_out_graph(10, 3, 0.5, seed=seed)
-pos = nx.spring_layout(G, seed=seed)
-
-node_sizes = [3 + 10 * i for i in range(len(G))]
-M = G.number_of_edges()
-edge_colors = range(2, M + 2)
-edge_alphas = [(5 + i) / (M + 4) for i in range(M)]
-cmap = plt.cm.plasma
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-nodes = nx.draw_networkx_nodes(G, pos, node_size=node_sizes, node_color="indigo")
-edges = nx.draw_networkx_edges(
- G,
- pos,
- node_size=node_sizes,
- arrowstyle="->",
- arrowsize=10,
- edge_color=edge_colors,
- edge_cmap=cmap,
- width=2,
-)
-# set alpha value for each edge
-for i in range(M):
- edges[i].set_alpha(edge_alphas[i])
-
-pc = mpl.collections.PatchCollection(edges, cmap=cmap)
-pc.set_array(edge_colors)
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-ax = plt.gca()
-ax.set_axis_off()
-plt.colorbar(pc, ax=ax)
-plt.show()
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