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Daniel Precioso
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Remove unusual characters from models
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modules/networks/models.qmd

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@@ -68,7 +68,7 @@ def plot_degree_histogram(G, title="Degree distribution"):
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plt.show()
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```
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## Random graphs (Erdős–Rényi / Gilbert)
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## Random graphs (Erdos–Rényi / Gilbert)
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In the **Gilbert** model $G(N, p)$, we consider every possible pair of nodes and include the edge independently with probability $p$.
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@@ -90,7 +90,7 @@ G_random = nx.erdos_renyi_graph(n=80, p=0.06, seed=SEED)
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pos = nx.spring_layout(G_random, seed=SEED)
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nx.draw(G_random, pos=pos, node_size=120, node_color="lightgray", edge_color="gray")
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plt.title("Erdős–Rényi random graph")
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plt.title("Erdos–Rényi random graph")
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plt.show()
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summarize_graph(G_random, name="Random (G(N,p))")
@@ -121,7 +121,7 @@ Watts–Strogatz networks start from a **ring lattice** (high clustering, long p
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Key properties:
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- For small $p$ (e.g. $p \in [0.01, 0.2]$), you often get **high clustering** *and* **short path lengths** (small-world).
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- For small $p$ (e.g. $p \in [0.01, 0.2]$), you often get **high clustering** *and* **short path lengths** ("small-world").
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- Degree distribution stays relatively **narrow** (most nodes have degree near $k$).
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In NetworkX:
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Key properties (typical):
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- Degree distribution is heavy-tailed (often summarized as scale-free).
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- Degree distribution is heavy-tailed (often summarized as "scale-free").
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- Small average path length (hubs create shortcuts).
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- Clustering is usually lower than small-world models (but there are variants that increase clustering).
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@@ -185,9 +185,9 @@ plot_degree_histogram(G_sf, title="Scale-free: degree distribution")
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```
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::: {.callout-tip collapse="true"}
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## Scale-free in NetworkX
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## "Scale-free" in NetworkX
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The BA model is the most common introduction to scale-free networks.
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The BA model is the most common introduction to "scale-free" networks.
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NetworkX also provides other generators (some return directed multigraphs), for example:
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- `nx.scale_free_graph(n, seed=...)`

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