python-igraph Manual

For using igraph from Python

Erdős-Rényi Graph¶

This example demonstrates how to generate Erdős-Rényi Graphs using `Erdos_Renyi()`. There are two variants of graphs:

• `Erdos_Renyi(n, p)` will generate a graph where each edge between any two pair of nodes has an independent probability `p` of existing.

• `Erdos_Renyi(n, m)` will pick a graph uniformly at random out of all graphs with `n` nodes and `m` edges.

We generate two graphs of each, so we can confirm that our graph generator is truly random.

```import igraph as ig
import matplotlib.pyplot as plt
import random

# Set a random seed for reproducibility
random.seed(0)

# Generate two Erdos Renyi graphs based on probability
g1 = ig.Graph.Erdos_Renyi(n=15, p=0.2, directed=False, loops=False)
g2 = ig.Graph.Erdos_Renyi(n=15, p=0.2, directed=False, loops=False)

# Generate two Erdos Renyi graphs based on number of edges
g3 = ig.Graph.Erdos_Renyi(n=20, m=35, directed=False, loops=False)
g4 = ig.Graph.Erdos_Renyi(n=20, m=35, directed=False, loops=False)

# Print out summaries of each graph
ig.summary(g1)
ig.summary(g2)
ig.summary(g3)
ig.summary(g4)

fig, axs = plt.subplots(2, 2)
# Probability
ig.plot(
g1,
target=axs[0, 0],
layout="circle",
vertex_color="lightblue"
)
ig.plot(
g2,
target=axs[0, 1],
layout="circle",
vertex_color="lightblue"
)
axs[0, 0].set_ylabel('Probability')
# N edges
ig.plot(
g3,
target=axs[1, 0],
layout="circle",
vertex_color="lightblue",
vertex_size=0.15
)
ig.plot(
g4,
target=axs[1, 1],
layout="circle",
vertex_color="lightblue",
vertex_size=0.15
)
axs[1, 0].set_ylabel('N. edges')
plt.show()
```

The received output is:

```IGRAPH U--- 15 18 --
IGRAPH U--- 15 21 --
IGRAPH U--- 20 35 --
IGRAPH U--- 20 35 --
```

Note

Even when using the same random seed, results can still differ depending on the machine the code is being run from.