"""
.. _tutorials-random:

=================
Erdős-Rényi Graph
=================

This example demonstrates how to generate `Erdős–Rényi graphs <https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model>`_ using :meth:`igraph.GraphBase.Erdos_Renyi`. There are two variants of graphs:

- ``Erdos_Renyi(n, p)`` will generate a graph from the so-called :math:`G(n,p)` model 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. This is referred to as the :math:`G(n,m)` model.

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

# %%
# First, we set a random seed for reproducibility
random.seed(0)

# %%
# Then, we generate two :math:`G(n,p)` Erdős–Rényi graphs with identical parameters:
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)

# %%
# For comparison, we also generate two :math:`G(n,m)` Erdős–Rényi graphs with a fixed 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)

# %%
# We can print out summaries of each graph to verify their randomness
ig.summary(g1)
ig.summary(g2)
ig.summary(g3)
ig.summary(g4)

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

# %%
# Finally, we can plot the graphs to illustrate their structures and
# differences:
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=15
)
ig.plot(
    g4,
    target=axs[1, 1],
    layout="circle",
    vertex_color="lightblue",
    vertex_size=15
)
axs[1, 0].set_ylabel('N. edges')
plt.show()