Eigenvalues

Create an G{n,m} random graph and compute the eigenvalues.

Out:

<class 'networkx.utils.decorators.argmap'> compilation 66:4: FutureWarning: normalized_laplacian_matrix will return a scipy.sparse array instead of a matrix in Networkx 3.0.
Largest eigenvalue: 1.5924617911776004
Smallest eigenvalue: -3.7052457897388446e-16

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, seed=5040)  # Seed for reproducibility

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()