Eigenvalues

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

Largest eigenvalue: (1.5924617911775951+0j)
Smallest eigenvalue: (2.0362257212593771e-16+0j)
/usr/lib64/python3.15/site-packages/matplotlib/cbook.py:1719: ComplexWarning: Casting complex values to real discards the imaginary part
  return math.isfinite(val)
/usr/lib64/python3.15/site-packages/numpy/lib/_histograms_impl.py:853: ComplexWarning: Casting complex values to real discards the imaginary part
  indices = f_indices.astype(np.intp)
/usr/lib64/python3.15/site-packages/matplotlib/axes/_axes.py:7135: ComplexWarning: Casting complex values to real discards the imaginary part
  bins = np.array(bins, float)  # causes problems if float16

import matplotlib.pyplot as plt
import networkx as nx
import numpy as np

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 = np.linalg.eigvals(L.toarray())
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()