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# Eigenvalues

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

    Largest eigenvalue: 1.5924617911775936
    Smallest eigenvalue: 7.27024810414381e-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.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()

Total running time of the script: (0 minutes 1.944 seconds)

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