Module spectrum

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Laplacian, adjacency matrix, and spectrum of graphs.

Needs numpy array package: numpy.scipy.org.

Author: Aric Hagberg (hagberg@lanl.gov) Pieter Swart (swart@lanl.gov) Dan Schult(dschult@colgate.edu)

Functions

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adj_matrix(G, nodelist=None)
Return adjacency matrix of graph as a numpy matrix.

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laplacian(G, nodelist=None)
Return standard combinatorial Laplacian of G as a numpy matrix.

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normalized_laplacian(G, nodelist=None)
Return normalized Laplacian of G as a numpy matrix.

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laplacian_spectrum(G)
Return eigenvalues of the Laplacian of G

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adjacency_spectrum(G)
Return eigenvalues of the adjacency matrix of G

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combinatorial_laplacian(G, nodelist=None)
Return standard combinatorial Laplacian of G as a numpy matrix.

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generalized_laplacian(G, nodelist=None)
Return normalized Laplacian of G as a numpy matrix.

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_test_suite()

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Function Details

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adj_matrix(G, nodelist=None)

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Return adjacency matrix of graph as a numpy matrix.

This just calls networkx.convert.to_numpy_matrix.

If you want a pure python adjacency matrix represntation try networkx.convert.to_dict_of_dicts with weighted=False, which will return a dictionary-of-dictionaries format that can be addressed as a sparse matrix.

laplacian(G, nodelist=None)

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Return standard combinatorial Laplacian of G as a numpy matrix.

Return the matrix L = D - A, where

D is the diagonal matrix in which the i'th entry is the degree of node i A is the adjacency matrix.

normalized_laplacian(G, nodelist=None)

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Return normalized Laplacian of G as a numpy matrix.

See Spectral Graph Theory by Fan Chung-Graham. CBMS Regional Conference Series in Mathematics, Number 92, 1997.

combinatorial_laplacian(G, nodelist=None)

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Return standard combinatorial Laplacian of G as a numpy matrix.

Return the matrix L = D - A, where

D is the diagonal matrix in which the i'th entry is the degree of node i A is the adjacency matrix.

generalized_laplacian(G, nodelist=None)

source code

Return normalized Laplacian of G as a numpy matrix.

See Spectral Graph Theory by Fan Chung-Graham. CBMS Regional Conference Series in Mathematics, Number 92, 1997.