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spectral_ordering(G, weight='weight', normalized=False, tol=1e-08, method='tracemin_pcg', seed=None)[source]

Compute the spectral_ordering of a graph.

The spectral ordering of a graph is an ordering of its nodes where nodes in the same weakly connected components appear contiguous and ordered by their corresponding elements in the Fiedler vector of the component.

  • G (NetworkX graph) – A graph.

  • weight (object, optional (default: None)) – The data key used to determine the weight of each edge. If None, then each edge has unit weight.

  • normalized (bool, optional (default: False)) – Whether the normalized Laplacian matrix is used.

  • tol (float, optional (default: 1e-8)) – Tolerance of relative residual in eigenvalue computation.

  • method (string, optional (default: ‘tracemin_pcg’)) – Method of eigenvalue computation. It must be one of the tracemin options shown below (TraceMIN), ‘lanczos’ (Lanczos iteration) or ‘lobpcg’ (LOBPCG).

    The TraceMIN algorithm uses a linear system solver. The following values allow specifying the solver to be used.

    Value Solver
    ‘tracemin_pcg’ Preconditioned conjugate gradient method
    ‘tracemin_chol’ Cholesky factorization
    ‘tracemin_lu’ LU factorization
  • seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.


spectral_ordering – Spectral ordering of nodes.

Return type:

NumPy array of floats.


NetworkXError – If G is empty.


Edge weights are interpreted by their absolute values. For MultiGraph’s, weights of parallel edges are summed. Zero-weighted edges are ignored.

To use Cholesky factorization in the TraceMIN algorithm, the scikits.sparse package must be installed.

See also