networkx.linalg.algebraicconnectivity.spectral_ordering

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.

Parameters
GNetworkX graph

A graph.

weightobject, optional (default: None)

The data key used to determine the weight of each edge. If None, then each edge has unit weight.

normalizedbool, optional (default: False)

Whether the normalized Laplacian matrix is used.

tolfloat, optional (default: 1e-8)

Tolerance of relative residual in eigenvalue computation.

methodstring, 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_lu’

LU factorization

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

Returns
spectral_orderingNumPy array of floats.

Spectral ordering of nodes.

Raises
NetworkXError

If G is empty.

See also

laplacian_matrix

Notes

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