spectral_bisection

spectral_bisection(G, weight='weight', normalized=False, tol=1e-08, method='tracemin_pcg', seed=None)

Bisect the graph using the Fiedler vector.

This method uses the Fiedler vector to bisect a graph. The partition is defined by the nodes which are associated with either positive or negative values in the vector.

Parameters:

GNetworkX Graph

weightstr, optional (default: weight)

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:

bisectiontuple of sets

Sets with the bisection of nodes

References

[1]

M. E. J Newman ‘Networks: An Introduction’, pages 364-370 Oxford University Press 2011.

Examples

>>> G = nx.barbell_graph(3, 0)
>>> nx.spectral_bisection(G)
({0, 1, 2}, {3, 4, 5})