laplacian_spectrum

laplacian_spectrum(G, weight='weight')

Returns eigenvalues of the Laplacian of G

Parameters:

Ggraph

A NetworkX graph

weightstring or None, optional (default=’weight’)

The edge data key used to compute each value in the matrix. If None, then each edge has weight 1.

Returns:

evalsNumPy array

Eigenvalues

See also

laplacian_matrix

Notes

For MultiGraph/MultiDiGraph, the edges weights are summed. See to_numpy_array() for other options.

Examples

The multiplicity of 0 as an eigenvalue of the laplacian matrix is equal to the number of connected components of G.

>>> G = nx.Graph()  # Create a graph with 5 nodes and 3 connected components
>>> G.add_nodes_from(range(5))
>>> G.add_edges_from([(0, 2), (3, 4)])
>>> nx.laplacian_spectrum(G)
array([0., 0., 0., 2., 2.])