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laplacian_matrix(G, nodelist=None, weight='weight')

The graph Laplacian is the matrix L = D - A, where A is the adjacency matrix and D is the diagonal matrix of node degrees.

Notes

For MultiGraph, the edges weights are summed.

Parameters

G : graph: A NetworkX graph
nodelist : list, optional: The rows and columns are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by G.nodes().
weight : string 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

L : SciPy sparse matrix: The Laplacian matrix of G.

Returns the Laplacian matrix of G.

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.linalg.spectrum.laplacian_spectrum networkx.linalg.laplacianmatrix.directed_combinatorial_laplacian_matrix networkx.linalg.algebraicconnectivity.spectral_ordering networkx.linalg.algebraicconnectivity.algebraic_connectivity networkx.linalg.laplacianmatrix.directed_laplacian_matrix networkx.linalg.algebraicconnectivity.fiedler_vector networkx.linalg.laplacianmatrix.normalized_laplacian_matrix networkx.linalg.bethehessianmatrix.bethe_hessian_matrix

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them