This documents the development version of NetworkX. Documentation for the current release can be found here.


laplacian_matrix(G, nodelist=None, weight='weight')[source]

Returns the Laplacian matrix of G.

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

  • 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.


L – The Laplacian matrix of G.

Return type

SciPy sparse matrix


For MultiGraph/MultiDiGraph, the edges weights are summed.

See also

to_numpy_array(), normalized_laplacian_matrix(), laplacian_spectrum()