This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.


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

Return 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_matrix(), normalized_laplacian_matrix()