laplacian_matrix#
- 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.
- Parameters:
- Ggraph
A NetworkX graph
- nodelistlist, 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().
- weightstring or None, optional (default=â€™weightâ€™)
The edge data key used to compute each value in the matrix. If None, then each edge has weight 1.
- Returns:
- LSciPy sparse array
The Laplacian matrix of G.
See also
to_numpy_array
normalized_laplacian_matrix
laplacian_spectrum
Notes
For MultiGraph, the edges weights are summed.
Examples
For graphs with multiple connected components, L is permutation-similar to a block diagonal matrix where each block is the respective Laplacian matrix for each component.
>>> G = nx.Graph([(1, 2), (2, 3), (4, 5)]) >>> print(nx.laplacian_matrix(G).toarray()) [[ 1 -1 0 0 0] [-1 2 -1 0 0] [ 0 -1 1 0 0] [ 0 0 0 1 -1] [ 0 0 0 -1 1]]