normalized_laplacian_matrix¶

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

Return the normalized Laplacian matrix of G.

The normalized graph Laplacian is the matrix

$NL = D^{-1/2} L D^{-1/2}$

where $L$ is the graph Laplacian and $D$ is the diagonal matrix of node degrees.

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 : NumPy matrix

The normalized Laplacian matrix of G.