This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.
directed_laplacian_matrix(G, nodelist=None, weight='weight', walk_type=None, alpha=0.95)¶
Return the directed Laplacian matrix of G.
The graph directed Laplacian is the matrix
where is the identity matrix, is the transition matrix of the graph, and a matrix with the Perron vector of in the diagonal and zeros elsewhere.
Depending on the value of walk_type, can be the transition matrix induced by a random walk, a lazy random walk, or a random walk with teleportation (PageRank).
- G (DiGraph) – 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.
- walk_type (string or None, optional (default=None)) – If None, is selected depending on the properties of the graph. Otherwise is one of ‘random’, ‘lazy’, or ‘pagerank’
- alpha (real) – (1 - alpha) is the teleportation probability used with pagerank
L – Normalized Laplacian of G.
NetworkXError– If NumPy cannot be imported
NetworkXNotImplemnted– If G is not a DiGraph
Only implemented for DiGraphs
 Fan Chung (2005). Laplacians and the Cheeger inequality for directed graphs. Annals of Combinatorics, 9(1), 2005