Linear algebra¶

Graph Matrix¶

Adjacency matrix and incidence matrix of graphs.

`adjacency_matrix`(G[, nodelist, weight])	Returns adjacency matrix of G.
`incidence_matrix`(G[, nodelist, edgelist, …])	Returns incidence matrix of G.

Laplacian matrix of graphs.

`laplacian_matrix`(G[, nodelist, weight])	Returns the Laplacian matrix of G.
`normalized_laplacian_matrix`(G[, nodelist, …])	Returns the normalized Laplacian matrix of G.
`directed_laplacian_matrix`(G[, nodelist, …])	Returns the directed Laplacian matrix of G.
`directed_combinatorial_laplacian_matrix`(G[, …])	Return the directed combinatorial Laplacian matrix of G.

Bethe Hessian or deformed Laplacian matrix of graphs.

Returns the Bethe Hessian matrix of G.

Algebraic connectivity and Fiedler vectors of undirected graphs.

`algebraic_connectivity`(G[, weight, …])	Returns the algebraic connectivity of an undirected graph.
`fiedler_vector`(G[, weight, normalized, tol, …])	Returns the Fiedler vector of a connected undirected graph.
`spectral_ordering`(G[, weight, normalized, …])	Compute the spectral_ordering of a graph.

Functions for constructing matrix-like objects from graph attributes.

`attr_matrix`(G[, edge_attr, node_attr, …])	Returns a NumPy matrix using attributes from G.
`attr_sparse_matrix`(G[, edge_attr, …])	Returns a SciPy sparse matrix using attributes from G.

Modularity matrix of graphs.

`modularity_matrix`(G[, nodelist, weight])	Returns the modularity matrix of G.
`directed_modularity_matrix`(G[, nodelist, weight])	Returns the directed modularity matrix of G.

Eigenvalue spectrum of graphs.

`adjacency_spectrum`(G[, weight])	Returns eigenvalues of the adjacency matrix of G.
`laplacian_spectrum`(G[, weight])	Returns eigenvalues of the Laplacian of G
`bethe_hessian_spectrum`(G[, r])	Returns eigenvalues of the Bethe Hessian matrix of G.
`normalized_laplacian_spectrum`(G[, weight])	Return eigenvalues of the normalized Laplacian of G
`modularity_spectrum`(G)	Returns eigenvalues of the modularity matrix of G.