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.

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.