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

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 Matrix

Bethe Hessian or deformed Laplacian matrix of graphs.

bethe_hessian_matrix(G[, r, nodelist])

Returns the Bethe Hessian matrix of G.

Algebraic Connectivity

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.

Attribute Matrices

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 Matrices

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.

Spectrum

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.