# 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.

## Spectrum¶

Eigenvalue spectrum of graphs.

 laplacian_spectrum(G[, weight]) Returns eigenvalues of the Laplacian of G adjacency_spectrum(G[, weight]) Returns eigenvalues of the adjacency matrix of G. modularity_spectrum(G) Returns eigenvalues of the modularity 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.