# Linear algebra¶

## Graph Matrix¶

Adjacency matrix and incidence matrix of graphs.

 `adjacency_matrix`(G[, nodelist, dtype, 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. Return the directed combinatorial 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 Returns eigenvalues of the modularity matrix of G.