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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.


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.