Linear Algebra

adjacency_matrix(g, dir=:out, T::DataType=Int)

Returns a sparse boolean adjacency matrix for a graph, indexed by [u, v] vertices. true values indicate an edge between u and v. Users may specify a direction (:in, :out, or :all are currently supported; :out is default for both directed and undirected graphs) and a data type for the matrix (defaults to Int).

incidence_matrix(g::AGraphOrDiGraph, T::DataType=Int; oriented=false)

Returns a sparse node-arc incidence matrix for a graph, indexed by [v, i], where i is in 1:ne(g), indexing an edge e. For directed graphs, a value of -1 indicates that src(e) == v, while a value of 1 indicates that dst(e) == v. Otherwise, the value is 0.

For undirected graphs, both entries are 1 if oriented=false, otherwise [v, i] -> -1 and [u, i] -> 1 if v < u.

laplacian_matrix(g, dir::Symbol=:out, T::DataType=Int)

Returns a sparse Laplacian matrix for a graph g, indexed by [u, v] vertices. dir has to be :in, :out or :all.

spectral_distance(G₁, G₂ [, k])

Compute the spectral distance between undirected n-vertex graphs G₁ and G₂ using the top k ≤ n greatest eigenvalues. If k is ommitted, uses full spectrum.

For further details, please refer to:

JOVANOVIC, I.; STANIC, Z., 2014. Spectral Distances of Graphs Based on their Different Matrix Representations

nonbacktracking_matrix(g)

Return a non-backtracking matrix B and an edgemap storing the oriented edges' positions in B. Given two arcs $A_{i j}` and `A_{k l}` in `g`, the non-backtraking matrix$B$is defined as$B{A{i j}, A{k l}} = δ{j k} * (1 - δ_{i l})``