FeaturedGraph

Construct a FeaturedGraph and graph representations

A FeaturedGraph is aimed to represent a composition of graph representation and graph signals. A graph representation is required to construct a FeaturedGraph object. Graph representation can be accepted in several forms: adjacency matrix, adjacency list or graph representation provided from JuliaGraphs.

julia> adj = [0 1 1;
              1 0 1;
              1 1 0]
3×3 Matrix{Int64}:
 0  1  1
 1  0  1
 1  1  0

julia> FeaturedGraph(adj)
FeaturedGraph(
	Undirected graph with (#V=3, #E=3) in adjacency matrix,
)

Currently, SimpleGraph and SimpleDiGraph from LightGraphs.jl, SimpleWeightedGraph and SimpleWeightedDiGraph from SimpleWeightedGraphs.jl, as well as MetaGraph and MetaDiGraph from MetaGraphs.jl are supported.

If a graph representation is not given, a FeaturedGraph object will be regarded as a NullGraph. A NullGraph object is just used as a special case of FeaturedGraph to represent a null object.

julia> FeaturedGraph()
NullGraph()

FeaturedGraph constructors

Graph Signals

Graph signals is a collection of any signals defined on a graph. Graph signals can be the signals related to vertex, edges or graph itself. If a vertex signal is given, it is recorded as a node feature in FeaturedGraph. A node feature is stored as the form of generic array, of which type is AbstractArray. A node feature can be indexed by the node index, which is the same index for given graph.

Node features can be optionally given in construction of a FeaturedGraph.

julia> fg = FeaturedGraph(adj, nf=rand(5, 3))
FeaturedGraph(
	Undirected graph with (#V=3, #E=3) in adjacency matrix,
	Node feature:	ℝ^5 <Matrix{Float64}>,
)

julia> has_node_feature(fg)
true

julia> node_feature(fg)
5×3 Matrix{Float64}:
 0.534928  0.719566  0.952673
 0.395465  0.268515  0.335446
 0.79428   0.18623   0.454377
 0.530675  0.402474  0.00920068
 0.642556  0.719674  0.772497

Users check node/edge/graph features are available by has_node_feature, has_edge_feature and has_global_feature, respectively, and fetch these features by node_feature, edge_feature and global_feature.

Getter methods

Check methods

Graph properties

FeaturedGraph is itself a graph, so we can query some graph properties from a FeaturedGraph.

julia> nv(fg)
3

julia> ne(fg)
3

julia> is_directed(fg)
false

Users can query number of vertex and number of edge by nv and ne, respectively. is_directed checks if the underlying graph is a directed graph or not.

Graph-related APIs

Pass FeaturedGraph to CUDA

Passing a FeaturedGraph to CUDA is easy. Just pipe a FeaturedGraph object to gpu provided by Flux.

julia> using Flux

julia> fg = fg |> gpu
FeaturedGraph(
	Undirected graph with (#V=3, #E=3) in adjacency matrix,
	Node feature:	ℝ^5 <CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}>,
)

Linear algebra for FeaturedGraph

FeaturedGraph supports the calculation of graph Laplacian matrix in inplace manner.

julia> fg = FeaturedGraph(adj, nf=rand(5, 3))
FeaturedGraph(
	Undirected graph with (#V=3, #E=3) in adjacency matrix,
	Node feature:	ℝ^5 <Matrix{Float64}>,
)

julia> laplacian_matrix!(fg)
FeaturedGraph(
	Undirected graph with (#V=3, #E=3) in Laplacian matrix,
	Node feature:	ℝ^5 <Matrix{Float64}>,
)

julia> laplacian_matrix(fg)
3×3 SparseArrays.SparseMatrixCSC{Int64, Int64} with 9 stored entries:
 -2   1   1
  1  -2   1
  1   1  -2

laplacian_matrix! mutates the adjacency matrix into a Laplacian matrix in a FeaturedGraph object and the Laplacian matrix can be fetched by laplacian_matrix. The Laplacian matrix is cached in a FeaturedGraph object and can be passed to a graph neural network model for training or inference. This way reduces the calculation overhead for Laplacian matrix during the training process.

FeaturedGraph supports not only Laplacian matrix, but also normalized Laplacian matrix and scaled Laplacian matrix calculation.

Inplaced linear algebraic APIs

Linear algebraic APIs

Non-inplaced APIs returns a vector or a matrix directly.