Temporal Graphs

Temporal Graphs are graphs with time varying topologies and node features. In GraphNeuralNetworks.jl temporal graphs with fixed number of nodes over time are supported by the TemporalSnapshotsGNNGraph type.

Creating a TemporalSnapshotsGNNGraph

A temporal graph can be created by passing a list of snapshots to the constructor. Each snapshot is a GNNGraph.

julia> snapshots = [rand_graph(10,20) for i in 1:5];

julia> tg = TemporalSnapshotsGNNGraph(snapshots)
TemporalSnapshotsGNNGraph:
  num_nodes: [10, 10, 10, 10, 10]
  num_edges: [20, 20, 20, 20, 20]
  num_snapshots: 5

A new temporal graph can be created by adding or removing snapshots to an existing temporal graph.

julia> new_tg = add_snapshot(tg, 3, rand_graph(10, 16)) # add a new snapshot at time 3
TemporalSnapshotsGNNGraph:
  num_nodes: [10, 10, 10, 10, 10, 10]
  num_edges: [20, 20, 16, 20, 20, 20]
  num_snapshots: 6

julia> snapshots = [rand_graph(10,20), rand_graph(10,14), rand_graph(10,22)];

julia> tg = TemporalSnapshotsGNNGraph(snapshots)
TemporalSnapshotsGNNGraph:
  num_nodes: [10, 10, 10]
  num_edges: [20, 14, 22]
  num_snapshots: 3

julia> new_tg = remove_snapshot(tg, 2) # remove snapshot at time 2
TemporalSnapshotsGNNGraph:
  num_nodes: [10, 10]
  num_edges: [20, 22]
  num_snapshots: 2

See rand_temporal_radius_graph and rand_temporal_hyperbolic_graph for generating random temporal graphs.

julia> tg = rand_temporal_radius_graph(10, 3, 0.1, 0.5)
TemporalSnapshotsGNNGraph:
  num_nodes: [10, 10, 10]
  num_edges: [32, 30, 34]
  num_snapshots: 3

Basic Queries

Basic queries are similar to those for GNNGraphs:

julia> snapshots = [rand_graph(10,20), rand_graph(10,14), rand_graph(10,22)];

julia> tg = TemporalSnapshotsGNNGraph(snapshots)
TemporalSnapshotsGNNGraph:
  num_nodes: [10, 10, 10]
  num_edges: [20, 14, 22]
  num_snapshots: 3

julia> tg.num_nodes         # number of nodes in each snapshot
3-element Vector{Int64}:
 10
 10
 10

julia> tg.num_edges         # number of edges in each snapshot
3-element Vector{Int64}:
 20
 14
 22

julia> tg.num_snapshots     # number of snapshots
3

julia> tg.snapshots         # list of snapshots
3-element Vector{GNNGraph{Tuple{Vector{Int64}, Vector{Int64}, Nothing}}}:
 GNNGraph(10, 20) with no data
 GNNGraph(10, 14) with no data
 GNNGraph(10, 22) with no data

julia> tg.snapshots[1]      # first snapshot, same as tg[1]
GNNGraph:
  num_nodes: 10
  num_edges: 20

Data Features

Node, edge, and graph features can be added at construction time or later using:

julia> snapshots = [rand_graph(10,20; ndata = rand(3,10)), rand_graph(10,14; ndata = rand(4,10)), rand_graph(10,22; ndata = rand(5,10))]; # node features at construction time

julia> tg = TemporalSnapshotsGNNGraph(snapshots);

julia> tg.tgdata.y = rand(3,1); # graph features after construction

julia> tg
TemporalSnapshotsGNNGraph:
  num_nodes: [10, 10, 10]
  num_edges: [20, 14, 22]
  num_snapshots: 3
  tgdata:
        y = 3×1 Matrix{Float64}

julia> tg.ndata # vector of Datastore for node features
3-element Vector{DataStore}:
 DataStore(10) with 1 element:
  x = 3×10 Matrix{Float64}
 DataStore(10) with 1 element:
  x = 4×10 Matrix{Float64}
 DataStore(10) with 1 element:
  x = 5×10 Matrix{Float64}

julia> typeof(tg.ndata.x) # vector containing the x feature of each snapshot
Vector{Matrix{Float64}}

Graph convolutions on TemporalSnapshotsGNNGraph

A graph convolutional layer can be applied to each snapshot independently, in the next example we apply a GINConv layer to each snapshot of a TemporalSnapshotsGNNGraph. The list of compatible graph convolution layers can be found here.

julia> using GraphNeuralNetworks, Flux

julia> snapshots = [rand_graph(10, 20; ndata = rand(3, 10)), rand_graph(10, 14; ndata = rand(3, 10))];

julia> tg = TemporalSnapshotsGNNGraph(snapshots);

julia> m = GINConv(Dense(3 => 1), 0.4);

julia> output = m(tg, tg.ndata.x);

julia> size(output[1])
(1, 10)