Undirected Graphs

[stefanbringuier]

Let me first state, I am new to GNNs. I'm trying to implement the CGCNN in this paper ([repo here])(https://github.com/txie-93/cgcnn). I started off with using FeaturedGraph data types from GraphSignals.jl since I was planning on using GeometricFlux.jl. However GraphNeuralNetworks.jl seems to be more active and where the community is focusing efforts on, 🤷‍♂️.

What I've been trying to wrap my head around is GNNGraphs data types have double the number of edges because they are directed by design, makes sense, but in my use case I want un-directed graphs. If I compare GNNGraphs to FeaturedGraphs I have:

GNNGraph

Tuple{GraphNeuralNetworks.GNNGraphs.GNNGraph{Tuple{Vector{Int64}, Vector{Int64}, Nothing}}, Float64}
GNNGraph(22, 358) with x: 92×22, e: 10×358 data
3.6833
GNNGraph(40, 800) with x: 92×40, e: 10×800 data
1.6222
GNNGraph(12, 116) with x: 92×12, e: 10×116 data
1.5476
GNNGraph(80, 2222) with x: 92×80, e: 10×2222 data
2.1634
GNNGraph(9, 90) with x: 92×9, e: 10×90 data
3.2824
GNNGraph(19, 340) with x: 92×19, e: 10×340 data
1.8759
GNNGraph(16, 168) with x: 92×16, e: 10×168 data
1.4667
GNNGraph(48, 1440) with x: 92×48, e: 10×1440 data
3.7994
GNNGraph(6, 42) with x: 92×6, e: 10×42 data
0.0

and

FeaturedGraph

Tuple{GraphSignals.FeaturedGraph{GraphSignals.SparseGraph{false, SparseArrays.SparseMatrixCSC{Int64, Int64}, Vector{Int64}, Int64}, GraphSignals.NodeSignal{Matrix{Float64}}, GraphSignals.EdgeSignal{Matrix{Float64}}, GraphSignals.NullGraphSignal, GraphSignals.NullDomain}, Float64}
FeaturedGraph:
	Undirected graph with (#V=22, #E=179) in adjacency matrix
	Node feature:	ℝ^92 <NodeSignal{Matrix{Float64}}>
	Edge feature:	ℝ^10 <EdgeSignal{Matrix{Float64}}>
3.6833
FeaturedGraph:
	Undirected graph with (#V=40, #E=400) in adjacency matrix
	Node feature:	ℝ^92 <NodeSignal{Matrix{Float64}}>
	Edge feature:	ℝ^10 <EdgeSignal{Matrix{Float64}}>
1.6222
FeaturedGraph:
	Undirected graph with (#V=12, #E=58) in adjacency matrix
	Node feature:	ℝ^92 <NodeSignal{Matrix{Float64}}>
	Edge feature:	ℝ^10 <EdgeSignal{Matrix{Float64}}>
1.5476
FeaturedGraph:
	Undirected graph with (#V=80, #E=1111) in adjacency matrix
	Node feature:	ℝ^92 <NodeSignal{Matrix{Float64}}>
	Edge feature:	ℝ^10 <EdgeSignal{Matrix{Float64}}>
2.1634
FeaturedGraph:
	Undirected graph with (#V=9, #E=45) in adjacency matrix
	Node feature:	ℝ^92 <NodeSignal{Matrix{Float64}}>
	Edge feature:	ℝ^10 <EdgeSignal{Matrix{Float64}}>
3.2824
FeaturedGraph:
	Undirected graph with (#V=19, #E=170) in adjacency matrix
	Node feature:	ℝ^92 <NodeSignal{Matrix{Float64}}>
	Edge feature:	ℝ^10 <EdgeSignal{Matrix{Float64}}>
1.8759
FeaturedGraph:
	Undirected graph with (#V=16, #E=84) in adjacency matrix
	Node feature:	ℝ^92 <NodeSignal{Matrix{Float64}}>
	Edge feature:	ℝ^10 <EdgeSignal{Matrix{Float64}}>
1.4667
FeaturedGraph:
	Undirected graph with (#V=48, #E=720) in adjacency matrix
	Node feature:	ℝ^92 <NodeSignal{Matrix{Float64}}>
	Edge feature:	ℝ^10 <EdgeSignal{Matrix{Float64}}>
3.7994
FeaturedGraph:
	Undirected graph with (#V=6, #E=21) in adjacency matrix
	Node feature:	ℝ^92 <NodeSignal{Matrix{Float64}}>
	Edge feature:	ℝ^10 <EdgeSignal{Matrix{Float64}}>
0.0

Is there a way to get un-directed graphs when using GraphNeuralNetworks.jl?

[aurorarossi]

Hello!
Yes, they are double and directed, but one is in one direction and one in the other, so it is equivalent to an undirected edge.

[stefanbringuier]

one is in one direction and one in the other, so it is equivalent to an undirected edge.

Okay this is intuitively what I guessed. So just to confirm the design of GNNGraph, there is a pair of directed edges with opposing directions and thus equate to an undirected edge. Some follow-on questions:

1. In a message passing scheme is the aggregation done for both directions of an edge by default? If so, is it balanced (e.g., using sum or average) to result in undirected message passing?
2. Will edge features for both directed edges (A →B and B→A) be treated in a way that respects the intended undirected nature?

Thank you very much in advance!

[aurorarossi]

Message passing is performed on each directed edge, and given the fact that we represent an undirected edge as two directed opposite edges, message passing is performed for both directions. Everything works as you would expect for an undirected graph, the only thing that changes is the representation of the graph.

[stefanbringuier]

Thank you very much!