Added Personalized PageRank Diffusion [ppr_diffusion function]

[rbSparky]

Continues Issue #412, takes inspiration from DGL implementation

This PR introduces a new function, ppr_diffusion. It calculates Personalized PageRank (PPR) diffusion based on the edge weight matrix and updates the graph with new edge weights derived from the PPR matrix.

Implementation:

The function operates in several key steps:

• Construct Modified Adjacency Matrix (A): Utilizes existing edge weights (w) to build a matrix $A$ representing the graph's structure, adjusted by $(α - 1)$, where $α$ is the damping factor. This adjustment incorporates both direct connections and global graph structure.

A[dst, src] += w[idx]
A .*= (alpha_f32 - 1)

• Incorporate Identity Matrix (I): Adds the identity matrix to A to account for self-transitions, forming $I + (α - 1) \times A$.

A[i, i] += 1

• Apply PPR Formula: Calculates the PPR diffusion matrix as $α \times (I + (α - 1) \times A)^{-1}$, which effectively models the probability of transitioning from one node to another, considering random jumps governed by α.

PPR = alpha_f32 * inv(A)

• Update Edge Weights: Assigns new weights to each edge based on the corresponding values in the PPR matrix, effectively updating the graph's edge weights to reflect the calculated PPR diffusion.

new_w = [PPR[dst, src] for (src, dst) in zip(s, t)]

[rbSparky]

Tests fail for

GATv2Conv: Test Failed at /home/runner/work/GraphNeuralNetworks.jl/GraphNeuralNetworks.jl/test/test_utils.jl:203

This should be checked, since this did not fail in the last commit and the only change in this commit was adding the reference paper.

[rbSparky]

Tests pass now, so the previous test fail was unrelated to this PR.

That should also be checked later.

[rbSparky]

Would this be GPU compatible now that non mutable operations are removed? Tested training and Zygote no longer gives single element operation error!

[CarloLucibello]

Let's have an implementation which works correctly with dense matrices on cpu and in later PRs we can add gpu support and add the sparse matrices performance optimization. So we are mostly fine with the current PR.

[rbSparky]

Let's have an implementation which works correctly with dense matrices on cpu and in later PRs we can add gpu support and add the sparse matrices performance optimization. So we are mostly fine with the current PR.

Should I change the code back to older commits where only dense matrices were used? Or would this be ok as it is?

[CarloLucibello]

bump. Also needs a rebase.

[rbSparky]

bump. Also needs a rebase.

done