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I am new to graph neural networks and their applications. I have an input graph $G = \{V, E\}$ and an output graph $G' = \{V', E'\}$ where the number of nodes $V$ and $V'$ are different. I am trying to learn the function where $f(G) = G'$ and $V > V'$, thus, the function is mapping many-to-one ($n$ number of nodes map to one). The Graph Convolution Network (GCN) seems to have the same number of nodes in input and output with the function being learnt. Could I utilize the GCN for my task?

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I suggest you look into link prediction. I have had good luck with the StellarGraph library. They have several algorithms implemented, including GCN.

Link prediction is a binary classification problem. Given two nodes, $v_i$ and $v_j$, does there exist a link between them? Using a library like StellarGraph will also produce node embeddings while performing link prediction.

For you scenario I'm picturing a three step process:

  1. Link prediction and node embeddings on $G$.
  2. Link prediction and node embeddings on $G'$.
  3. Link prediction reusing existing embeddings where each link is between the two graphs. So each link is a tuple of the form: $(v_i, v_j')$ where $v_i \in V$ and $v_j' \in V'$. If there were no links predicted from $v_i$ to $v_j'$ then that might suggest to remove $v_j'$.

In the link prediction tasks that I've outlined, you can use GCN with StellarGraph. So there should be no problems in terms of the number of nodes.

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  • $\begingroup$ Thanks. So in case, where none of the edges exist, the node is removed? Also wouldnt that lead to lot of computation if the V' is much smaller than V. $\endgroup$
    – shunyo
    Feb 12, 2021 at 15:42

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