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I'm interested in the following problem in statistical characteristics of graph embedding, and it seems to fall between traditional graph theory and Graph neural networks.

I looked up:

  • William L. Hamilton, "Graph Representation Learning Book",
  • Ravindra B. Bapat "Graps and Matrices"

Suppose we have a DAG and its adjacency matrix factorization (e.g. A = WH). If we take a row vector of the out-degree matrix and obtain a new node by perturbing the vector, how it tranlsates back to adjacency matrix? Particularly, what is the probability of the new node pointing to any of the existing 0 in-degree nodes?

Or is it so obvious that we do not need any detailed reasoning?

Any suggestions appreciated!

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