Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In a number of methodologies for joint inference across graphs, it is assumed that an explicit vertex correspondence is a priori known across the vertex sets of the graphs. While this assumption is often reasonable, in practice these correspondences may be unobserved and/or errorfully observed, and graph matching---aligning a pair of graphs to minimize their edge disagreements---is used to align the graphs before performing subsequent inference. Herein,  explore the duality beten the loss of mutual information due to an errorfully observed vertex correspondence and the ability of graph matching algorithms to recover the true correspondence across graphs.  then demonstrate the practical effect that graph shuffling---and matching---can have on subsequent inference, with examples from two sample graph hypothesis testing and joint graph clustering.
['Vince Lyzinski']
I am writing a research paper on a idea Information Recovery in Shuffled Graphs via Graph Matching
[{"from": "human", "value": "I am writing a research paper on a idea Information Recovery in Shuffled Graphs via Graph Matching"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In a number of methodologies for joint inference across graphs, it is assumed that an explicit vertex correspondence is a priori known across the vertex sets of the graphs. While this assumption is often reasonable, in practice these correspondences may be unobserved and/or errorfully observed, and graph matching---aligning a pair of graphs to minimize their edge disagreements---is used to align the graphs before performing subsequent inference. Herein,  explore the duality beten the loss of mutual information due to an errorfully observed vertex correspondence and the ability of graph matching algorithms to recover the true correspondence across graphs.  then demonstrate the practical effect that graph shuffling---and matching---can have on subsequent inference, with examples from two sample graph hypothesis testing and joint graph clustering."}]