Encoding of graphs as an input to neural nets
So I ask myself this question:


  Suppose 2 encoding contains the same amount of information, that is,
  all the information about the graph. What factor would make one
  encoding better than the other in terms of performance of neural nets
  (trained with the same number of iterations, etc)


The my personal answer to that is:

Trained neural net (in its simplest version) is just a linear function of its input. So, do you suspect that the function you want to learn can be expressed as a linear function of the input? And this is where the choice of encoding makes a difference.

My stance on these kind of algorithm is that. Ultimately, if you want it to perform well, you need to have a good hypothesis on what kind of function your answer should actually be.