Based on a beam search algorithm in what does de probability of each node of the graph depends on? I mean like what characteristics gives the node its probability for the search?
The probability at every step is given by the model you use. For instance in seq2seq model it is the probability distribution trained by the model in the output of the neural network.
I think this simple demo may help: https://stackoverflow.com/a/50304227/3552975
The prob there is from a random matrix output_projection but in real context this matrix is trained by lots of data and it should be a trainable variable.