Protein interaction prediction- how to input this data structure
https://en.wikipedia.org/wiki/Adjacency_matrix



For such problems, you can tabulate these connections as adjacency matrix and create a network to predict weights for the matrix given some properties of nodes (Say for a social graph; given properties of User1 and User2 [for example Zipcode, school ...] output 1, or 0),   

Some examples are :

https://www.biorxiv.org/content/biorxiv/early/2018/01/14/247577.full.pdf
http://kawahara.ca/convolutional-neural-networks-for-adjacency-matrices/

Edit : Illustration of Train_X and Train_Y 



Columns A through H form Train_X and Column I is Train_Y.