First, we have calculated the path cost using Eq. 1 and hop count for each path in the network, and after that, we have applied genetic algorithm for finding the optimal path.
We calculated the shortest path for all known indications (i.e., shortest path between a known disease and drug pair) in the protein interactions network using JUNG [ 35].
Over this sub-network, we calculated the shortest path length between every pair of genes (dij is the shortest path length between gene i and gene j).
Since they showed that signaling in proteins, at the basis of protein allosteric behavior, is mediated through shortest paths, we calculated the shortest paths for all pairs (APSP) of residues in the protein for every given frame.
At last, we calculated the characteristic path length among age-related miRNAs to evaluate the communication efficiency in the network.
Note that the directionality of each edge in the network was considered when we calculated the shortest path for the network in order to calculate the closeness and the betweenness.
To test the connection between our predicted key enzyme-coding genes and known disease genes in database, we calculated the shortest path lengths between each pair of genes in a functional association network, specifically the FunCoup [ 15] network.
Then, we calculated the shortest path distance (δ g h (s t r g ) ) for every pair of proteins (g and h) in this network and converted it into a value in the range of 0 and 1 (ω g h (s t r g ) = 1 - δ g h (s t r g ) / max δ g h (s t r g ) ).
Next, we calculated the shortest path distance (δ g h (p s e q ) ) for every pair of proteins (g and h) in this network and converted it to a similarity value in the range of 0 and 1 (ω g h (p s e q ) = 1 - δ g h (p s e q ) / max δ g h (p s e q ) ).
To determine the significance of these findings, we calculated the total paths covered by single melanosomes.
