Prioritization of Potential BC-Associated Risk Factors With RWR

We thus conducted an RWR method on the BC-specific CRN to prioritize potential BC-associated risk factors. Here, the obtained known BC-associated factors were employed as seed nodes. We denoted S₀ as the initial score vector and S_t as a process vector in which the ith element represented the probability of the random walker appearing at node i in step t. We let α measure the restart probability of the random walk at the initial nodes in each step. Also P represented the probability transition matrix (PTM), and it was obtained from the adjacency matrix of the BC-associated CRN. The formula is described as

where p(i, j) is the entry in the PTM and M (i, j) is the entry in the adjacency matrix. The score vector in step t + 1 can be defined as follows:

Here, the restart probability α was set as 0.5, and the initial score S₀ of each seed node was set as 1/n (where n was the number of total seed BC-associated factors). The initial scores of all other nodes were set as 0 (Li and Patra, 2010; Chen et al., 2016). It is natural that the score of each node will become stable with the iteration steps going on. We set the stable scores as S_∞ when the difference between S_t and S_t+1 was no more than 10^–10. Then the final stable scores S_∞ could be used to measure the proximity of each node to the seed nodes. Thus, all candidate nodes in the BC-specific CRN could be ranked based on S_∞, and the top-ranked nodes could be speculated to be closely related with BC.