A Comprehensive Algorithm for Evaluating Node Influences in Social Networks Based on Preference Analysis and Random Walk

Algorithm 1

PARW-Rank Algorithm.

Input: (1) the degree measures () of all nodes in the given network;

   (2) the betweenness measures () of all nodes;

   (3) the closeness measures () of all nodes;

   (4) the step number () of iterations in random walk.

Output: The rank () of nodes in the social network.

1. for each basic measure in do

2. apply the min-max normalization to convert the current measure vector;

3. analyze the preference relation of each node pair;

4. build a partial dependence graph (PPG) based on the above preference relations;

5. represent current PPG to the corresponding matrix, i.e., , or ;

6. end for

7. combine three basic PPGs together to form a CPG, its matrix () is the weighted sum of , and ;

8. apply the regularization on each row in to form a regularized matrix ;

9. set as the initial probabilities for nodes in network;

10. for is from 1 to do

11. apply rule to update the vector of probability;

12. end for

13. generate the ranking () of node influences by sorting in ascending order;

14. return ;