Node Importance Ranking in Complex Networks Based on Multicriteria Decision Making

Algorithm 1

Specific steps of node importance ranking in complex networks.

Input: Decision matrix .

Output: The result of ranking .

Step 1. Constitute the weighted decision matrix.

(i) Calculate the normalized decision matrix by Equations (7a) and (7b).

(ii) Determine the weights of the criteria using Equation (9) based on the entropy weighting method.

(iii) The weight of each criterion is brought into Equation (10), and the weighted decision matrix is constructed.

Step 2. Calculate the distance to the ideal solution.

(i) Calculate the positive ideal solution and the negative ideal solution by Equations (11a) and (11b), respectively.

(ii) Obtain the distance of each scheme to the ideal solution by Equations (12a) and (12b), respectively.

Step 3. Output the result of ranking.

(i) Calculate the closeness degree to the ideal solution by Equation (13).

(ii) Rank the nodes’ importance in descending order using Equation (15), and the result of the node importance

ranking can be obtained as .