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Identifying the importance of nodes of complex networks is of interest to theresearch of Social Networks, Biological Networks etc.. Current researchers haveproposed several measures or algorithms, such as betweenness, PageRank and HITSetc., to identify the node importance. However, these measures are based ondifferent aspects of properties of nodes, and often conflict with the others. Areasonable, fair standard is needed for evaluating and comparing thesealgorithms. This paper develops a framework as the standard for ranking theimportance of nodes. Four intuitive rules are suggested to measure the nodeimportance, and the equivalence classes approach is employed to resolve theconflicts and aggregate the results of the rules. To quantitatively compare thealgorithms, the performance indicators are also proposed based on a similaritymeasure. Three widely used real-world networks are used as the test-beds. Theexperimental results illustrate the feasibility of this framework and show thatboth algorithms, PageRank and HITS, perform well with bias when dealing withthe tested networks. Furthermore, this paper uses the proposed approach toanalyze the structure of the Internet, and draws out the kernel of the Internetwith dense links.

Ranking the Importance of Nodes of Complex Networks by the Equivalence Classes Approach