Abstract
Centrality is one of the most studied concepts in network analysis. Despite an abundance of methods for measuring centrality in social networks has been proposed, each approach exclusively characterizes limited parts of what it implies for an actor to be “vital” to the network. In this paper, a novel mechanism is proposed to quantitatively measure centrality using the re-defined entropy centrality model, which is based on decompositions of a graph into subgraphs and analysis on the entropy of neighbor nodes. By design, the re-defined entropy centrality which describes associations among node pairs and captures the process of influence propagation can be interpreted explained as a measure of actor potential for communication activity. We evaluate the efficiency of the proposed model by using four real-world datasets with varied sizes and densities and three artificial networks constructed by models including Barabasi-Albert, Erdos-Renyi and Watts-Stroggatz. The four datasets are Zachary’s karate club, USAir97, Collaboration network and Email network URV respectively. Extensive experimental results prove the effectiveness of the proposed method.
Highlights
A variety of problems in, e.g., management science, mathematics, computer science, chemistry, biology, sociology, epidemiology etc. deal with quantifying centrality in complex networks.numerous measures have been proposed including Freeman’s degree centrality [1], Katz’s centrality [2], Hubbell’s centrality [3], Bonacich’s eigenvector centrality designed for systematic networks [4], Bonacich and Lloyd’s alpha centrality conceptualized for asymmetric networks [5], Stephenson and Zelen’s information centrality [6], etc
Fei and Deng [49] addressed the problem of how to identify influential nodes in complex networks by using relative entropy and the TOPSIS method, which combines the advantages of existing centrality measures and demonstrated the effectiveness of the proposed method based on experimental results
If a node does not belong to the shortest path two measures are eight and nine, respectively in eigenvector centrality (EC) and CC. It can be of other node pairs, the value of betweenness centrality (BC) of that node will be zero, which is exactly the concluded that the proposed method is proved to be effective on identifying the ten most influential dilemma we face when betweenness nodes in the selected networks. centrality is utilized to identify the powerful nodes in Zachary’s karate club network and USAir network.method
Summary
A variety of problems in, e.g., management science, mathematics, computer science, chemistry, biology, sociology, epidemiology etc. deal with quantifying centrality in complex networks. Since Katz centrality [2] takes all the paths between the nodes pairs in the process of calculating influence, its high computational complexity makes it hard to be applied in large-scale networks. Bonchev [15] suggested that the structure of a given network can be treated as a consequence of an arbitrary function Inspired by this novel insight, for a given network, Shannon’s information entropy is applied to compute its structural information content and measure its uncertainty. The proposed method can be well qualified to depict the uncertain of social influence, can be useful for detecting vital nodes.
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