An improvement method for degree and its extending centralities in directed networks

Vital nodes identification in social networks keeps attracting lots of attention in recent years because of its great theoretical and practical significance for many applications. Degree centrality is one of the most efficient neighborhood-based metrics and has been widely used because of its simplicity and low computation complexity. Many other centralities derived from degree have been proposed to try to further improve the accuracy on ranking performance by extending the coverage area of neighbors. But a common problem of degree and its extensional centralities is that the directivity of edges between nodes is not considered. In directed network, nodes’ importance are not only related with their neighbor numbers but also related with the relationships between the nodes and their neighbors. In this paper, we propose a modification method with an adjustable parameter α on degree to improve its ranking accuracy in directed networks. This method redefines the degree of a node by separately taking into account its out-degree and in-degree and uses parameter α to flexibly set the relative weights between out-degree and in-degree when evaluating nodes’ importance in different scenes, which can effectively avoid the situation that too many neighbors from one direction could lead to extreme high value of centrality. We also apply this method on another two centralities: semi-local and k-hop, and for the two centralities that considering multi-step neighbors, the corresponding improvement centralities could eliminate the irrelevant multi-step neighbors when evaluating nodes’ importance. Experimental results in 3 real social networks and 1 artificial network indicate that, setting α to be appropriate value the improvement centralities can better estimate nodes’ connection abilities, propagation abilities and immunization abilities while keeping the same compute complexity with the corresponding original centralities, especially in the network with low percentage of bidirectional edges. Moreover, the improvement method proposed in this paper also can be applied to other centralities, such as eigenvector centrality, neighborhood centrality, Exdegree centrality and percolation based centrality, to improve their performances in directed networks.