Identifying multiple influential nodes based on region density curve in complex networks

Complex networks are ubiquitous in natural science and social science, ranging from social and information networks to technological and biological networks. The roles of nodes in networks are often distinct, the most influential nodes often play an important role in understanding the spreading process and developing strategies to control epidemic spreading or accelerating the information diffusion. Therefore, identifying the influential nodes in complex networks has great theoretical and practical significance. Some centrality indices have been proposed to identify the influential nodes in recent years, but most of the existing algorithms are only appropriate to the identifying of single influential node. Many times, spreading process is initiated by simultaneously choosing multiple nodes as the spreading sources, such as rumors, opinions, advertisements, etc. Therefore, it is necessary to develop efficient methods of identifying the multiple influential nodes in complex networks. In this paper, a method based on region density curve of networks (RDC) is proposed to identify the multiple influential nodes in complex networks. Firstly, we rearrange all nodes of network in a new sequence, and then plot the region density curve for network. Finally, we identify the multiple influential nodes based on the valley points of region density curve. Using two kinds of spreading models, we compare RDC index with other indices in different real networks, such as degree, degree discount, k-shell, betweenness and their corresponding coloring methods. The results show that the influential nodes chosen according to our method are not only dispersively distributed, but also are relatively important nodes in networks. In addition, the time complexity of our method is low because it only depends on the local information of networks.