基于区域密度曲线识别网络上的多影响力节点

复杂网络多影响力节点的识别可以帮助理解网络的结构和功能，具有重要的理论意义和应用价值.本文提出一种基于网络区域密度曲线的多影响力节点的识别方法.应用两种不同的传播模型，在不同网络上与其他中心性指标进行了比较.结果表明，基于区域密度曲线的识别方法能够更好地识别网络中的多影响力节点，选中的影响力节点之间的分布较为分散，自身也比较重要.本文所提方法是基于网络的局部信息，计算的时间复杂度较低.

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.