Path diversity improves the identification of influential spreaders

Identifying influential spreaders in complex networks is a crucial problem which relates to wide applications. Many methods based on the global information such as k-shell and PageRank have been applied to rank spreaders. However, most of related previous works overwhelmingly focus on the number of paths for propagation, while whether the paths are diverse enough is usually overlooked. Generally, the spreading ability of a node might not be strong if its propagation depends on one or two paths while the other paths are dead ends. In this Letter, we introduced the concept of path diversity and find that it can largely improve the ranking accuracy. We further propose a local method combining the information of path number and path diversity to identify influential nodes in complex networks. This method is shown to outperform many well-known methods in both undirected and directed networks. Moreover, the efficiency of our method makes it possible to be applied to very large systems. Introduction. – How to identify influential nodes in complex networks is a crucial issue since it is highly related to the information spreading and epidemic controlling [1–4]. So far, a number of centrality indices have been proposed to address this problem such as degree, betweenness [5, 6], closeness [7, 8] and eigenvector centralities [9]. Among these indices, degree centrality is a very straightforward and efficient one. However, the performance of degree centrality is not satisfying enough. Recently, Kitsak et al. [1] claimed that the location of a node in the network actually plays a more important role than the degree of it. They accordingly proposed a coarse-grained method by using k-shell decomposition to quantify a node’s influence based on the assumption that nodes in the same shell have similar influence and nodes in higher shells are likely to infect more nodes. After this, some methods are proposed to further improve the ranking performance of this network decomposition process [10, 11]. In directed networks, the ranking methods are mainly based on the iterative process. The representative methods include the well-known HITs [12] and PageRank [13], as well as some recently proposed algorithms like LeaderRank [14] and TwitterRank [15]. It has been demonstrated that these methods (a)E-mail: [email protected] outperform out-degree centrality in terms of ranking effectiveness. With big data era coming, the design of ranking algorithms on very large-scale social networks is becoming a big challenge nowadays [16]. The online social systems can have millions of users or even more. The spreader ranking algorithms will be very time-consuming if they are based on global information of the network. Therefore, the spreader ranking algorithm should be not only effective but also efficient. To solve this problem, it is better to design the ranking algorithm based on local information of the network. For example, a semi-local index by considering the second nearest neighbors is devised [17]. This index is shown to well identify influential nodes and obtain a good trade off on effectiveness and efficiency comparing with global indices. Moreover, most of previous ranking methods are designed based on the number of paths for propagation. Actually, the diversity of paths for spreading is also very important. The spreading ability of a node will be significantly lowered if many of its propagation paths overlapped. In this case, if the virus/information fails to go through the overlapped path, the following spreading of many paths will be terminated. However, this factor hasn’t been taken into account in designing the spreading