Identifying effective multiple spreaders by coloring complex networks

How to identify influential nodes in social networks is of theoretical significance, which relates to how to prevent epidemic spreading or cascading failure, how to accelerate information diffusion, and so on. In this Letter, we make an attempt to find effective multiple spreaders in complex networks by generalizing the idea of the coloring problem in graph theory to complex networks. In our method, each node in a network is colored by one kind of color and nodes with the same color are sorted into an independent set. Then, for a given centrality index, the nodes with the highest centrality in an independent set are chosen as multiple spreaders. Comparing this approach with the traditional method, in which nodes with the highest centrality from the entire network perspective are chosen, we find that our method is more effective in accelerating the spreading process and maximizing the spreading coverage than the traditional method, no matter in network models or in real social networks. Meanwhile, the low computational complexity of the coloring algorithm guarantees the potential applications of our method. Introduction. – Spreading phenomenon is ubiquitous in nature, which describes many important activities in society [1]. Examples include the propagation of infectious diseases, the dissemination of information (e.g., ideas, rumors, opinions, behaviors), and the diffusion of new technological innovations. With the advancement of complex network theory, spreading dynamics on complex networks have been intensively studied in the past decades. Many studies have revealed that the spreading process is strongly influenced by the network topologies [2, 3]. An important issue in analyzing complex networks is to identify the most influential nodes in a spreading process, which is crucial for developing efficient strategies to control epidemic spreading, or accelerate information diffusion. For this reason, more and more attentions have been paid to identify the most influential nodes in networks [4–10]. (a)[email protected] (b)[email protected] Many centrality indices have been proposed, such as, degree centrality (defined as the degree of a node) [11], betweenness centrality (measured by the number of times that all shortest paths travel through the node) [12], eigenvector centrality (defined as the dominant eigenvector of the adjacency matrix) [13], neighborhood centrality (defined as the average connectivity of all neighbors) [14] and closeness centrality (reciprocal of the sum of the lengths of the geodesic distance to every other node) [15]. Recently Kitsak et al. proposed a k -core decomposition to identify the most influential spreaders, which is found to be better than the degree centrality index in many real networks [5]. However, most of these methods measure the influence of each node from the viewpoint of entire network, which may be particularly suitable to the case in which single spreader of information is considered (i.e., only one node is selected as the initial spreader) [16, 17]. Many times, the spreading processes of rumors, ideas, opinions, or advertisements may initiate from different spreaders. In this