Vital nodes identification in complex networks

Real networks exhibit heterogeneous nature with nodes playing far different roles in structure and function. To identify vital nodes is thus very significant, allowing us to control the outbreak of epidemics, to conduct advertisements for e-commercial products, to predict popular scientific publications, and so on. The vital nodes identification attracts increasing attentions from both computer science and physical societies, with algorithms ranging from simply counting the immediate neighbors to complicated machine learning and message passing approaches. In this review, we clarify the concepts and metrics, classify the problems and methods, as well as review the important progresses and describe the state of the art. Furthermore, we provide extensive empirical analyses to compare well-known methods on disparate real networks, and highlight the future directions. In despite of the emphasis on physics-rooted approaches, the unification of the language and comparison with cross-domain methods would trigger interdisciplinary solutions in the near future.

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Identifying influential nodes in very large-scale directed networks is a big challenge relevant to disparate applications, such as accelerating information propagation, controlling rumors and diseases, designing search engines, and understanding hierarchical organization of social and biological networks. Known methods range from node centralities, such as degree, closeness and betweenness, to diffusion-based processes, like PageRank and LeaderRank. Some of these methods already take into account the influences of a node’s neighbors but do not directly make use of the interactions among it’s neighbors. Local clustering is known to have negative impacts on the information spreading. We further show empirically that it also plays a negative role in generating local connections. Inspired by these facts, we propose a local ranking algorithm named ClusterRank, which takes into account not only the number of neighbors and the neighbors’ influences, but also the clustering coefficient. Subject to the susceptible-infected-recovered (SIR) spreading model with constant infectivity, experimental results on two directed networks, a social network extracted from delicious.com and a large-scale short-message communication network, demonstrate that the ClusterRank outperforms some benchmark algorithms such as PageRank and LeaderRank. Furthermore, ClusterRank can also be applied to undirected networks where the superiority of ClusterRank is significant compared with degree centrality and k-core decomposition. In addition, ClusterRank, only making use of local information, is much more efficient than global methods: It takes only 191 seconds for a network with about nodes, more than 15 times faster than PageRank.

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Identifying influential nodes in large-scale directed networks: the role of clustering

Information cascades are important dynamical processes in complex networks. An information cascade can describe the spreading dynamics of rumour, disease, memes, or marketing campaigns, which initially start from a node or a set of nodes in the network. If conditions are right, information cascades rapidly encompass large parts of the network, thus leading to epidemics or epidemic spreading. Certain network topologies are particularly conducive to epidemics, while others decelerate and even prohibit rapid information spreading. Here we review models that describe information cascades in complex networks, with an emphasis on the role and consequences of node centrality. In particular, we present simulation results on sample networks that reveal just how relevant the centrality of initiator nodes is on the latter development of an information cascade, and we define the spreading influence of a node as the fraction of nodes that is activated as a result of the initial activation of that node. A systemic review of existing results shows that some centrality measures, such as the degree and betweenness, are positively correlated with the spreading influence, while other centrality measures, such as eccentricity and the information index, have negative correlation. A positive correlation implies that choosing a node with the highest centrality value will activate the largest number of nodes, while a negative correlation implies that the node with the lowest centrality value will have the same effect.We discuss possible applications of these results, and we emphasize how information cascades can help us identify nodes with the highest spreading capability in complex networks.

Information cascades in complex networks

How to identify the influential spreaders in social networks is crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases and rumors, and so on. In this paper, by viewing the k-shell value of each node as its mass and the shortest path distance between two nodes as their distance, then inspired by the idea of the gravity formula, we propose a gravity centrality index to identify the influential spreaders in complex networks. The comparison between the gravity centrality index and some well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as synthetic networks. We also use the classical Susceptible–Infected–Recovered (SIR) epidemic model to verify the good performance of our method.

Identifying influential spreaders in complex networks based on gravity formula

Identifying influential spreaders is crucial for understanding and controlling spreading processes on social networks. Via assigning degree-dependent weights onto links associated with the ground node, we proposed a variant to a recent ranking algorithm named LeaderRank (Lu et al., 2011). According to the simulations on the standard SIR model, the weighted LeaderRank performs better than LeaderRank in three aspects: (i) the ability to find out more influential spreaders; (ii) the higher tolerance to noisy data; and (iii) the higher robustness to intentional attacks.

Qian Li

Papers

Identifying influential spreaders by weighted LeaderRank