Real networks exhibit heterogeneous nature with nodes playing far differentroles in structure and function. To identify vital nodes is thus verysignificant, allowing us to control the outbreak of epidemics, to conductadvertisements for e-commercial products, to predict popular scientificpublications, and so on. The vital nodes identification attracts increasingattentions from both computer science and physical societies, with algorithmsranging from simply counting the immediate neighbors to complicated machinelearning and message passing approaches. In this review, we clarify theconcepts and metrics, classify the problems and methods, as well as review theimportant progresses and describe the state of the art. Furthermore, we provideextensive empirical analyses to compare well-known methods on disparate realnetworks, and highlight the future directions. In despite of the emphasis onphysics-rooted approaches, the unification of the language and comparison withcross-domain methods would trigger interdisciplinary solutions in the nearfuture.
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