Quantifying the virality of cascades is an important question across disciplines such as the transmission of disease, the spread of information and the diffusion of innovations. An appropriate virality metric should be able to disambiguate between a shallow, broadcast-like diffusion process and a deep, multi-generational branching process. Although several valuable works have been dedicated to this field, most of them fail to take the position of the diffusion source into consideration, which makes them fall into the trap of graph isomorphism and would result in imprecise estimation of cascade virality inevitably under certain circumstances. In this letter, we propose a root-aware approach to quantifying the virality of cascades with proper consideration of the root node in a diffusion tree. With applications on synthetic and empirical cascades, we show the properties and potential utility of the proposed virality measure. Based on preferential attachment mechanisms, we further ...

中文翻译：

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病毒与广播：表征级联的病毒性和增长

量化级联的病毒性是跨学科的一个重要问题，例如疾病的传播，信息的传播和创新的传播。适当的病毒学度量应该能够消除浅的，类似于广播的扩散过程和深的，多代的分支过程之间的歧义。尽管已为此领域投入了许多有价值的工作，但其中大多数都没有考虑到扩散源的位置，这使它们陷入了图同构的陷阱，并且在某些情况下不可避免地会导致级联病毒性的不精确估计。在这封信中，我们提出了一种基于根的方法，通过适当考虑扩散树中的根节点来量化级联的病毒性。随着在合成和经验级联上的应用，我们展示了拟议的病毒测度的性质和潜在效用。基于优先的依恋机制，我们进一步...