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Despite a long history of use of citation count as a measure to assess theimpact or influence of a scientific paper, the evolution of follow-up workinspired by the paper and their interactions through citation links have rarelybeen explored to quantify how the paper enriches the depth and breadth of aresearch field. We propose a novel data structure, called Influence DispersionTree (IDT) to model the organization of follow-up papers and their dependenciesthrough citations. We also propose the notion of an ideal IDT for every paperand show that an ideal (highly influential) paper should increase the knowledgeof a field vertically and horizontally. Upon suitably exploring the structuralproperties of IDT, we derive a suite of metrics, namely Influence DispersionIndex (IDI), Normalized Influence Divergence (NID) to quantify the influence ofa paper. Our theoretical analysis shows that an ideal IDT configuration shouldhave equal depth and breadth (and thus minimize the NID value). We establishthe superiority of NID as a better influence measure in two experimentalsettings. First, on a large real-world bibliographic dataset, we show that NIDoutperforms raw citation count as an early predictor of the number of newcitations a paper will receive within a certain period after publication.Second, we show that NID is superior to the raw citation count at identifyingthe papers recognized as highly influential through Test of Time Award amongall their contemporary papers (published in the same venue). We conclude thatin order to quantify the influence of a paper, along with the total citationcount, one should also consider how the citing papers are organized amongthemselves to better understand the influence of a paper on the research field.For reproducibility, the code and datasets used in this study are being madeavailable to the community.

Go Wide, Go Deep: Quantifying the Impact of Scientific Papers through Influence Dispersion Trees