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Register a new userUniversality of citation distributions: towards an objective measure of scientific impact
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We study the distributions of citations received by a single publication within several disciplines, spanning broad areas of science. We show that the probability that an article is cited $c$ times has large variations between different disciplines, but all distributions are rescaled on a universal curve when the relative indicator $c_f=c/c_0$ is considered, where $c_0$ is the average number of citations per article for the discipline. In addition we show that the same universal behavior occurs when citation distributions of articles published in the same field, but in different years, are compared. These findings provide a strong validation of $c_f$ as an unbiased indicator for citation performance across disciplines and years. Based on this indicator, we introduce a generalization of the h-index suitable for comparing scientists working in different fields.
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Whether a scientific paper is cited is related not only to the influence of its author(s) but also to the journal publishing it. Scientists, either proficient or tender, usually submit their most important work to prestigious journals which receives higher citations than the ordinary. How to model the role of scientific journals in citation dynamics is of great importance. In this paper we address this issue through two folds. One is the intrinsic heterogeneity of a paper determined by the impact factor of the journal publishing it. The other is the mechanism of a paper being cited which depends on its citations and prestige. We develop a model for citation networks via an intrinsic nodal weight function and an intuitive ageing mechanism. The nodes weight is drawn from the distribution of impact factors of journals and the ageing transition is a function of the citation and the prestige. The node-degree distribution of resulting networks shows nonuniversal scaling: the distribution decays exponentially for small degree and has a power-law tail for large degree, hence the dual behaviour. The higher the impact factor of the journal, the larger the tipping point and the smaller the power exponent that are obtained. With the increase of the journal rank, this phenomenon will fade and evolve to pure power laws.
We discuss microscopic mechanisms of complex network growth, with the special emphasis of how these mechanisms can be evaluated from the measurements on real networks. As an example we consider the network of citations to scientific papers. Contrary to common belief that its growth is determined by the linear preferential attachment, our microscopic measurements show that it is driven by the nonlinear autocatalytic growth. This invalidates the scale-free hypothesis for the citation network. The nonlinearity is responsible for a dramatic dynamical phase transition: while the citation lifetime of majority of papers is 6-10 years, the highly-cited papers have practically infinite lifetime.
Structural inequalities persist in society, conferring systematic advantages to some people at the expense of others, for example, by giving them substantially more influence and opportunities. Using bibliometric data about authors of scientific publications, we identify two types of structural inequalities in scientific citations. First, female authors, who represent a minority of researchers, receive less recognition for their work (through citations) relative to male authors; second, authors affiliated with top-ranked institutions, who are also a minority, receive substantially more recognition compared to other authors. We present a model for the growth of directed citation networks and show that citations disparities arise from individual preferences to cite authors from the same group (homophily), highly cited or active authors (preferential attachment), as well as the size of the group and how frequently new authors join. We analyze the model and show that its predictions align well with real-world observations. Our theoretical and empirical analysis also suggests potential strategies to mitigate structural inequalities in science. In particular, we find that merely increasing the minority group size does little to narrow the disparities. Instead, reducing the homophily of each group, frequently adding new authors to a research field while providing them an accessible platform among existing, established authors, together with balanced group sizes can have the largest impact on reducing inequality. Our work highlights additional complexities of mitigating structural disparities stemming from asymmetric relations (e.g., directed citations) compared to symmetric relations (e.g., collaborations).
Universality or near-universality of citation distributions was found empirically a decade ago but its theoretical justification has been lacking so far. Here, we systematically study citation distributions for different disciplines in order to characterize this putative universality and to understand it theoretically. Using our calibrated model of citation dynamics, we find microscopic explanation of the universality of citation distributions and explain deviations therefrom. We demonstrate that citation count of the paper is determined, on the one hand, by its fitness -- the attribute which, for most papers, is set at the moment of publication. The fitness distributions for different disciplines are very similar and can be approximated by the log-normal distribution. On another hand, citation dynamics of a paper is related to the mechanism by which the knowledge about it spreads in the scientific community. This viral propagation is non-universal and discipline-specific. Thus, universality of citation distributions traces its origin to the fitness distribution, while deviations from universality are associated with the discipline-specific citation dynamics of papers.
In citation networks, the activity of papers usually decreases with age and dormant papers may be discovered and become fashionable again. To model this phenomenon, a competition mechanism is suggested which incorporates two factors: vigorousness and dormancy. Based on this idea, a citation network model is proposed, in which a node has two discrete stage: vigorous and dormant. Vigorous nodes can be deactivated and dormant nodes may be activated and become vigorous. The evolution of the network couples addition of new nodes and state transitions of old ones. Both analytical calculation and numerical simulation show that the degree distribution of nodes in generated networks displays a good right-skewed behavior. Particularly, scale-free networks are obtained as the deactivated vertex is target selected and exponential networks are realized for the random-selected case. Moreover, the measurement of four real-world citation networks achieves a good agreement with the stochastic model.
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