Emergence of Structural Disparities in theWeb of Scientific Citations

TL;DR

This paper tackles the problem of uneven scientific attention by introducing a robust, directed-graph measure of power-disparity in author-citation networks and a tractable dynamical model (DMPA) that jointly accounts for gender and institutional prestige. It demonstrates that disparities emerge from the interplay of homophily, cumulative advantage, and group size, and provides a fixed-point framework to predict the limiting power-disparity. Fitting the model to real networks across multiple fields shows that minority status alone does not determine power; rather, interaction with homophily and elite status drives persistent inequality and elitism. The work further offers field- and policy-relevant mitigation strategies, such as reducing homophily, boosting cross-group visibility, and revising exposure mechanisms in search and publishing systems, to promote a fairer and more inclusive web of science.

Abstract

Scientific attention is unevenly distributed, creating inequities in recognition and distorting access to opportunities. Using citations as a proxy, we quantify disparities in attention by gender and institutional prestige. We find that women receive systematically fewer citations than men, and that attention is increasingly concentrated among authors from elite institutions -- patterns not fully explained by underrepresentation alone. To explain these dynamics, we introduce a model of citation network growth that incorporates homophily (tendency to cite similar authors), preferential attachment (favoring highly cited authors) and group size (underrepresentation). The model shows that disparities arise not only from group size imbalances but also from cumulative advantage amplifying biased citation preferences. Importantly, increasing representation alone is often insufficient to reduce disparities. Effective strategies should also include reducing homophily, amplifying the visibility of underrepresented groups, and supporting equitable integration of newcomers. Our findings highlight the challenges of mitigating inequities in asymmetric networks like citations, where recognition flows in one direction. By making visible the mechanisms through which attention is distributed, we contribute to efforts toward a more responsible web of science that is fairer, more transparent, and more inclusive, and that better sustains innovation and knowledge production.

Figures (10)

• Figure 1: A subgraph of the Management citation network partitioned by (a) gender and (b) institutional prestige. The subgraph is constructed by sampling a linked pair of nodes and including all nodes that cite or are cited by them, along with their edges. In (a), nodes are partitioned by gender (red are women); in (b), they represent authors from top-100 vs. other institutions (Shanghai Rankings). Edges take the color of the cited author. The gender-partitioned network shows disproportionate citations to the majority male group, while the prestige-partitioned network shows disproportionate citations to the minority elite group. The lower panels plot power-disparity (Eq. \ref{['eq:power_inequality']}) over time for six large fields. Values are averaged over a four-year sliding window, with confidence intervals showing standard error. In (a), values consistently below 1 indicate women hold less power than men; in (b), values consistently above 1 indicate top-ranked institutions hold more power despite being a minority. Appendix \ref{['appn:empirical_details']} provide additional details on our datasets.
• Figure 2: Citation edge creation events considered in the proposed DMPA model. The first two events correspond to the appearance of a new node that is either cited by (Event 1) or cites an existing node. In Event 3 (densification) an existing node cites another existing node.
• Figure 3: The figures display the power-disparity values for various parameter regimes of the DMPA model. The three rows correspond to different values of the parameters $p, q$ that capture the growth dynamics of the DMPA model. The three columns correspond to three different values of the homophily parameter of the blue group: $\rho_{\mathcal{B}} = 0.1$ (heterophilic), $\rho_{\mathcal{B}} = 0.5$ (unbiased), $\rho_{\mathcal{B}} = 0.9$ (homophilic). In each subplot, lines in different colors correspond to various values of the parameter $r$ that determines the asymptotic class balance. In addition, $\delta = 10$ for each case and another figure for $\delta = 100$ (Fig. \ref{['fig:PowerInequalityTheoretical_delta100']}) is given in the Appendix \ref{['appn:additional_results']}. The power disparity values are computed using the recursive method based on Theorem \ref{['th:convergence_DMPA']} (discussed in Sec. \ref{['subsec:theoretical_analysis']}).
• Figure 4: Empirically estimated DMPA parameters for gender-partitioned (filled markers) and affiliation-partitioned (open markers) networks; exact values are listed in Table \ref{['tab:params']} (gender-partitioned networks) and Appendix Table \ref{['tab:params2']} (affiliation-partitioned networks). Subplot (a) shows that, across most fields, new nodes are more likely to cite existing authors than the reverse ($q > p$). Subplot (b) indicates that in gender-partitioned networks, minority female authors are typically heterophilic ($\rho_{\mathcal{R}} < 0.5$) while the majority male authors are homophilic ($\rho_{\mathcal{B}} > 0.5$), with Psychology and Computer Science as exceptions where disparities are smaller. In affiliation-partitioned networks the pattern is reversed: elite authors (minority) are homophilic, while non-elite authors are heterophilic. Subplot (c) shows close agreement between empirical and model-based estimates of power-disparity, confirming that the DMPA model captures how disparities emerge in real-world networks and can inform strategies for mitigation.
• Figure 5: The figures illustrate how (a) power inequality and, (b) homophily parameters of the two groups, vary with the minority group size in affiliation networks by defining "top-ranked universities" to be the top 10, 20, 50 and 100 universities in Shanghai University Rankings (SUR). We use $\delta$ from Table \ref{['tab:params']} for each field of study. The figure shows that smaller the minority group is, the more powerful it is, as a consequence of minority and majority groups being increasingly homophilic and heterophilic, respectively. This observation agrees with the predictions of the DMPA model shown in Fig. \ref{['fig:PowerInequalityTheoretical']}(a)

Theorems & Definitions (3)

• Definition 1: power-disparity
• Theorem 1: Almost sure convergence of the state in DMPA model
• Theorem 2: Convergence w.p. 1 with Martingale difference noise kushner2003