[Purpose/Significance] Null models are crucial tools in network analysis for controlling potential confounding factors and reducing bias in research conclusions. This study aims to propose efficient and scalable randomization strategies to improve the feasibility and accuracy of null models when applied to large-scale network analyses. [Method/Process] We systematically review the foundational principles and methodologies of null models, discussing their advantages and limitations and identifying appropriate research scenarios for their application. Building upon the Fisher-Yates reshuffle algorithm, we develop a suite of efficient randomization algorithms tailored to common constraints in citation networks, such as node attributes, preferential attachment, and the exclusion of self-loops. The reshuffle strategies are further optimized by integrating a random value optimization method and a max-heap data structure, which ensures strict adherence to constraints while reducing time complexity to O(Mlog M). Furthermore, through an empirical analysis of citation preferences among journals in the library and information science field, we compare outcomes generated by different null models to demonstrate the effectiveness of the proposed approaches. [Result/Conclusion] Our findings indicate that the selection of an appropriate null model must correspond to the specific research question. This work indicates that the choice of a null model must align with the research question(s): simple models may lead to “straw man” conclusions, while overly complex models risk overfitting. Moreover, different null models can produce varying results, emphasizing the necessity for cautious model selection grounded in the research context. This work discusses three scenarios of constraints; future research directions include the examination of specialized constraints and their combinations to broaden applicability.
Chen Hongkan
,
Tian Yifan
,
Bu Yi
. Analysis and Discovery of Citation Networks in Library and Information Science Based on Null Models[J]. Library and Information Service, 2026
, 70(17)
: 97
-108
.
DOI: 10.13266/j.issn.0252-3116.2026.17.007
[1] BU Y. Understanding the citation-based impact of scientific publications through ego-centered citation networks[D]. Bloomington:Indiana University, 2020.
[2] WALTMAN L. A review of the literature on citation impact indicators[J]. Journal of informetrics, 2016, 10(2):365-391.
[3] 步一,许家伟,黄文彬.基于引文的科学文献定量评价:引文影响力指标评述[J]. 图书情报知识, 2021, 38(6):47-59.(BU Y,XU J W, HUANG W B. Citation-based quantitative evaluations on scientific publications:a literature review on citation-based impact indicator[J]. Document, Information&Knowledge, 2021,38(6):47-59.)
[4] 赵丹群,王心玥,郭磬馨.开放科学时代学术评价研究的新机遇与新挑战——从系列开放获取宣言/倡议或行动计划谈起[J]. 情报学进展, 2024, 15:247-277.(ZHAO D Q, WANG X Y, GUO Q X. New opportunities and challenges for academic evaluation research in open science era:starting from a series of open declarations/initiatives/action Plans[J]. Advances in information science, 2024, 15:247-277.)
[5] LEYDESDORFF L. Theories of citation?[J]. Scientometrics,1998, 43(1):5-25.
[6] UZZI B, MUKHERJEE S, STRINGER M, et al. Atypical combinations and scientific impact[J]. Science, 2013, 342(6157):468-472.
[7] 杨建梅.复杂网络与社会网络研究范式的比较[J]. 系统工程理论与实践, 2010(11):2046-2055.(YANG J M. Comparison of research paradigms between complex network and social network[J]. Systems engineering-theory&practice, 2010(11):2046-2055.)
[8] 陈泉,杨建梅,曾进群.零模型及其在复杂网络研究中的应用[J]. 复杂系统与复杂性科学, 2013, 10(1):8-17.(CHEN Q, YANG J M, ZENG J Q. Null model and its application in the research of complex networks[J]. Complex systems and complexity science, 2013, 10(1):8-17.)
[9] 李欢,卢罡,郭俊霞.复杂网络零模型的量化评估[J]. 计算机应用, 2015, 35(6):1560-1563.(LI H, LU G, GUO J X.Quantitative evaluation for null models of complex networks[J]. Journal of computer applications, 2015, 35(6):1560-1563.)
[10] ERDÖS P, RÉNYI A. On random graphs I[J]. Publicationes mathematicae debrecen, 1959, 6(290-297):18.
[11] WATTS D J, STROGATZ S H. Collective dynamics of‘smallworld’ networks[J]. Nature, 1998, 393(6684):440-442.
[12] BARABÁSI A L, ALBERT R. Emergence of Scaling in Random Networks[J]. Science, 1999, 286(5439):509-512.
[13] ROBINS G, PATTISON P, KALISH Y, et al. An introduction to exponential random graph(p*)models for social networks[J]. Social networks, 2007, 29(2):173-191.
[14] WANG B, BU Y, XU Y. A quantitative exploration on reasons for citing articles from the perspective of cited authors[J]. Scientometrics, 2018, 116(2):675-687.
[15] RADICCHI F, FORTUNATO S, VESPIGNANI A. Citation Networks[M]. SCHARNHORST A, BÖRNER K, VAN DEN BESSELAAR P. Models of science dynamics. Berlin:Springer,2012:233-257.
[16] HASTINGS W K. Monte Carlo sampling methods using Markov chains and their applications[J]. Biometrika, 1970, 57(1):97-109.
[17] FISHER R A, YATES F. Statistical tables for biological,agricultural and medical research[M]. New York:Hafner Publishing Company, 1953.
[18] ITZKOVITZ S, MILO R, KASHTAN N, et al. Subgraphs in random networks[J]. Physical review E, 2003, 68(2):026127.
[19] PRICE D DE S. A general theory of bibliometric and other cumulative advantage processes[J]. Journal of the American Society for Information Science, 1976, 27(5):292-306.
[20] WANG M, YU G, YU D. Measuring the preferential attachment mechanism in citation networks[J]. Physica A:statistical mechanics and its applications, 2008, 387(18):4692-4698.
[21] 梁兴堃.守正能否创新?——基于我国图情领域论文新颖性和传统性的分析[J]. 图书情报工作, 66(20):148.(LIANG X K. Novelty, conventionality, and scientific impact of papers in library and information science in China:evidence from papers in CSSCI(2000-2019)[J]. Library and information service, 66(20):148.)
[22] TEH Y W, JORDAN M I, BEAL M J, et al. Sharing clusters among related groups:hierarchical dirichlet processes[C] //Advances in Neural Information Processing Systems 17[Neural Information Processing Systems, Vancouver:NIPS, 2004:1385-1392.)
[23] HALL P. On representatives of subsets[J]. Journal of the London Mathematical Society, 1935, s1-10(1):26-30.
[24] VÁŠA F, MIŠIĆB. Null models in network neuroscience[J]. Nature reviews neuroscience, 2022, 23(8):493-504.
[25] DUPRE E, HOLDGRAF C, KARAKUZU A, et al. Beyond advertising:new infrastructures for publishing integrated research objects[J]. PLOS computational biology, 2022, 18(1):e1009651.
[26] XU J, ZHENG Z, MIN C, et al. Knowledge integration and diffusion structures of interdisciplinary research:a large-scale analysis based on propensity score matching[J]. Journal of the Association for Information Science and Technology, 2025,76(9):1210-1226.
[27] FARINE D R. A guide to null models for animal social network analysis[J]. Methods in ecology and evolution, 2017, 8(10):1309-1320.
