Publications

Showing 56 of 56 publications

Introduction to structural causal models in science studies

Thomas Klebel, Vincent Antonio Traag

Quantitative Science Studies, 159–178 2026 Journal DOI SocArXiv
Sound causal inference is crucial for advancing the study of science. Incorrectly interpreting predictive effects as causal might lead to ineffective or even detrimental policy recommendations. Many publications in science studies lack appropriate methods to substantiate causal claims. We here provide an introduction to structural causal models for science studies. Structural causal models, usually represented in a graphical form, allow researchers to make their causal assumptions transparent and provide a foundation for causal inference. We illustrate how to use structural causal models to conduct causal inference using regression models based on simulated data of a hypothetical structural causal model of Open Science. The graphical representation of structural causal models allows researchers to clearly communicate their assumptions and findings, thereby fostering further discussion. We hope our introduction helps more researchers in science studies to consider causality explicitly.

Heuristic and exact modularity optimization with size-constrained communities

Filipi N. Silva, Samin Aref, Vincent Antonio Traag, Santo Fortunato

Physical Review E 114(4):044314 2026 Journal DOI arXiv
When searching for communities in networks, domain experts may have some prior expectations about the size of communities. Yet, community detection methods normally do not optimize communities under cluster size constraints. Multi-resolution techniques allow users to indirectly control the average community size through changing a resolution parameter, but this practice does not control the size of individual communities. We here study the problem of size-constrained community detection, where the size of all communities is limited to a user-specified range of values, in the context of modularity optimization. We propose a heuristic for modularity optimization under community size constraints. To demonstrate the reliability of our proposed heuristic, we also formulate an exact integer optimization model and use its results as a baseline. Our analysis based on synthetic benchmarks and real networks demonstrate the issues with the currently common practice of changing resolution parameters and reveal the advantages of the proposed methods as a principled way of obtaining size-constrained communities. The proposed method is publicly available in the Python Leiden algorithm package.

igraph 1.0 enables fast and robust network analysis across programming languages

Michael Antonov, Gábor Csárdi, Szabolcs Horvát, Kirill Müller, Tamás Nepusz, Daniel Noom, Maëlle Salmon, Vincent Antonio Traag, Brooke Foucault Welles, Fabio Zanini

PLOS One 21(8):e0355108 2026 Journal DOI arXiv
Networks or graphs are widely used across the sciences to represent relationships of many kinds. The igraph (https://igraph.org) software library supports graph construction, analysis, and visualisation, combining fast and robust performance with a low entry barrier. igraph pairs a fast core written in C with beginner-friendly interfaces in Python, R, and Mathematica. After twenty years of development, igraph 1.0 has been released, enabling public access to a robust and stable network analysis with over a million monthly downloads. Thanks to its cross-language design, igraph delivers both speed and flexibility: it can handle billions of edges, supports interactive plotting, integrates with notebooks, facilitates conversions to and from other network libraries, includes a rich library of graph layout and community detection algorithms, and has a detailed documentation including non-English translations. Modern testing features such as continuous integration, address sanitizers, stricter typing, and memory-managed vectors have also increased robustness. Hundreds of bug reports have been fixed and a community forum has been opened to connect users and developers. Specific effort has been made to broaden use and community participation by women, non-binary people, and other demographic groups typically underrepresented in open source software.

How do grant application criteria influence gender differences in research funding?

Vincent Traag, Esraa Aldalooj, Gert V. Balling, Henrik Barslund Fosse, Clemens-Hugo Schally, Antonio Campello, Rebecca Fawcett, Saioa Lopez, Emer Brady, Kwun-Hang Lai, Helen Buckley Woods, Matt Thakur

Research on Research Institute, Working Paper No. 22 2026 Preprint Figshare
Despite shifting demographics at the student level, gender differences remain pronounced across global academia, impacting authorship, institutional rank, productivity, and citation rates. Access to research funding is a critical mechanism in career advancement, yet how grant evaluation criteria directly influence these gender differences remains causally unclear. This working paper presents the results of a large-scale, international multi-funder analysis conducted under the CRITERIA project by the Research on Research Institute (RoRI). The study examines gender differences in research funding using observational data from over 70,000 applications in 43 funding programmes from 8 funders across the globe. By analyzing diverse selection processes across different global contexts, the study explores how specific grant evaluation criteria and procedural mechanisms relate to funding outcomes for different genders.

Persistent geographical biases in global scientific collaboration and citations

Leyan Wu, Yong Huang, Wei Lu, Akrati Saxena, Vincent Antonio Traag

arXiv:2604.01602 2026 Preprint arXiv
Scientific knowledge flows enable cumulative progress by connecting researchers across disciplines, institutions, and countries. Yet it remains unclear how geography and national structures continue to shape these exchanges in an increasingly connected world. Using a large-scale bibliometric dataset from OpenAlex, which covers 39.35 million publications across 95 countries and 3,794 cities between 2000 and 2022, we examine global knowledge diffusion through two complementary channels: co-authorship and citation. We find that the constraining effect of geographic distance on collaboration has not diminished over time but has instead intensified, suggesting persistent structural or institutional barriers. Citation flows, by contrast, are less sensitive to spatial proximity, indicating that intellectual influence may diffuse more freely across borders. At the country level, research networks exhibit strong domestic preferences and a shared citation orientation toward the United States. China, while increasingly favored as a collaboration partner by other countries, continues to be systematically undercited within global citation flows. International mobility increases researchers' collaboration with scholars in their host country but has limited effects on citation flows. These results highlight the structural persistence of spatial and country biases in global science, with implications for equitable participation and recognition across regions.

Targeted funding and changing research landscapes

Vincent Traag, Emer Brady, Cristina Simón-Martínez, Ismael Rafols, Jesper Schneider

Research on Research Institute, Working Paper No. 18 2026 Preprint Figshare
As demands intensify for research to address societal missions or challenges such as climate change, ageing or pandemic preparedness, research funders have developed funding instruments targeted at specific topics. We asked: does targeted funding shape the overall research landscape and what researchers work on in the longer term? This study examines this question by analysing targeted funding programmes from the Research Council of Norway (RCN) and the Swiss National Science Foundation (SNSF), comparing them with non-targeted (response-mode) funding.

The Different Voices of Scholarly Publication Communication on Twitter: Analysis of Chinese-language Tweets

Dongyi Wang, Vincent Antonio Traag, Rodrigo Costas

SSRN 2026 Preprint SSRN
Although science communication on Twitter, now also known as X, is predominantly conducted in English, Chinese-speaking users constitute a significant portion of Twitter/X users. Therefore, the study of science communication in Chinese-language, especially during the surge of Chinese users on Twitter/X during the COVID-19 pandemic, is relevant. This study collects data on scientific papers mentioned in Chinese-language tweets based on Altmetric, distinguishing between Simplified and Traditional Chinese. The Chinese-language tweets were compared with English-language tweets across three dimensions: characteristics of the papers mentioned, content characteristics of the tweets, and the association of the tweets. Unlike most English-speaking users who primarily focus on papers published in high-impact journals, Chinese users are less focused on high-association journals, and also mention papers from local sources. In terms of content, Chinese-language tweets tend to be more emotional and original compared to English-language tweets. However, although English is the dominant language on Twitter/X, Chinese-language tweets are more likely to attract user engagement on average.

Science of science: citation models and research evaluation

V A Traag

In: Taha Yasseri (ed.), Handbook of computational social science, pp. 780–808. Edward Elgar Publishing 2025 Book chapter DOI arXiv
Citations in science are being studied from several perspectives, among which approaches such as scientometrics and science of science. In this chapter I briefly review some of the literature on citations, citation distributions and models of citations. These citations feature prominently in another part of the literature which is dealing with research evaluation and the role of metrics and indicators in that process. Here I briefly review part of the discussion in research evaluation. This also touches on the subject of how citations relate to peer review. Finally, I conclude by trying to integrate the two literatures. The fundamental problem in research evaluation is that research quality is unobservable. This has consequences for conclusions that we can draw from quantitative studies of citations and citation models. The term “indicators” is a relevant concept in this context, which I try to clarify. Causality is important for properly understanding indicators, especially when indicators are used in practice: when we act on indicators, we enter causal territory. Even when an indicator might have been valid, through its very use, the consequences of its use may invalidate it. By combining citation models with proper causal reasoning and acknowledging the fundamental problem about unobservable research quality, we may hope to make progress.

The Matthew effect and early-career setbacks in research funding—a replication study

Vincent Antonio Traag, Emer Brady, Philippe Vincent-Lamarre, Flavie Bidel, Cindy Lopes-Bento, Jens Peter Andersen, Carter Bloch

eLife 14 2025 Journal DOI Figshare
Research funding plays an important role in academic careers. Previous research showed that researchers who obtain early-career funding are more likely to obtain later-career funding, whereas researchers who do not obtain early-career funding show a higher citation impact when reapplying for later-career funding. We replicate the so-called Matthew effect and early-career setback effect across fourteen different funding programmes from six research funders across Europe and North America. Earlier studies rely on studying applicants close to the funding line, and the inferred effects are limited to this “grey zone”. We study the robustness and generalisability of both effects to the whole population, beyond applicants in the “grey zone”. We find that the Matthew effect replicates, is robust across funders and model specifications, and generalises to the whole population. The early-career setback effect also replicates, but is not robust across funders and model specifications, and does not generalise to the whole population. We suggest that the early-career setback observation is due to a selection effect of unfunded applicants being particularly more likely to reapply later if they have a high citation impact. To address the Matthew effect, research funders and research organisations could consider stimulating promising rejected applicants to reapply. Another possibility would be to diminish potential deleterious effects of funding on academic careers.

Contested Citations: The Role of Open Access Publications in Wikipedia's Scientific Disputes

Puyu Yang, Vincent Antonio Traag, Rodrigo Costas, Giovanni Colavizza

arXiv:2510.14071 2025 Preprint DOI arXiv
Wikipedia is one of the largest online encyclopedias, which relies on scientific publications as authoritative sources. The increasing prevalence of open access (OA) publishing has expanded the public availability of scientific knowledge; however, its impact on the dynamics of knowledge contestation within collaborative environments such as Wikipedia remains underexplored. To address this gap, we analyze a large-scale dataset that combines Wikipedia edit histories with metadata from scientific publications cited in disputed Wikipedia articles. Our study investigates the characteristics of scientific publications involved in disputes and examines whether OA articles are more likely to be contested than paywalled ones. We find that scientific disputes on Wikipedia are more frequent in the social sciences and humanities, where topics often involve social values and interpretative variability. Publications with higher citation counts and publications in high-impact journals are more likely to be involved in disputes. OA publications are significantly more likely to be involved in disputes and tend to be contested sooner after publication than paywalled articles. This pattern suggests that increased accessibility accelerates both engagement and scrutiny. The relationship between OA status and dispute involvement also varies across disciplines, reflecting differences in Wikipedia editorial practices and norms. These findings highlight the dual role of OA in both expanding access to scientific knowledge and increasing its visibility in contexts of public negotiation and debate. This study contributes to a broader understanding of how scientific knowledge is collaboratively constructed and contested on open platforms, offering insights for research on open science, scholarly communication, and digital knowledge governance.

Mapping the interaction between science and misinformation in COVID-19 tweets

Lucila G. Alvarez-Zuzek, Juan P. Bascur, Anna Bertani, Riccardo Gallotti, Vincent A. Traag

arXiv:2507.01481 2025 Preprint DOI arXiv
During the COVID-19 pandemic, scientific understanding related to the topic evolved rapidly. Along with scientific information being discussed widely, a large circulation of false information, labelled an infodemic by the WHO, emerged. Here, we study the interaction between misinformation and science on Twitter (now X) during the COVID-19 pandemic. We built a comprehensive database of ~407M COVID-19 related tweets and classified the reliability of URLs in the tweets based on Media Bias/Fact Check. In addition, we use Altmetric data to see whether a tweet refers to a scientific publication. We find that many users find that many users share both scientific and unreliable content; out of the ~1.2M users who share science, 45% also share unreliable content. Publications that are more frequently shared by users who also share unreliable content are more likely to be preprints, slightly more often retracted, have fewer citations, and are published in lower-impact journals on average. Our findings suggest that misinformation is not related to a “deficit” of science. In addition, our findings raise some critical questions about certain open science practices and their potential for misuse. Given the fundamental opposition between science and misinformation, our findings highlight the necessity for proactive scientific engagement on social media platforms to counter false narratives during global crises.

Fostering trustworthy information: countering disinformation when there are no bare facts

Marcel Boumans, Joras Ferwerda, Maya J. Goldenberg, Sabina Leonelli, Federica Russo, Vincent Antonio Traag, Arjan Wardekker

Royal Society Open Science 12(6):250654 2025 Journal DOI SSRN
At a time when the dissemination of online information is synonymous with an abundance of disinformation and misinformation, it is important to extend our reflection beyond debunking and fact-checking. In this article, we consider the cases of (dis-, mis- and mal-)information regarding scientific results. We argue that countering misinformation requires a better understanding of the root cause of the problem. We believe the root cause is trust rather than truth. We argue that trust should be approached from a distinct social epistemological perspective that recognizes differences between data and facts and that treats trust as part of the scientific process and as part of the way publics interpret and use scientific information.

Metrics and peer review agreement at the institutional level

V. A. Traag, M. Malgarini, S. Sarlo

Quantitative Science Studies 6:328–350 2025 Journal DOI arXiv
In recent decades, many countries have started funding academic institutions based on the evaluation of their scientific performance. Postpublication peer review is often used in this context. Bibliometric indicators have been suggested as an alternative to peer review. A recurrent question is whether peer review and metrics yield similar outcomes. In this paper, we study this question based on a sample of publications submitted to the national Italian research assessment exercise (2011–2014). In particular, we study the agreement between peer review and metrics at the institutional level, and compare this to the internal agreement of peer review. We base our analysis on a hierarchical Bayesian model using cross-validation. We find that the level of agreement is higher at the institutional level than at the publication level. Overall, the agreement between metrics and peer review is low, but on par with the similarly low internal agreement among two reviewers for certain fields of science. The low agreement between metrics and peer review is no reason for rejecting the use of metrics for some fields in the Italian national research assessment exercise. Our results provide input to the broader discussion of research evaluation, in which other factors also play an important role.

The academic impact of Open Science: a scoping review

Thomas Klebel, Vincent Antonio Traag, Ioanna Grypari, Lennart Stoy, Tony Ross-Hellauer

Royal Society Open Science 12(3):241248 2025 Journal DOI SocArXiv
Open Science seeks to make research processes and outputs more accessible, transparent and inclusive, ensuring that scientific findings can be freely shared, scrutinized and built upon by researchers and others. To date, there has been no systematic synthesis of the extent to which Open Science (OS) reaches these aims. We use the PRISMA scoping review methodology to partially address this gap, scoping evidence on the academic (but not societal or economic) impacts of OS. We identify 485 studies related to all aspects of OS, including Open Access (OA), Open/FAIR Data (OFD), Open Code/Software, Open Evaluation and Citizen Science (CS). Analysing and synthesizing findings, we show that the majority of studies investigated effects of OA, CS and OFD. Key areas of impact studied are citations, quality, efficiency, equity, reuse, ethics and reproducibility, with most studies reporting positive or at least mixed impacts. However, we also identified significant unintended negative impacts, especially those regarding equity, diversity and inclusion. Overall, the main barrier to academic impact of OS is lack of skills, resources and infrastructure to effectively re-use and build on existing research. Building on this synthesis, we identify gaps within this literature and draw implications for future research and policy.

Perspectives on scientific error

D. van Ravenzwaaij, M. Bakker, R. Heesen, F. Romero, N. van Dongen, S. Crüwell, S. M. Field, L. Held, M. R. Munafò, M. M. Pittelkow, L. Tiokhin, V. A. Traag, O. R. van den Akker, A. E. van ‘t Veer, E. J. Wagenmakers

Royal Society Open Science 10(7):230448 2023 Journal DOI PsyArXiv
Theoretical arguments and empirical investigations indicate that a high proportion of published findings do not replicate and are likely false. The current position paper provides a broad perspective on scientific error, which may lead to replication failures. This broad perspective focuses on reform history and on opportunities for future reform. We organize our perspective along four main themes: institutional reform, methodological reform, statistical reform and publishing reform. For each theme, we illustrate potential errors by narrating the story of a fictional researcher during the research cycle. We discuss future opportunities for reform. The resulting agenda provides a resource to usher in an era that is marked by a research culture that is less error-prone and a scientific publication landscape with fewer spurious findings.

IGraph/M: graph theory and network analysis for Mathematica

Szabolcs Horvát, Jakub Podkalicki, Gábor Csárdi, Tamás Nepusz, Vincent Antonio Traag, Fabio Zanini, Daniel Noom

Journal of Open Source Software 8(81):4899 2023 Journal DOI arXiv
IGraph/M is an efficient general purpose graph theory and network analysis package for Mathematica. IGraph/M serves as the Wolfram Language interfaces to the igraph C library, and also provides several unique pieces of functionality not yet present in igraph, but made possible by combining its capabilities with Mathematica's. The package is designed to support both graph theoretical research as well as the analysis of large-scale empirical networks.

Large network community detection by fast label propagation

Vincent A Traag, Lovro Šubelj

Scientific Reports 13:2701 2022 Journal DOI arXiv
Many networks exhibit some community structure. There exists a wide variety of approaches to detect communities in networks, each offering different interpretations and associated algorithms. For large networks, there is the additional requirement of speed. In this context, the so-called label propagation algorithm (LPA) was proposed, which runs in near-linear time. In partitions uncovered by LPA, each node is ensured to have most links to its assigned community. We here propose a fast variant of LPA (FLPA) that is based on processing a queue of nodes whose neighbourhood recently changed. We test FLPA exhaustively on benchmark networks and empirical networks, finding that it can run up to 700 times faster than LPA. In partitions found by FLPA, we prove that each node is again guaranteed to have most links to its assigned community. Our results show that FLPA is generally preferable to LPA.

Causal foundations of bias, disparity and fairness

V A Traag, L Waltman

arXiv:2207.13665 2022 Preprint arXiv
The study of biases, such as gender or racial biases, is an important topic in the social and behavioural sciences. However, the literature does not always clearly define the concept. Definitions of bias are often ambiguous or not provided at all. To study biases in a precise manner, it is important to have a well-defined concept of bias. We propose to define bias as a direct causal effect that is unjustified. We propose to define the closely related concept of disparity as a direct or indirect causal effect that includes a bias. Our proposed definitions can be used to study biases and disparities in a more rigorous and systematic way. We compare our definitions of bias and disparity with various criteria of fairness introduced in the artificial intelligence literature. In addition, we discuss how our definitions relate to discrimination. We illustrate our definitions of bias and disparity in two case studies, focusing on gender bias in science and racial bias in police shootings. Our proposed definitions aim to contribute to a better appreciation of the causal intricacies of studies of biases and disparities. We hope that this will also promote an improved understanding of the policy implications of such studies.

Use of the journal impact factor for assessing individual articles: Statistically flawed or not?

L. Waltman, V. A. Traag

F1000Research 9(366) 2021 Journal DOI arXiv Slides
Most scientometricians reject the use of the journal impact factor for assessing individual articles and their authors. The well-known San Francisco Declaration on Research Assessment also strongly objects against this way of using the impact factor. Arguments against the use of the impact factor at the level of individual articles are often based on statistical considerations. The skewness of journal citation distributions typically plays a central role in these arguments. We present a theoretical analysis of statistical arguments against the use of the impact factor at the level of individual articles. Our analysis shows that these arguments do not support the conclusion that the impact factor should not be used for assessing individual articles. In fact, our computer simulations demonstrate the possibility that the impact factor is a more accurate indicator of the value of an article than the number of citations the article has received. It is important to critically discuss the dominant role of the impact factor in research evaluations, but the discussion should not be based on misplaced statistical arguments. Instead, the primary focus should be on the socio-technical implications of the use of the impact factor.

Investigating scientific mobility in co-authorship networks using multilayer temporal motifs

Hanjo D. Boekhout, Vincent A. Traag, Frank W. Takes

Network Science 9(3):354–386 2021 Journal DOI
This paper introduces a framework for understanding complex temporal interaction patterns in large-scale scientific collaboration networks. In particular, we investigate how two key concepts in science studies, scientific collaboration and scientific mobility, are related and possibly differ between fields. We do so by analyzing multilayer temporal motifs: small recurring configurations of nodes and edges. Driven by the problem that many papers share the same publication year, we first provide a methodological contribution: an efficient counting algorithm for multilayer temporal motifs with concurrent edges. Next, we introduce a systematic categorization of the multilayer temporal motifs, such that each category reflects a pattern of behavior relevant to scientific collaboration and mobility. Here, a key question concerns the causal direction: does mobility lead to collaboration or vice versa? Applying this framework to scientific collaboration networks extracted from Web of Science (WoS) consisting of up to 7.7 million nodes (authors) and 94 million edges (collaborations), we find that international collaboration and international mobility reciprocally influence one another. Additionally, we find that Social sciences & Humanities (SSH) scholars co-author to a greater extent with authors at a distance, while Mathematics & Computer science (M&C) scholars tend to continue to collaborate within the established knowledge network and organization.

Inferring the causal effect of journals on citations

Vincent Antonio Traag

Quantitative Science Studies 2(2):496–504 2021 Journal DOI arXiv PDF Slides
Articles in high-impact journals are, on average, more frequently cited. But are they cited more often because those articles are somehow more “citable”? Or are they cited more often simply because they are published in a high-impact journal? Although some evidence suggests the latter, the causal relationship is not clear. We here compare citations of preprints to citations of the published version to uncover the causal mechanism. We build on an earlier model of citation dynamics to infer the causal effect of journals on citations. We find that high-impact journals select articles that tend to attract more citations. At the same time, we find that high-impact journals augment the citation rate of published articles. Our results yield a deeper understanding of the role of journals in the research system. The use of journal metrics in research evaluation has been increasingly criticized in recent years and article-level citations are sometimes suggested as an alternative. Our results show that removing impact factors from evaluation does not negate the influence of journals. This insight has important implications for changing practices of research evaluation.

Italian sociologists: a community of disconnected groups

Aliakbar Akbaritabar, Vincent Antonio Traag, Alberto Caimo, Flaminio Squazzoni

Scientometrics 124:2361–2382 2020 Journal DOI
Examining coauthorship networks is key to study scientific collaboration patterns and structural characteristics of scientific communities. Here, we studied coauthorship networks of sociologists in Italy, using temporal and multi-level quantitative analysis. By looking at publications indexed in Scopus, we detected research communities among Italian sociologists. We found that Italian sociologists are fractured in many disconnected groups. The giant connected component could be split into five main groups with a mix of three main disciplinary topics: sociology of culture and communication (present in two groups), economic sociology (present in three groups) and general sociology (present in three groups). By applying an exponential random graph model, we found that collaboration ties are mainly driven by the research interests of these groups. Other factors, such as preferential attachment, gender and affiliation homophily are also important, but the effect of gender fades away once other factors are controlled for. Our research shows the advantages of multi-level and temporal network analysis in revealing the complexity of scientific collaboration patterns.

A scientometric overview of CORD-19

Giovanni Colavizza, Rodrigo Costas, Vincent A. Traag, Nees Jan van Eck, Thed van Leeuwen, Ludo Waltman

PLOS ONE 16(1):e0244839 2020 Journal DOI bioRxiv
As the COVID-19 pandemic unfolds, researchers from all disciplines are coming together and contributing their expertise. CORD-19, a dataset of COVID-19 and coronavirus publications, has been made available alongside calls to help mine the information it contains and to create tools to search it more effectively. We analyse the delineation of the publications included in CORD-19 from a scientometric perspective. Based on a comparison to the Web of Science database, we find that CORD-19 provides an almost complete coverage of research on COVID-19 and coronaviruses. CORD-19 contains not only research that deals directly with COVID-19 and coronaviruses, but also research on viruses in general. Publications from CORD-19 focus mostly on a few well-defined research areas, in particular: coronaviruses (primarily SARS-CoV, MERS-CoV and SARS-CoV-2); public health and viral epidemics; molecular biology of viruses; influenza and other families of viruses; immunology and antivirals; clinical medicine. CORD-19 publications that appeared in 2020, especially editorials and letters, are disproportionately popular on social media. While we fully endorse the CORD-19 initiative, it is important to be aware that CORD-19 extends beyond research on COVID-19 and coronaviruses.

Intermediacy of publications

Lovro Šubelj, Ludo Waltman, Vincent Antonio Traag, Nees Jan van Eck

Royal Society open science 7(1):190207 2020 Journal DOI arXiv PDF
Citation networks of scientific publications offer fundamental insights into the structure and development of scientific knowledge. We propose a new measure, called intermediacy, for tracing the historical development of scientific knowledge. Given two publications, an older and a more recent one, intermediacy identifies publications that seem to play a major role in the historical development from the older to the more recent publication. The identified publications are important in connecting the older and the more recent publication in the citation network. After providing a formal definition of intermediacy, we study its mathematical properties. We then present two empirical case studies, one tracing historical developments at the interface between the community detection literature and the scientometric literature and one examining the development of the literature on peer review. We show both conceptually and empirically how intermediacy differs from main path analysis, which is the most popular approach for tracing historical developments in citation networks. Main path analysis tends to favour longer paths over shorter ones, whereas intermediacy has the opposite tendency. Compared to the main path analysis, we conclude that intermediacy offers a more principled approach for tracing the historical development of scientific knowledge.

Systematic analysis of agreement between metrics and peer review in the UK REF

V. A. Traag, L. Waltman

Palgrave Communications 5(1):29 2019 Journal DOI arXiv PDF Slides
When performing a national research assessment, some countries rely on citation metrics whereas others, such as the UK, primarily use peer review. In the influential Metric Tide report, a low agreement between metrics and peer review in the UK Research Excellence Framework (REF) was found. However, earlier studies observed much higher agreement between metrics and peer review in the REF and argued in favour of using metrics. This shows that there is considerable ambiguity in the discussion on agreement between metrics and peer review. We provide clarity in this discussion by considering four important points: (1) the level of aggregation of the analysis; (2) the use of either a size-dependent or a size-independent perspective; (3) the suitability of different measures of agreement; and (4) the uncertainty in peer review. In the context of the REF, we argue that agreement between metrics and peer review should be assessed at the institutional level rather than at the publication level. Both a size-dependent and a size-independent perspective are relevant in the REF. The interpretation of correlations may be problematic and as an alternative we therefore use measures of agreement that are based on the absolute or relative differences between metrics and peer review. To get an idea of the uncertainty in peer review, we rely on a model to bootstrap peer review outcomes. We conclude that particularly in Physics, Clinical Medicine, and Public Health, metrics agree relatively well with peer review and may offer an alternative to peer review.

From the margin to the centre? A relational analysis of discursive contention in the minority integration debate in the Low Countries

Anna Berbers, Justus Uitermark, Vincent A Traag, Leen D'Haenens

International Communication Gazette 82(8):705–725 2019 Journal DOI
Minority integration is a highly contested topic in public debates, and assimilationist actors appear to have gained discursive ground. However, it remains difficult to accurately depict how power relations in debates change and evolve. In this study, the public debates on minority integration in Flanders and the Netherlands between 2006 and 2012 are studied to ascertain changing power relations. We use a relational method to identify clusters formed through discursive contention and study polarization in the debates as well as several aspects of discursive power between and within clusters. In the Netherlands, a pattern identified in earlier research is reproduced, whereby a unified but small cluster of assimilationists with strong discursive leaders is able to dominate the debate on integration. In Flanders, group consolidation is too low, so the clusters cannot be viewed as cohesive groups. Another difference to the Dutch debate is that the volume of opinion articles is much lower and the actors in the Flemish debate are more often foreign opinion leaders. We conclude that the assimilationists have increased their discursive power in the Dutch debate, while the anti-assimilationists have lost power. The stark contrast between the Dutch and Flemish discursive landscape highlights the need for more research on the causal mechanism behind discursive struggles.

From Louvain to Leiden: guaranteeing well-connected communities

Vincent Antonio Traag, Ludo Waltman, Nees Jan van Eck

Scientific Reports 9(1):5233 2019 Journal DOI arXiv PDF
Community detection is often used to understand the structure of large and complex networks. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. To address this problem, we introduce the Leiden algorithm. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. In addition, we prove that, when the Leiden algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are locally optimally assigned. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees.

Partitioning signed networks

Vincent Antonio Traag, Patrick Doreian, Andrej Mrvar

In: Patrick Doreian, Vladimir Batagelj, Anuška Ferligoj (eds.), Advances in network clustering and blockmodeling. Wiley-Interscience 2018 Book chapter DOI arXiv PDF
This chapter is concerned with signed networks, where each link is associated with either a positive (+) or negative sign (-). Blockmodeling, as a way of partitioning social networks, started with a clear substantive rationale expressed in terms of social roles. However, the availability of algorithms for partitioning (unsigned) networks, based on ideas of structural equivalence, led to a rather mechanical application to simply partition social networks with a subsequent ad hoc interpretation of what was identified. Consistent with this, the approach known as structural balance theory has a clear substantive foundation. The chapter briefly reviews the basics of balance theory as it connects directly to partitioning signed social networks. It then reviews some methods for partitioning networks in practice, and examines how they connect to balance theory. The chapter also briefly explores how structural balance evolves through time in an empirical example of international alliances and conflict.

Modelling the distance impedance of protest attendance

V. A. Traag, R. Quax, P. M. A. Sloot

Physica A 468:171–182 2017 Journal DOI PDF
Protesters are usually young, relatively well educated, middle class people that are politically engaged. But where do protesters come from? We here show, based on mobile phone data, that distance is an important impedance to protest attendance. Most protesters come from nearby regions, suggesting distance forms an obstacle to participation. Although this effect can be partly explained by social network effects, which show similar spatial dependencies, an effect of distance remains. This suggests distance still acts as an obstacle to participation, although it may also be that long-range contacts are less effective for recruitment. Face-to-face contacts seem more important in spreading protests through earlier participants, whereas central recruitment works better by telephone. Our results are important for understanding processes of recruitment.

Clean up or mess up: the effect of sampling biases on measurements of degree distributions in mobile phone datasets

Adeline Decuyper, Arnaud Browet, Vincent Antonio Traag, Vincent D. Blondel, Jean-Charles Delvenne

arXiv:1609.09413 2016 Preprint arXiv PDF
Mobile phone data have been extensively used in the recent years to study social behavior. However, most of these studies are based on only partial data whose coverage is limited both in space and time. In this paper, we point to an observation that the bias due to the limited coverage in time may have an important influence on the results of the analyses performed. In particular, we observe significant differences, both qualitatively and quantitatively, in the degree distribution of the network, depending on the way the dataset is pre-processed and we present a possible explanation for the emergence of Double Pareto LogNormal (DPLN) degree distributions in temporal data.

Complex contagion of campaign donations

Vincent A. Traag

PLOS ONE 11(4):e0153539 2016 Journal DOI arXiv PDF Slides
Money is central in US politics, and most campaign contributions stem from a tiny, wealthy elite. Like other political acts, campaign donations are known to be socially contagious. We study how campaign donations diffuse through a network of more than 50,000 elites and examine how connectivity among previous donors reinforces contagion. We find that the diffusion of donations is driven by independent reinforcement contagion: people are more likely to donate when exposed to donors from different social groups than when they are exposed to equally many donors from the same group. Counter-intuitively, being exposed to one side may increase donations to the other side. Although the effect is weak, simultaneous cross-cutting exposure makes donation somewhat less likely. Finally, the independence of donors in the beginning of a campaign predicts the amount of money that is raised throughout a campaign. We theorize that people infer population-wide estimates from their local observations, with elites assessing the viability of candidates, possibly opposing candidates in response to local support. Our findings suggest that theories of complex contagions need refinement and that political campaigns should target multiple communities.

Structure of a media co-occurrence network

V. A. Traag, R. Reinanda, G. van Klinken

In: Stefano Battiston, Francesco De Pellegrini, Guido Caldarelli, Emanuela Merelli (eds.), Proceedings of ECCS 2014, pp. 81–91. Springer International Publishing 2016 Conference DOI arXiv PDF Slides
Social networks have been of much interest in recent years. We here focus on a network structure derived from co-occurrences of people in traditional newspaper media. We find three clear deviations from what can be expected in a random graph. First, the average degree in the empirical network is much lower than expected, and the average weight of a link much higher than expected. Secondly, high degree nodes attract disproportionately much weight. Thirdly, relatively much of the weight seems to concentrate between high degree nodes. We believe this can be explained by the fact that most people tend to co-occur repeatedly with the same people. We create a model that replicates these observations qualitatively based on two self-reinforcing processes: (1) more frequently occurring persons are more likely to occur again; and (2) if two people co-occur frequently, they are more likely to co-occur again. This suggest that the media tends to focus on people that are already in the news, and that they reinforce existing co-occurrences.

Dissecting discursive contention: A relational analysis of the Dutch debate on minority integration, 1990–2006

Justus Uitermark, Vincent A. Traag, Jeroen Bruggeman

Social Networks 47:107–115 2016 Journal DOI PDF
This paper elaborates a relational approach to examine discursive contention. We develop a network method to identify groups forming through contentious interactions as well as relational measures of polarization, leadership, solidarity and various aspects of discursive power. The paper analyzes how an assimilationist movement confronted its adversaries in the Dutch debate on minority integration. Over different periods in the debate, we find a recurrent pattern: a small yet cohesive group of challengers with strong discursive leaders forces their framing of integration issues upon other participants. We suggest that the pattern found in our study may exemplify a more universal network pattern behind discursive contention.

Faster unfolding of communities: Speeding up the Louvain algorithm

V. A. Traag

Physical Review E 92(3):032801 2015 Journal DOI arXiv PDF
Many complex networks exhibit a modular structure of densely connected groups of nodes. Usually, such a modular structure is uncovered by the optimization of some quality function. Although flawed, modularity remains one of the most popular quality functions. The Louvain algorithm was originally developed for optimizing modularity, but has been applied to a variety of methods. As such, speeding up the Louvain algorithm enables the analysis of larger graphs in a shorter time for various methods. We here suggest to consider moving nodes to a random neighbor community, instead of the best neighbor community. Although incredibly simple, it reduces the theoretical runtime complexity from O(m) to O(nlog〈k〉) in networks with a clear community structure. In benchmark networks, it speeds up the algorithm roughly 2-3 times, while in some real networks it even reaches 10 times faster runtimes. This improvement is due to two factors: (1) a random neighbor is likely to be in a "good" community and (2) random neighbors are likely to be hubs, helping the convergence. Finally, the performance gain only slightly diminishes the quality, especially for modularity, thus providing a good quality-performance ratio. However, these gains are less pronounced, or even disappear, for some other measures such as significance or surprise.

Old questions, new techniques: a research note on the computational identification of political elites

Jacqueline Hicks, Vincent A. Traag, Ridho Reinanda

Comparative Sociology 14(3):386–401 2015 Journal DOI PDF
This paper presents a new method of identifying a nation’s political elite using computational techniques on digitised newspaper articles. It begins by describing the three most widely used methods of identifying political elites: positional, decisional and reputational. It then introduces the “reported elite method”, exploring the kinds of elites it detects and how well it reflects the composition of political elites in our case study of Indonesia. Compared to the other existing methods, we find that our method casts a much wider net when searching for political elites, resulting in many more people from civil society, far fewer formal politicians, and challenging conventional notions of who is a political elite. The method has two major underlying assumptions: (1) the newspapers from which the texts are drawn are free and fairly representative and (2) political power can be inferred from frequent appearance in newspapers alongside other frequently appearing individuals in computational “communities” of political elite.

Detecting communities using asymptotical surprise

V. A. Traag, R. Aldecoa, J.-C. Delvenne

Physical Review E 92(2):022816 2015 Journal DOI arXiv PDF
Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a community. We here analyze a recently proposed measure called surprise, which assesses the quality of the partition of a network into communities. In its current form, the formulation of surprise is rather difficult to analyze. We here therefore develop an accurate asymptotic approximation. This allows for the development of an efficient algorithm for optimizing surprise. Incidentally, this leads to a straightforward extension of surprise to weighted graphs. Additionally, the approximation makes it possible to analyze surprise more closely and compare it to other methods, especially modularity. We show that surprise is (nearly) unaffected by the well-known resolution limit, a particular problem for modularity. However, surprise may tend to overestimate the number of communities, whereas they may be underestimated by modularity. In short, surprise works well in the limit of many small communities, whereas modularity works better in the limit of few large communities. In this sense, surprise is more discriminative than modularity and may find communities where modularity fails to discern any structure.

Turning digitised newspapers into networks of political elites

Jacqueline Hicks, Vincent A. Traag, Ridho Reinanda

Asian Journal of Social Science 43(5):567–587 2015 Journal DOI PDF
This paper introduces the Elite Network Shifts (ENS) project to the Asian Studies community where computational techniques are used with digitised newspaper articles to describe changes in relations among Indonesian political elites. Reflecting on how “political elites” and “political relations” are understood by the elites, as well as across the disciplinary boundaries of the social and computational sciences, it suggests ways to operationalise these concepts for digital research. It then presents the results of a field trip where six Indonesian political elites were asked to evaluate the accuracy of their own computational networks generated by the project. The main findings of the paper are: (1) The computational identification of political elites is relatively successful, while much work remains on categorising their relations, (2) social scientists should focus on capturing single dimensions of complex social phenomena when using computational techniques, and (3) computational techniques are not able to capture multiple understandings of social concepts.

Elite co-occurrence in the media

Vincent A. Traag, Ridho Reinanda, Gerry van Klinken

Asian Journal of Social Science 43(5):588–612 2015 Journal DOI PDF
We present a new computational methodology to identify national political elites, and demonstrate it for Indonesia. On the basis that elites have an “organised capacity to make real and continuing political trouble”, we identify them as those individuals who occur most frequently in a large corpus of politically-oriented newspaper articles. Doing this requires mainly well-established named entity recognition techniques and appears to work well. More ambitiously, we also experiment with a new technique to map the relational networks among them. To establish these networks, we assume that individuals co-occurring in one sentence are related. The co-occurrence technique has rarely been applied to identify elite networks. The resulting network has a core-periphery structure. Although this in line with our sociological expectations of an elite network, we find that this structure does not differ significantly from that of a randomly generated co-occurrence network. We explain that this unexpected result arises as an artefact of the data. Finally, we assess the future potential of our elite network mapping technique. We conclude it remains promising, but only if we are able to add more sociological meaning to relations between elites.

Dynamics of media attention

V. A. Traag, R. Reinanda, J. Hicks, G. van Klinken

In: Proceedings of ICCSA 2014, pp. 301–304 2014 Conference arXiv PDF Slides
Studies of human attention dynamics analyses how attention is focused on specific topics, issues or people. In online social media, there are clear signs of exogenous shocks, bursty dynamics, and an exponential or powerlaw lifetime distribution. We here analyse the attention dynamics of traditional media, focussing on co-occurrence of people in newspaper articles. The results are quite different from online social networks and attention. Different regimes seem to be operating at two different time scales. At short time scales we see evidence of bursty dynamics and fast decaying edge lifetimes and attention. This behaviour disappears for longer time scales, and in that regime we find Poissonian dynamics and slower decaying lifetimes. We propose that a cascading Poisson process may take place, with issues arising at a constant rate over a long time scale, and faster dynamics at a shorter time scale.

Numerical modelling and graph theory tools to study ecological connectivity in the Great Barrier Reef

Christopher J. Thomas, Jonathan Lambrechts, Eric Wolanski, V. A. Traag, Vincent D. Blondel, Eric Deleersnijder, Emmanuel Hanert

Ecological Modelling 272:160–174 2014 Journal DOI PDF
The process of coral larval dispersal is important for coral reef ecosystems, but remains poorly understood and hard to gauge. Better knowledge of inter-reef connectivity patterns would be useful in enabling better management of coral reef waters however. By employing a spatially explicit numerical modelling approach, we simulate larval dispersal through the central section of the Great Barrier Reef (GBR), comprising over 1000 reefs, and identify spatial patterns in the inter-reef connectivity network using a community detection method from network science. This paper presents the modelling approach used and discusses the significance of the results. Inter-reef connectivity networks were estimated for 4 different coral species, and significant differences between them were found. We show how we can partition reefs into clusters, or “communities”, that are sparsely connected with each other, and therefore identify important barriers to larval dispersal. By fine-tuning a resolution parameter in the community detection method, we can find dispersal barriers of varying strength. Finally, we show that the average connectivity length scale varies significantly across the different reef communities, and suggest that this may have repercussions for the optimal placement of marine protected areas (MPAs) to maximise connectivity with surrounding reefs.

Trading Communities, the Networked Structure of International Relations, and the Kantian Peace

Yonatan Lupu, Vincent Antonio Traag

Journal of Conflict Resolution 57(6):1011–1042 2013 Journal DOI SSRN PDF Corrigendum
The authors argue that theories regarding the relationship between trade and conflict could benefit greatly from accounting for the networked structure of international trade. Indirect trade relations reduce the probability of conflict by creating (1) opportunity costs of conflict beyond those reflected by direct trade ties and (2) negative externalities for the potential combatants’ trading partners, giving them an incentive to prevent the conflict. Trade flows create groups of states with relatively dense trade ties, which we call trading communities. Within these groups, the interruptions to trade caused by conflict create relatively large costs. As a result, joint members of trading communities are less likely to go to war; however little they directly trade with each other. The authors systematically measure and define trading communities across various levels of aggregation using the network analytic tool of modularity maximization. The authors find significant support for their hypothesis, indicating that interdependence theory can be extended to extra-dyadic relations.

Dynamical Models Explaining Social Balance and Evolution of Cooperation

Vincent Antonio Traag, Paul Van Dooren, Patrick De Leenheer

PLOS ONE 8(4):e60063 2013 Journal DOI arXiv PDF
Social networks with positive and negative links often split into two antagonistic factions. Examples of such a split abound: revolutionaries versus an old regime, Republicans versus Democrats, Axis versus Allies during the second world war, or the Western versus the Eastern bloc during the Cold War. Although this structure, known as social balance, is well understood, it is not clear how such factions emerge. An earlier model could explain the formation of such factions if reputations were assumed to be symmetric. We show this is not the case for non-symmetric reputations, and propose an alternative model which (almost) always leads to social balance, thereby explaining the tendency of social networks to split into two factions. In addition, the alternative model may lead to cooperation when faced with defectors, contrary to the earlier model. The difference between the two models may be understood in terms of the underlying gossiping mechanism: whereas the earlier model assumed that an individual adjusts his opinion about somebody by gossiping about that person with everybody in the network, we assume instead that the individual gossips with that person about everybody. It turns out that the alternative model is able to lead to cooperative behaviour, unlike the previous model.

Exploring the mobility of mobile phone users

Balázs Cs. Csáji, Arnaud Browet, Vincent Antonio Traag, Jean-Charles Delvenne, Etienne Huens, Paul Van Dooren, Zbigniew Smoreda, Vincent D. Blondel

Physica A: Statistical Mechanics and its Applications 392(6):1459–1473 2013 Journal DOI arXiv PDF
Mobile phone datasets allow for the analysis of human behavior on an unprecedented scale. The social network, temporal dynamics and mobile behavior of mobile phone users have often been analyzed independently from each other using mobile phone datasets. In this article, we explore the connections between various features of human behavior extracted from a large mobile phone dataset. Our observations are based on the analysis of communication data of 100000 anonymized and randomly chosen individuals in a dataset of communications in Portugal. We show that clustering and principal component analysis allow for a significant dimension reduction with limited loss of information. The most important features are related to geographical location. In particular, we observe that most people spend most of their time at only a few locations. With the help of clustering methods, we then robustly identify home and office locations and compare the results with official census data. Finally, we analyze the geographic spread of users' frequent locations and show that commuting distances can be reasonably well explained by a gravity model.

Significant scales in community structure

V. A. Traag, Gautier Krings, Paul Van Dooren

Scientific Reports 3:2930 2013 Journal DOI arXiv PDF Slides
Many complex networks show signs of modular structure, uncovered by community detection. Although many methods succeed in revealing various partitions, it remains difficult to detect at what scale some partition is significant. This problem shows foremost in multi-resolution methods. We here introduce an efficient method for scanning for resolutions in one such method. Additionally, we introduce the notion of "significance" of a partition, based on subgraph probabilities. Significance is independent of the exact method used, so could also be applied in other methods, and can be interpreted as the gain in encoding a graph by making use of a partition. Using significance, we can determine "good" resolution parameters, which we demonstrate on benchmark networks. Moreover, optimizing significance itself also shows excellent performance. We demonstrate our method on voting data from the European Parliament. Our analysis suggests the European Parliament has become increasingly ideologically divided and that nationality plays no role.

Detecting Communities through Network Data

J. Bruggeman, V. A. Traag, J. Uitermark

American Sociological Review 77(6):1050–1063 2012 Journal DOI PDF
Social life coalesces into communities through cooperation and conflict. As a case in point, Shwed and Bearman (2010) studied consensus and contention in scientific communities. They used a sophisticated modularity method to detect communities on the basis of scientific citations, which they then interpreted as directed positive network ties. They assumed that a lack of citations implies disagreement. Some scientific citations, however, are contentious and should therefore be represented by negative ties, like conflicting relations in general. After expanding the modularity method to incorporate negative ties, we show that a small proportion of negative ties, commonly present in science, is sufficient to significantly alter the community structure. In addition, our research suggests that without distinguishing negative ties, scientific communities actually represent specialized subfields, not contentious groups. Finally, we cast doubt on the assumption that lack of cites would signal disagreement. To show the general importance of discerning negative ties for understanding conflict and its impact on communities, we also analyze a public debate.

De strijd om discursieve macht: een relationele discoursanalyse van het Nederlandse integratiedebat, 1990-2005

J. Uitermark, Vincent Antonio Traag, J. Bruggeman

Sociologie 8(2):219–247 2012 Journal DOI PDF
Het is algemeen bekend dat in publieke debatten sommige deelnemers domineren en andere veel minder gehoor vinden. Maar hoe kunnen we zulke verschillen in discursieve macht conceptualiseren, meten en verklaren? Dit artikel ontwikkelt een aanpak voor relationele discoursanalyse om samenwerking en strijd tussen deelnemers in het Nederlandse integratiedebat te analyseren.

Social Event Detection in Massive Mobile Phone Data Using Probabilistic Location Inference

V. A. Traag, A. Browet, F. Calabrese, F. Morlot

In: Proceedings IEEE SocialCom'2011, pp. 625–628. IEEE 2011 Conference DOI HAL PDF Slides
The unprecedented amount of data from mobile phones creates new possibilities to analyze various aspects of human behavior. Over the last few years, much effort has been devoted to studying the mobility patterns of humans. In this paper we will focus on unusually large gatherings of people, i.e. unusual social events. We introduce the methodology of detecting such social events in massive mobile phone data, based on a Bayesian location inference framework. More specifically, we also develop a framework for deciding who is attending an event. We demonstrate the method on a few examples. Finally, we discuss some possible future approaches for event detection, and some possible analyses of the detected social events.

Narrow scope for resolution-limit-free community detection

V. A. Traag, P. Van Dooren, Y. Nesterov

Physical Review E 84(1):016114 2011 Journal DOI arXiv PDF Slides
Detecting communities in large networks has drawn much attention over the years. While modularity remains one of the more popular methods of community detection, the so-called resolution limit remains a significant drawback. To overcome this issue, it was recently suggested that instead of comparing the network to a random null model, as is done in modularity, it should be compared to a constant factor. However, it is unclear what is meant exactly by "resolution-limit-free," that is, not suffering from the resolution limit. Furthermore, the question remains what other methods could be classified as resolution-limit-free. In this paper we suggest a rigorous definition and derive some basic properties of resolution-limit-free methods. More importantly, we are able to prove exactly which class of community detection methods are resolution-limit-free. Furthermore, we analyze which methods are not resolution-limit-free, suggesting there is only a limited scope for resolution-limit-free community detection methods. Finally, we provide such a natural formulation, and show it performs superbly.

Indirect reciprocity through gossiping can lead to cooperative clusters

V. A. Traag, P Van Dooren, Y Nesterov

In: IEEE Symposium on Artificial Life 2011, pp. 154–161. IEEE 2011 Conference DOI PDF Slides
Explaining how cooperation can emerge, and persist over time in various species is a prime challenge for both biologists and social scientists. Whereas cooperation in non-human species might be explained through mechanisms such as kinship selection or reciprocity, this is usually regarded as insufficient to explain the extent of cooperation observed in humans. It has been theorized that indirect reciprocity-I help you, and someone else later helps me-could explain the breadth of human cooperation. Reputation is central to this idea, since it conveys important information to third parties whether to cooperate or not with a focal player. In this paper we analyze a model for reputation dynamics through gossiping, and pay specific attention to the possible cooperation networks that may arise. We show that gossiping agents can organize into cooperative clusters, i.e. cooperate within clusters, and defect between them, which can be regarded as socially balanced. We also deduce conditions for these gossiping cooperators to be evolutionary stable.

Exponential Ranking: taking into account negative links

Vincent A Traag, Yurii E Nesterov, Paul Van Dooren

Lecture Notes in Computer Science 6430:192–202 2010 Journal DOI PDF Slides
Networks have attracted a great deal of attention the last decade, and play an important role in various scientific disciplines. Ranking nodes in such networks, based on for example PageRank or eigenvector centrality, remains a hot topic. Not only does this have applications in ranking web pages, it also allows peer-to-peer systems to have effective notions of trust and reputation and enables analyses of various (social) networks. Negative links however, confer distrust or dislike as opposed to positive links, and are usually not taken into account. In this paper we propose a ranking method we call exponential ranking, which allows for negative links in the network. We show convergence of the method, and demonstrate that it takes into account negative links effectively.

Community detection in networks with positive and negative links

V. A. Traag, Jeroen Bruggeman

Physical Review E 80(3):036115 2009 Journal DOI arXiv PDF Slides
Detecting communities in complex networks accurately is a prime challenge, preceding further analyses of network characteristics and dynamics. Until now, community detection took into account only positively valued links, while many actual networks also feature negative links. We extend an existing Potts model to incorporate negative links as well, resulting in a method similar to the clustering of signed graphs, as dealt with in social balance theory, but more general. To illustrate our method, we applied it to a network of international alliances and disputes. Using data from 1993-2001, it turns out that the world can be divided into six power blocs similar to Huntington's civilizations, with some notable exceptions.

Popularity Distributions with Social Influence

V. A. Traag

Master's thesis, University of Amsterdam 2008 Thesis PDF Slides
This thesis considers a model for popularity based on a ‘rich-get-richer’ effect. Basically, popular items tend to become increasingly popular. However, quality of items also plays a role in popularity. The model thus incorporates both a ‘rich-get-richer’ as well as a ‘good-get-richer’ effect. The balance between these two effects is interpreted as the amount of social influence. Formal analysis of the model suggests that the distribution of popularity becomes more unequal and more uncertain with rising social influence. Higher quality has a dual role: it results in a higher average popularity, but increases the uncertainty as well. The model is tested against data from the YouTube market and the Hollywood movie industry. Comparing the results for these two markets suggests that social influence is higher for on-line markets than for traditional markets. When markets go on-line, producers should be prepared to take the increase in risk into account. Some books might break all records, while others remain on the shelf, and it becomes harder to predict which books that will be.
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