How Influencers and Multipliers Drive Polarization and Issue Alignment on Twitter/X

Armin Pournaki; Eckehard Olbrich; Felix Gaisbauer

REVIEW 5 major objections 5 minor 61 references

How Influencers and Multipliers Drive Polarization and Issue Alignment on Twitter/X

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The German-speaking Twitter/X public sphere is split into two stable ideological camps, and a small set of hyperactive users—influencers who create content and multipliers who retweet and curate it—produces the strong alignment of…

desk verdict Solid descriptive finding on German Twitter polarization; the influencer/multiplier distinction is worth taking seriously, but the causal framing overreaches. read the letter →

arxiv 2505.14280 v1 pith:HZG4NVNL submitted 2025-05-20 cs.SI

Armin Pournaki , Felix Gaisbauer , Eckehard Olbrich This is my paper · ORCID

classification cs.SI

keywords polarizationissuealignmentretweetnetworksinfluencersmultiplierstopicmodelingGermanTwitterstochasticblockmodel

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that the German-speaking Twitter/X public sphere is divided into two stable ideological camps, and that separate political issues—Covid, migration, climate, even greetings—are strongly aligned onto this single left-right divide. It argues that this alignment is not a natural property of the issues themselves but is driven by two small groups of hyperactive users: influencers, who produce most of the content that gets retweeted, and multipliers, who retweet heavily and bundle content from influencers into ideologically consistent packages. The multipliers are the more distinctive mechanism, acting as intermediaries between content creators and the wider audience and aligning issues more consistently than the influencers they amplify. If the claim is right, platform-level polarization is largely an outcome of curation and amplification by a few active accounts, not a simple reflection of the opinions of the general user base.

What carries the argument

The central object is the retweet network treated as an endorsement graph: a directed link is drawn from i to j when i retweets j, and densely connected groups are interpreted as opinion camps. For each of 1,726 trending-topic networks, the paper infers whether a one-block or two-block structure is most likely using a degree-corrected stochastic block model, validated with force-directed layouts and a silhouette threshold, and encodes each user's cluster membership as +1, -1, or 0. From these partitions it builds the user alignment α(i,j), the average product of two users' cluster memberships over trends in which both participate, and the issue alignment τ(T1,T2), the average product of topic-wise camp membership scores. Influencers are defined as the most-retweeted users and multipliers as the most-retweeting users; the alignment matrices for these two groups are then clustered and labeled as left- and right-leaning by manual inspection of the accounts.

What would settle it

Take a random sample of retweets from users in each inferred camp and have annotators judge whether the retweeting user's own accompanying text or profile signals agreement with the retweeted account's stance; if a large share of retweets are hostile, mocking, or neutral amplifications, the endorsement assumption—and with it the two-camp and issue-alignment results—would fail.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the German Twittersphere exhibits strong issue alignment: the opinion clusters inferred from retweet networks sort users into the same left- and right-leaning camps across a wide range of political topics, with the strongest core around Covid, journalism/media, and German politics. Comparing users with the highest in-degree (influencers) and highest out-degree (multipliers), the authors find that multipliers participate in more trends and align issues more consistently, and that deviations such as migration and Ukraine arise when users are retweeted into the opposing camp or break with their camp on a single issue. The paper reads this as evidence that the polarized public sphere is produced by two cores of strongly active users: influencers who generate ideologically charged content and multipliers who curate and amplify it.

Load-bearing premise

The entire two-camp structure rests on the assumption that retweets are endorsements, so clusters of retweeters can be read as opinion camps; if many retweets are critical, mocking, or algorithmic amplifications, the inferred camps and alignments could be artifacts.

Editorial extensions

If this is right

Separate political issues on German Twitter do not each produce their own division; they reproduce one global left-right split, so studying a single issue such as Covid already exposes the same camp structure as the rest of the political agenda.
Multipliers, not just influencers, carry the alignment effect: they are active across more trends and their topic-wise alignments are more consistent, making retweet amplification a plausible target for platform interventions.
The alignment measure based on user alignment avoids the small-overlap problem of partition-similarity scores, because it can compare users even when the overlapping node set between two networks is small.
The contrast with survey-based findings of low issue alignment is explained by the different 'surveyed' population: Twitter users are younger, more politicized, and trending topics are likely trigger points that evoke stronger engagement than neutral survey questions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

This reading implies that the multiplier mechanism should be testable on other platforms: if hyperactive curators exist on Facebook or TikTok, the same alignment pattern should be measurable in their share or reshare networks.
A testable extension would separate passive from active sorting into a camp: the migration example suggests users can be pulled into the opposing cluster by being retweeted there, which would not necessarily mean their own opinions are aligned.
One consequence of the algorithm-amplification argument is that multipliers may shape content exposure beyond their own follower counts; an audit comparing feed exposure with and without multiplier retweets would quantify this channel.
If trending topics are disproportionately triggering, the issue-alignment result may overstate alignment in everyday political talk; sampling non-trending political tweets would show whether the alignment persists outside high-engagement content.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First, the honest bottom line: the descriptive core is solid, and the influencer/multiplier split is the most interesting thing in the paper. The authors make a real contribution by showing that German political Twitter over 2021–2023 sorts into two recurring camps, and that issue alignment is strong across topics—against what survey-based work would predict. The distinction between high in-degree (influencers) and high out-degree (multipliers) users, and the finding that multipliers show stronger cross-topic alignment than influencers, is a genuine addition to the polarization literature. They also ship code and anonymized data, and they validate their user-centric alignment measure with ANMI and ARI in the appendix. That is the right kind of robustness work, and it gives me confidence the descriptive result is not a method artifact.

Where the paper falls short is in the gap between the evidence and the causal framing. The abstract says alignment is 'driven by' influencers and multipliers. The data are associational: multipliers are more active, appear in more trends, and their alignment values are higher. Nothing in the design identifies a mechanism—there is no exogenous variation, no temporal test, and no placebo. The authors are more careful in the discussion, where they write that they 'may only speculate about the precise logic.' The abstract should match that caution. 'Associated with' is the defensible claim; 'driven by' is a hypothesis.

The circularity worry the reader raised is real but mild. The global camps are built from the same alignment matrix used later for per-topic anchoring. But the ANMI/ARI checks do not use those camps, and they reproduce the pattern, so the main result survives. The retweet-as-endorsement assumption is load-bearing, but it is standard in this literature and the authors flag it.

Minor issues: several thresholds (silhouette 0.4, top-1000 cutoffs) are manual, and there is no uncertainty quantification. That is a limitation, not a fatal flaw.

My recommendation: send it to referees. This is a solid descriptive paper that deserves publication with revision. Ask the authors to soften the causal language and to make the threshold choices more transparent. I would engage with it.

Referee Report

5 major / 5 minor

Summary. The paper studies the German Twittersphere between March 2021 and July 2023 using trending-topic data. A topic model assigns tweets to political issues, and retweet networks per trending topic are clustered into one or two opinion camps. The authors define user alignment across trends, extract global left- and right-leaning camps by clustering the alignment matrix of highly active users, and then compute topic-level issue alignment. They compare three user groups: top in-degree users ('influencers'), top out-degree users ('multipliers'), and a random user sample. The main empirical findings are that political discussions divide users into two broad camps, that issues align strongly across topics, and that multipliers show higher cross-topic alignment than influencers. The paper interprets this as evidence that influencers and multipliers 'drive' polarization and issue alignment.

Significance. If the descriptive findings hold, this is a valuable large-scale study of issue alignment in a European Twittersphere, adding to the scarce multi-topic evidence beyond US survey-based studies. The paper has notable strengths: a long observation window, a publicly shared code and data repository, explicit bot-authenticity checks, and an independent validation using ANMI and ARI in Appendix A.6. However, the central causal claim is not established by the observational design, and several methodological choices need clarification before the claimed mechanism can be accepted. The paper is likely to be of interest to the ICWSM community, but the abstract's 'driven by' wording overstates what the evidence supports.

major comments (5)

[Abstract; Section 5] The central causal claim that issue alignment is 'driven by' influencers and multipliers is not supported by the analysis. Sections 4.2 and 4.3 report associational differences: top out-degree users have higher pairwise alignment and higher cross-topic alignment than influencers or random users. There is no exogenous variation in multiplier activity, no temporal precedence test, and no control for reverse causation or confounders such as ideological extremity. The authors themselves state in Section 5 that they 'may only speculate about the precise logic by which they act' and that 'more thorough analyses need to be conducted.' The abstract and discussion should therefore replace 'driven by' with a weaker formulation such as 'is associated with' or should add a counterfactual or temporal test.
[Section 3.2; Appendix A.3] The silhouette threshold that decides whether a retweet network is polarized is stated with opposite directions in the main text and the appendix. Section 3.2 says: 'If the score is higher than 0.4, we keep the SBM-based cluster assignment, otherwise assume that there is only one cluster.' Appendix A.3 says: 'If the silhouette score S(K) ≤ 0.4, then we keep the clustering. Else, we discard it and assume that the network is best described by only a single cluster.' Since this threshold determines which trends enter the alignment computation, the contradiction materially affects all downstream results. The authors must correct the typo and report robustness of the main findings to the threshold choice.
[Section 3.2; Section 4.3; Section 5] The retweet-as-endorsement assumption is load-bearing, and the paper's own migration example shows that retweets are not always endorsements. In Section 4.3, the authors describe left-leaning influencers being 'pulled' into the right-leaning cluster because right-leaning accounts retweet them. If retweets can be critical or purely amplifying, then c_k(i) is not a reliable stance signal, and the derived alignment values could be partly an artifact of this signal. The paper should explicitly discuss this limitation in the main text and ideally validate the stance interpretation on a sample of retweets with text-based stance labeling.
[Section 3.4; Section 3.5; Appendix A.6] The issue alignment measure in Eq. (10) uses the global left/right camp labels that were themselves obtained by clustering the user alignment matrix computed over all trends. This creates a circular dependency that could inflate the measured topic alignment. The independent ANMI/ARI checks in Appendix A.6 go some way toward validating the overall issue-alignment pattern, but they do not validate the specific influencer-vs-multiplier comparison. The authors should either provide an anchor-free validation of the multiplier findings or explicitly qualify the anchor-based results as dependent on the global camp construction.
[Section 4.3; Figures 4 and 5] The claim that 'multipliers align issues more strongly than influencers' is made on the basis of visual inspection of the alignment matrices. No distributions, effect sizes, confidence intervals, or statistical tests are reported for this comparison. Given that this difference is one of the main supports for the proposed mechanism, the paper should quantify the alignment difference and test whether it is larger than expected from activity levels or other observable user characteristics.

minor comments (5)

[Section 5] The phrase 'a part of of coordinated inauthentic behavior' contains a duplicated 'of.'
[Appendix A.1] The sentence 'The F1-scores for the logistic classifier and the stochastic gradient descent based classifier are reported in Tab. 1' should refer to Table A1, since the main-text Table 1 reports topics and polarization shares.
[Section 4.1] The phrase 'The topic Drug Legalisation , mainly related to cannabis' has an extra space before the comma.
[Figure 5 caption] The caption should state whether the optimal leaf ordering is computed separately for the influencer and multiplier matrices; the two matrices appear to use different orderings, which makes direct comparison of individual entries less straightforward.
[Section 3.4] The definition of J_i as the subset of influencers and multipliers who occur jointly with user i in at least one trend should clarify whether user i itself can be included in J_i even when i is not an influencer or multiplier.

Circularity Check

1 steps flagged · score 3.0 of 10

Mild self-referential anchor construction in the issue-alignment measure; central claims retain independent support via anchor-free replication.

self definitional [Section 3.4-3.5, Eq. (2), (4), (6)-(10)]
"We can now use these “global” camps made of influencers and multipliers as anchors and compute, for any given user, how well they align with these camps... The alignment τ (T1, T2) ∈ [0, 1] between two topics T1 and T2 is then defined as τ (T1, T2) = 1 n P i µT1 (i)µT2 (i)"

The global camp labels c(j) used as anchors in Eqs. (8)-(9) are obtained by clustering the all-trend user-alignment matrix α(i,j) of Eq. (2), which averages products of per-trend cluster assignments c_k(i)c_k(j) over all trends I. Each topic T judged by τ(T1,T2) is therefore compared against anchors that were constructed from data containing T's own trend partitions. Thus part of the measured topic alignment is the self-consistency of the anchor-building step rather than an independent comparison between topics. The loop is not complete: other topics also shape the anchors, and the paper's Appendix A.6 reproduces the issue-alignment pattern with anchor-free ANMI and ARI measures, so the circularity is partial and not the sole basis for the claim.

full rationale

The main claimed derivation chain is largely self-contained: retweet networks are clustered per trend, user alignment is computed from those cluster assignments, and the influencer/multiplier distinction is based on in-/out-degree, not on the alignment outcome. Self-citations (Gaisbauer et al. 2021, 2023; Pournaki et al. 2021) are used for methodological continuity and prior expectations, but they are not the load-bearing evidence for the two-camp structure or the issue-alignment result; the two-camp structure is also shown for a random user sample, and the issue-alignment pattern is independently replicated with ANMI and ARI in Appendix A.6. The causal wording that multipliers 'drive' alignment is an identification limitation rather than a circularity, since it is an interpretive leap from associational evidence, not an equation reducing to its own input. The only concrete circular dependency is the anchor-based topic-alignment measure described in the step above, which mildly inflates self-consistency but is mitigated by the anchor-free validation. Score 3 reflects that partial self-reference without treating it as the dominant reason the paper's conclusions hold.

Assumptions & free parameters 6 free parameters · 4 assumptions · 1 invented entities

The central claims rest on a chain of manually set thresholds (silhouette 0.4, degree cutoffs, UMAP/HDBScan parameters) and on interpretive assumptions (retweets as endorsement, two-camp structure, force-layout validity, manual left/right labeling). The multiplier is a new analytical entity but is defined entirely within this dataset.

free parameters (6)

silhouette_score_threshold = 0.4
Used to accept or reject the two-block SBM partition. The paper states 'The threshold of 0.4 was found through manual exploration' (Sec. A.2), so it is a hand-fitted value that directly determines which nodes are treated as polarized.
influencer_boundary = min in-degree 1833
The top influencers are defined by the in-degree cutoff shown in Fig. A2; the specific number is derived from the dataset's degree distribution.
multiplier_boundary = min out-degree 1150
Defines which users count as multipliers; derived from the dataset's degree distribution and shown in Fig. A2.
topic_model_top_k = 50
Number of most-retweeted tweets per trend used to build the topic-model training set (Sec. 3.1); affects which content defines the topics.
umap_n_components = 5
UMAP embedding dimension for BERTopic (Sec. A.1); hyperparameter chosen to achieve tractable clustering.
hdbscan_min_cluster_size = 100
HDBScan minimum cluster size (Sec. A.1); influences the granularity of topics.

assumptions (4)

domain assumption Retweets are endorsements, so retweet network clusters correspond to opinion camps.
Invoked in Sec. 3.2, citing boyd et al. (2010). The entire opinion extraction and all alignment measures rest on this interpretive step.
ad hoc to paper Each trending discussion is best modeled as either one or two opinion camps.
The SBM inference is constrained to Nblocks in {1,2} (Sec. 3.2). This imposes a binary structure on every trend and may miss multi-polar or non-assortative structures.
domain assumption The force-directed layout (ForceAtlas2) geometry is a faithful representation of ideological closeness.
Silhouette scores validating the SBM clustering are computed on the 2D force-layout embedding (Sec. A.2), so the layout is assumed to preserve latent ideological distances.
ad hoc to paper The global left/right camp labels, assigned by manual inspection of accounts, are stable and transferable across topics.
Manual labeling is described in Sec. 3.4; the camp labels anchor all user membership scores and topic alignment values.

invented entities (1)

Multiplier
purpose: A user type with very high retweet out-degree who acts as an intermediary, curating and amplifying ideologically consistent content. This is the paper's novel explanatory category.
Operationalized by a degree threshold within this dataset (min out-degree 1150). The paper provides descriptive statistics and authenticity checks, but no out-of-sample prediction that would independently confirm the category exists beyond this study.

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Cite this review

Pith. "Pith review of How Influencers and Multipliers Drive Polarization and Issue Alignment on Twitter/X." pith.science (2026). https://pith.science/paper/HZG4NVNL

@misc{pith2026250514280,
  author       = {Pith},
  title        = {Pith review of: How Influencers and Multipliers Drive Polarization and Issue Alignment on Twitter/X},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HZG4NVNL}},
  note         = {Machine review of arXiv:2505.14280}
}

read the original abstract

We investigate the polarization of the German Twittersphere by extracting the main issues discussed and the signaled opinions of users towards those issues based on (re)tweets concerning trending topics. The dataset covers daily trending topics from March 2021 to July 2023. At the opinion level, we show that the online public sphere is largely divided into two camps, one consisting mainly of left-leaning, and another of right-leaning accounts. Further we observe that political issues are strongly aligned, contrary to what one may expect from surveys. This alignment is driven by two cores of strongly active users: influencers, who generate ideologically charged content, and multipliers, who facilitate the spread of this content. The latter are specific to social media and play a crucial role as intermediaries on the platform by curating and amplifying very specific types of content that match their ideological position, resulting in the overall observation of a strongly polarized public sphere. These results contribute to a better understanding of the mechanisms that shape online public opinion, and have implications for the regulation of platforms.

Figures

Figures reproduced from arXiv: 2505.14280 by the authors.

**Figure 1.** Analysis pipeline. The raw text data of the tweets is processed in a topic model to extract the main issues discussed, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Force-directed layout representation of two [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** User alignment for influencers, multipliers and a random sample of users. We compute the pairwise user alignment [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Global and topic-wise cluster membership score for influencers (left) and multipliers (right). A membership score [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Issue alignment for influencers (left) and multipliers (right). Both matrices are sorted according to optimal leaf [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Issue alignment of regular users that participate in [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

61 extracted references · 54 canonical work pages

[1]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...
[2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...
[3]

M.; Mason, W

Bakshy, E.; Hofman, J. M.; Mason, W. A.; and Watts, D. J. 2011. Everyone's an Influencer: Quantifying Influence on Twitter. In Proceedings of the Fourth ACM International Conference on Web Search and Data Mining , WSDM '11, 65--74. New York, NY, USA: Association for Computing Machinery. ISBN 978-1-4503-0493-1

work page 2011
[4]

Baldassarri, D.; and Gelman, A. 2008. Partisans without Constraint : Political Polarization and Trends in American Public Opinion . American Journal of Sociology, 114(2): 408--446

work page 2008
[5]

Bornschier, S. 2010. The New Cultural Divide and the Two-Dimensional Political Space in Western Europe. West European Politics, 33(3): 419--444

work page 2010
[6]

Bouchaud, P.; Chavalarias, D.; and Panahi, M. 2023. Crowdsourced Audit of Twitter 's Recommender Systems. Scientific Reports, 13(1): 16815

work page 2023
[7]

Tweet Tweet Retweet: Conversational Aspects of Retweeting on Twitter

boyd, d.; Golder, S.; and Lotan, G. 2010. Tweet, Tweet, Retweet: Conversational Aspects of Retweeting on Twitter. In 43rd Hawaii International Conference on Social Systems (HICSS). IEEE. Citation: boyd, danah, Scott Golder, and Gilad Lotan (Forthcoming, 2010)."Tweet Tweet Retweet: Conversational Aspects of Retweeting on Twitter." Proceedings of HICSS-42, ...

work page 2010
[8]

a -Anttila , T.; and Kivel \

Chen, T. H. Y.; Salloum, A.; Gronow, A.; Yl \"a -Anttila , T.; and Kivel \"a , M. 2021. Polarization of Climate Politics Results from Partisan Sorting: Evidence from Finnish Twittersphere . Global Environmental Change, 71: 102348

work page 2021

Show all 61 references

[9]

Cinelli, M.; Cresci, S.; Quattrociocchi, W.; Tesconi, M.; and Zola, P. 2022. Coordinated Inauthentic Behavior and Information Spreading on Twitter . Decision Support Systems, 160: 113819

2022
[10]

Conover, M.; Ratkiewicz, J.; Francisco, M.; Goncalves, B.; Menczer, F.; and Flammini, A. 2011. Political Polarization on Twitter . Proceedings of the International AAAI Conference on Web and Social Media, 5(1)

2011
[11]

Converse, P. E. 1964. The Nature of Belief Systems in Mass Publics. Critical Review, 18(1-3): 1--74

1964
[12]

Darius, P. 2022. Who Polarizes Twitter ? Ideological Polarization, Partisan Groups and Strategic Networked Campaigning on Twitter during the 2017 and 2021 German Federal Elections ' Bundestagswahlen '. Social Network Analysis and Mining, 12(1): 151

2022
[13]

Dekoninck, H.; and Schmuck, D. 2022. The Mobilizing Power of Influencers for Pro-Environmental Behavior Intentions and Political Participation . Environmental Communication, 16(4): 458--472

2022
[14]

Egger, R.; and Yu, J. 2022. A Topic Modeling Comparison Between LDA , NMF , Top2Vec , and BERTopic to Demystify Twitter Posts . Frontiers in Sociology, 7

2022
[15]

Elmas, T.; Overdorf, R.; and Aberer, K. 2022. Characterizing Retweet Bots : The Case of Black Market Accounts . Proceedings of the International AAAI Conference on Web and Social Media, 16: 171--182

2022
[16]

Falkenberg, M.; Galeazzi, A.; Torricelli, M.; Di Marco, N.; Larosa, F.; Sas, M.; Mekacher, A.; Pearce, W.; Zollo, F.; Quattrociocchi, W.; and Baronchelli, A. 2022. Growing Polarization around Climate Change on Social Media. Nature Climate Change, 12(12): 1114--1121

2022
[17]

N.; and Neuberger, C

Friemel, T. N.; and Neuberger, C. 2023. The public sphere as a dynamic network. Communication Theory, 33(2-3): 92--101

2023
[18]

Gaisbauer, F.; Pournaki, A.; Banisch, S.; and Olbrich, E. 2021. Ideological Differences in Engagement in Public Debate on Twitter . PLOS ONE, 16(3): e0249241

2021
[19]

Gaisbauer, F.; Pournaki, A.; Banisch, S.; and Olbrich, E. 2023. Grounding Force-Directed Network Layouts with Latent Space Models. Journal of Computational Social Science

2023
[20]

Gaumont, N.; Panahi, M.; and Chavalarias, D. 2018. Reconstruction of the Socio-Semantic Dynamics of Political Activist Twitter Networks--- Method and Application to the 2017 French Presidential Election. PLOS ONE, 13(9): e0201879

2018
[21]

J.; Lukito, J.; and Woolley, S

Goodwin, A.; Joseff, K.; Riedl, M. J.; Lukito, J.; and Woolley, S. 2023. Political Relational Influencers : The Mobilization of Social Media Influencers in the Political Arena . International Journal of Communication, 17(0): 21

2023
[22]

Green, J.; McCabe, S.; Shugars, S.; Chwe, H.; Horgan, L.; Cao, S.; and Lazer, D. 2025. Curation bubbles. American Political Science Review, 1--19

2025
[23]

Grootendorst, M. 2022. BERTopic : Neural Topic Modeling with a Class-Based TF-IDF Procedure. arXiv:2203.05794

2022 arXiv
[24]

Grootendorst, M. 2024. Supervised Topic Modeling - BERTopic . https://maartengr.github.io/BERTopic/getting_started/supervised/supervised.html. Accessed: 2025-04-17

2024
[25]

Hemsley, J. 2019. Followers Retweet ! The Influence of Middle-Level Gatekeepers on the Spread of Political Information on Twitter . Policy & Internet, 11(3): 280--304

2019
[26]

Hindman, M.; Lubin, N.; and Davis, T. 2022. Facebook Has a Superuser - Supremacy Problem . The Atlantic. Section: Technology

2022
[27]

Hong, L.; and Davison, B. D. 2010. Empirical Study of Topic Modeling in Twitter . In Proceedings of the First Workshop on Social Media Analytics , SOMA '10, 80--88. New York, NY, USA: Association for Computing Machinery. ISBN 978-1-4503-0217-3

2010
[28]

Hsiao, Y.; and Yang, Y. 2022. Participatory propaganda: The role of super commenters in producing propaganda on Breitbart News. OSF Preprints. URL: https://osf.io/preprints/osf/9xjtk

2022
[29]

Hubert, L.; and Arabie, P. 1985. Comparing Partitions. Journal of Classification, 2(1): 193--218

1985
[30]

Hughes, S. W. a. A. 2019. Sizing Up Twitter Users . Technical report, Pew Research Center

2019
[31]

Jacomy, M.; Venturini, T.; Heymann, S.; and Bastian, M. 2014. ForceAtlas2 , a Continuous Graph Layout Algorithm for Handy Network Visualization Designed for the Gephi Software . PLOS ONE, 9(6): e98679

2014
[32]

C.; and Murphy, J

Kozlowski, A. C.; and Murphy, J. P. 2021. Issue Alignment and Partisanship in the American Public: Revisiting the `Partisans without Constraint' Thesis. Social Science Research, 94: 102498

2021
[33]

Kriesi, H.; Grande, E.; Lachat, R.; Dolezal, M.; Bornschier, S.; and Frey, T. 2006. Globalization and the Transformation of the National Political Space: Six European Countries Compared. European Journal of Political Research, 45(6): 921--956

2006
[34]

Lancaster, H. O. H. O. 1969. The Chi-Squared Distribution. New York, Wiley. ISBN 978-0-471-51230-1

1969
[35]

Liang, F.; and Lu, S. 2023. The Dynamics of Event-Based Political Influencers on Twitter : A Longitudinal Analysis of Influential Accounts During Chinese Political Events . Social Media + Society, 9(2): 20563051231177946

2023
[36]

X.; Alexander, T

Liu, C. X.; Alexander, T. J.; and Altmann, E. G. 2023. Non-Assortative Relationships between Groups of Nodes Are Typical in Complex Networks. PNAS Nexus, pgad364

2023
[37]

Lorenz-Spreen , P.; Oswald, L.; Lewandowsky, S.; and Hertwig, R. 2023. A Systematic Review of Worldwide Causal and Correlational Evidence on Digital Media and Democracy. Nature Human Behaviour, 7(1): 74--101

2023
[38]

Lux, T.; Mau, S.; and Jacobi, A. 2022. New Inequalities, New Cleavages? An International Comparison of Attitudes in Four Fields of Inequality. Berliner Journal f \"u r Soziologie , 32(2): 173--212

2022
[39]

Mau, S.; Lux, T.; and Westheuser, L. 2023. Triggerpunkte: Konsens und Konflikt in der Gegenwartsgesellschaft . Berlin: Suhrkamp Verlag, originalausgabe edition edition. ISBN 978-3-518-02984-8

2023
[40]

McInnes, L.; and Healy, J. 2017. Accelerated Hierarchical Density Clustering . arXiv:1705.07321 [stat]

2017 arXiv
[41]

McInnes, L.; Healy, J.; and Melville, J. 2020. UMAP : Uniform Manifold Approximation and Projection for Dimension Reduction . arXiv:1802.03426 [cs, stat]

2020 arXiv
[42]

Meil a , M. 2003. Comparing Clusterings by the Variation of Information . In Sch \"o lkopf, B.; and Warmuth, M. K., eds., Learning Theory and Kernel Machines , Lecture Notes in Computer Science , 173--187. Berlin, Heidelberg: Springer. ISBN 978-3-540-45167-9

2003
[43]

Noack, A. 2009. Modularity Clustering Is Force-Directed Layout. Physical review. E, Statistical, nonlinear, and soft matter physics

2009
[44]

C.; and Creech, B

Papacharissi, Z.; Lashley, M. C.; and Creech, B. 2017. Voices for a New Vernacular : A Forum on Digital Storytelling Interview with Zizi Papacharissi . International Journal of Communication, 11(0): 5

2017
[45]

Peixoto, T. P. 2014. The Graph-Tool Python Library. figshare

2014
[46]

Pless, A.; Khoudja, Y.; and Grunow, D. 2023. How Polarized Is Europe ? Public Opinion Disagreement, Issue Alignment, and Sorting across European Countries

2023
[47]

Pournaki, A.; Gaisbauer, F.; Banisch, S.; and Olbrich, E. 2021. The Twitter Explorer: A Framework for Observing Twitter through Interactive Networks. Journal of Digital Social Research, 3(1): 106--118

2021
[48]

O.; Reimann, R.; Cheong, M.; Alfano, M.; and Klein, C

Quintana, I. O.; Reimann, R.; Cheong, M.; Alfano, M.; and Klein, C. 2022. Polarization and trust in the evolution of vaccine discourse on Twitter during COVID -19. PLOS ONE, 17(12): e0277292. Publisher: Public Library of Science

2022
[49]

Riedl, M.; Schwemmer, C.; Ziewiecki, S.; and Ross, L. M. 2021. The Rise of Political Influencers --- Perspectives on a Trend Towards Meaningful Content . Frontiers in Communication, 6

2021
[50]

Rogers, R. 2018. Social media research after the fake news debacle. Partecipazione e Conflitto, 11(2): 557--570

2018
[51]

Rousseeuw, P. J. 1987. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20: 53--65

1987
[52]

Salloum, A.; Chen, T. H. Y.; and Kivel \"a , M. 2024. Anatomy of Elite and Mass Polarization in Social Networks . arXiv:2406.12525

2024
[53]

Sehl, A.; and Sch \"u tzeneder, J. 2023. Political Knowledge to Go : An Analysis of Selected Political Influencers and Their Formats in the Context of the 2021 German Federal Election . Social Media + Society, 9(2): 20563051231177916

2023
[54]

Starbird, K.; DiResta, R.; and DeButts, M. 2023. Influence and Improvisation : Participatory Disinformation during the 2020 US Election . Social Media + Society, 9(2): 20563051231177943

2023
[55]

K.; Al-Rawi , A.; Celestini, C.; and Worku, N

Stewart, N. K.; Al-Rawi , A.; Celestini, C.; and Worku, N. 2023. Hate Influencers ' Mediation of Hate on Telegram : `` We Declare War Against the Anti-White System ''. Social Media + Society, 9(2): 20563051231177915

2023
[56]

Trilling, D.; et al. 2019. Conceptualizing and Measuring News Exposure as Network of Users and news items. Measuring Media Use and Exposure Recent Developments and Challenges, 297--317

2019
[57]

X.; Epps, J.; and Bailey, J

Vinh, N. X.; Epps, J.; and Bailey, J. 2010. Information Theoretic Measures for Clusterings Comparison : Variants , Properties , Normalization and Correction for Chance . J. Mach. Learn. Res., 11: 2837--2854

2010
[58]

J.; and Dodds, P

Watts, D. J.; and Dodds, P. S. 2007. Influentials, Networks , and Public Opinion Formation . Journal of Consumer Research, 34(4): 441--458

2007
[59]

X/Twitter. 2025. X Trends FAQ -- Trending Hashtags and Topics. https://help.x.com/en/using-x/x-trending-faqs. Accessed: 2025-04-17

2025
[60]

Yoon, N.; Hemsley, J.; Smith, A.; Simpson, E.; and Eakins, J. 2022. Super-Amplifiers! The Role of Twitter Extended Party Networks in Political Elections. Policy & Internet, 14(3): 711--730

2022
[61]

V.; Mihaylov, T.; Ott, M.; Shleifer, S.; Shuster, K.; Simig, D.; Koura, P

Zhang, S.; Roller, S.; Goyal, N.; Artetxe, M.; Chen, M.; Chen, S.; Dewan, C.; Diab, M.; Li, X.; Lin, X. V.; Mihaylov, T.; Ott, M.; Shleifer, S.; Shuster, K.; Simig, D.; Koura, P. S.; Sridhar, A.; Wang, T.; and Zettlemoyer, L. 2022. OPT : Open Pre-trained Transformer Language M...

2022 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

[3] [3]

M.; Mason, W

Bakshy, E.; Hofman, J. M.; Mason, W. A.; and Watts, D. J. 2011. Everyone's an Influencer: Quantifying Influence on Twitter. In Proceedings of the Fourth ACM International Conference on Web Search and Data Mining , WSDM '11, 65--74. New York, NY, USA: Association for Computing Machinery. ISBN 978-1-4503-0493-1

work page 2011

[4] [4]

Baldassarri, D.; and Gelman, A. 2008. Partisans without Constraint : Political Polarization and Trends in American Public Opinion . American Journal of Sociology, 114(2): 408--446

work page 2008

[5] [5]

Bornschier, S. 2010. The New Cultural Divide and the Two-Dimensional Political Space in Western Europe. West European Politics, 33(3): 419--444

work page 2010

[6] [6]

Bouchaud, P.; Chavalarias, D.; and Panahi, M. 2023. Crowdsourced Audit of Twitter 's Recommender Systems. Scientific Reports, 13(1): 16815

work page 2023

[7] [7]

Tweet Tweet Retweet: Conversational Aspects of Retweeting on Twitter

boyd, d.; Golder, S.; and Lotan, G. 2010. Tweet, Tweet, Retweet: Conversational Aspects of Retweeting on Twitter. In 43rd Hawaii International Conference on Social Systems (HICSS). IEEE. Citation: boyd, danah, Scott Golder, and Gilad Lotan (Forthcoming, 2010)."Tweet Tweet Retweet: Conversational Aspects of Retweeting on Twitter." Proceedings of HICSS-42, ...

work page 2010

[8] [8]

a -Anttila , T.; and Kivel \

Chen, T. H. Y.; Salloum, A.; Gronow, A.; Yl \"a -Anttila , T.; and Kivel \"a , M. 2021. Polarization of Climate Politics Results from Partisan Sorting: Evidence from Finnish Twittersphere . Global Environmental Change, 71: 102348

work page 2021