Structural Bias Beyond Homophily: A Study of Fairness in Link Prediction

Charlotte Laclau; Lilian Marey; Mathilde Perez; Tiphaine Viard

REVIEW 4 major objections 6 minor 37 references

Structural Bias Beyond Homophily: A Study of Fairness in Link Prediction

T0 review · 4 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The fairness of link prediction is largely determined by graph topology, and current fairness-aware methods remain sensitive to structural biases beyond homophily.

desk verdict A useful benchmark toolkit for fair link prediction, but the beyond-homophily claim needs confounder control before it can carry weight. read the letter →

arxiv 2602.11802 v2 pith:MVPUD5AM submitted 2026-02-12 cs.LG

Lilian Marey , Mathilde Perez , Tiphaine Viard , Charlotte Laclau This is my paper

classification cs.LG

keywords linkpredictionfairnessstructuralbiashomophilygraphgenerationpreferentialattachmenttopologicalbenchmarking

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

This paper tries to establish that fairness in link prediction—who gets recommended as a friend, collaborator, or job candidate—is strongly shaped by the graph's topology, not just by homophily, the tendency of similar people to connect. The authors formalize a taxonomy of structural bias measures (degree, centrality, neighborhood heterogeneity, information flow, and more) and use an extended preferential-attachment graph generator to create thousands of synthetic graphs with controlled bias profiles. They show that fairness scores can be predicted from these structural measures with regression R^2 above 0.8 across three use cases and multiple link-prediction models. They then show that even when homophily (assortativity) is held constant, fairness outcomes still change as heterogeneity, information unfairness, and power-exponent biases vary. The conclusion a sympathetic reader would draw is that fair link prediction cannot be evaluated with homophily alone; fairness-aware methods must be stress-tested across a broader range of structural biases.

What carries the argument

The central mechanism is the combination of a taxonomy of structural bias measures and an extended Barabási-Albert (preferential attachment) graph generator. The taxonomy classifies biases into node-level measures (closeness, betweenness, prestige, degree, constraint, density, heterogeneity, and effective-resistance-based isolation, diameter, and control) and graph-level measures (assortativity, average mixed distance, power exponent, and information unfairness), each defined as a normalized difference between sensitive groups. The generator extends the standard preferential-attachment model with four modular controls: sensitive attribute imbalance (α), homophily intensity (β), anchor-based

What would settle it

A concrete check: use the generator to create graphs where each structural measure is residualized on assortativity (so they vary independently), and test whether fairness still changes when assortativity is fixed. If fairness no longer changes with heterogeneity, information unfairness, or power exponent, the claim of sensitivity to beyond-homophily biases is falsified. Alternatively, compare fairness of a model on real-world graphs matched for assortativity but differing on these other biases; if fairness is invariant, the claim is refuted.

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Extended reading notes

Core claim

The paper's central claim is that fairness outcomes in link prediction are strongly correlated with graph topology, and that current fairness-aware methods remain sensitive to structural biases beyond homophily. Empirically, the authors report R^2 > 0.8 when regressing fairness scores on structural bias measures across three synthetic use cases (opinion blogs, friendship ego-networks, and collaboration networks) and multiple models (Node2Vec, SVD, NMF, Fairwalk, DeBayes, CrossWalk, FairAdj, FLIP). They also show, in Section 5.3, that when graphs are partitioned by assortativity, fairness metrics still change as heterogeneity, information unfairness, and power exponent vary, indicating that t

Load-bearing premise

The extended Barabási-Albert generator is assumed to vary structural biases independently enough that subsets matched on assortativity isolate each named bias; in fact, all bias measures vary with both class imbalance and homophily parameters, so the observed fairness changes may be driven by other correlated structural features.

Editorial extensions

If this is right

If fairness is strongly determined by topology, a fairness-aware method validated on one graph may not transfer to another graph with the same homophily but different heterogeneity or information flow; benchmarking must therefore vary multiple structural biases.
The proposed taxonomy and generator provide a reusable testbed for fair link prediction, enabling stress-testing of methods under controlled bias configurations.
Reporting fairness metrics alone is insufficient; papers should report the structural bias profile of the evaluation graph to make results comparable.
The high R^2 (above 0.8) implies fairness scores are largely predictable from structural measures, suggesting structural bias measures could serve as diagnostics or proxies for fairness when sensitive attributes are incomplete.

Reading between the lines

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

Because the paper's own Appendix C shows the bias measures are correlated, the independent effect of each beyond-homophily bias is not fully isolated; a generator that orthogonalizes these measures would provide stronger evidence for the specific attributions.
The strong R^2 may partly reflect the generator's parameterization; testing on real-world graphs with varied topologies would clarify whether the topology–fairness link is as strong outside the synthetic corpus.
The paper's conclusions imply that homophily-focused fairness methods (such as fair random walks) should be re-evaluated in low-assortativity, high-heterogeneity networks, where their assumptions may break down.
The taxonomy could be extended to multivalued or multivariate sensitive attributes, and the same generation framework could test whether the conclusions hold when groups are defined by more than one attribute.

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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 thing to know: this is a genuinely useful benchmarking package — a taxonomy plus a tunable BA-style generator for fair link prediction — and the broad empirical claim that fairness metrics track graph topology is credible. The sharper claim, that fairness-aware models stay sensitive to non-homophily biases when assortativity is fixed, is not yet established by the experiments as written.

What's new: they unify existing node/group bias measures into one taxonomy, extend BA with alpha (class imbalance), beta (homophily), gamma variance, anchor-based community attachment, and calibrate three synthetic scenarios to Polblogs, Facebook ego, and coauthorship. Running N2V, SVD, NMF plus Fairwalk, Debayes, CrossWalk, FairAdj, FLIP over 1,000 graphs per scenario is real work. The R2 values in Table 3 are high and consistent; Figure 3's pattern — assortativity driven by beta, heterogeneity by alpha — is plausible and useful.

Soft spots. The evidence for the 'beyond homophily' part is weaker than the abstract implies. RQ1 regresses fairness on collinear bias measures with a fitted Random Forest; high R2 and impurity importance do not tell you which structural feature causes what. RQ3 partitions graphs by measured assortativity and attributes fairness differences to heterogeneity, info unfairness, or power exponent. But the generator only varies alpha and beta directly; all other bias measures are emergent from those two, and Appendix C shows every measure moves with both. So within an assortativity bin, the subsets also differ in alpha, degree disparity, density, and the rest. The Mann-Whitney tests only show distributions differ, not which feature drives it. This is a load-bearing flaw for the specific attribution, though not for the broader 'topology matters' claim.

Also: no code or data released, and no error bars on the R2 or percentage differences. Those are fixable. I would not desk-reject; I'd send it to review and ask for code, confidence intervals, and a proper confounder analysis — partial correlations or generator-level controls that hold alpha and collinear measures fixed. The paper is aimed at fair graph learning researchers who want a controlled benchmark; with revisions it could be a standard reference. My own verdict is skeptical on the headline claim but positive on the toolkit.

Referee Report

4 major / 6 minor

Summary. The paper introduces a benchmarking framework for fair link prediction centered on structural biases in graphs. It proposes a taxonomy of node-level and graph-level bias measures, extends the Barabási–Albert generator with sensitive-attribute imbalance α, homophily intensity β, anchor-based community structure, and Gamma-distributed degree variability, and evaluates eight LP models on synthetic graphs fitted to three real datasets (Polblogs, Facebook ego, co-authorship). Using a corpus of over 1,000 graphs per setting, the authors report high Random Forest R² values (Table 3) when regressing fairness metrics on structural-bias measures, analyze feature importances, and claim in RQ3 that fairness-aware methods remain sensitive to HETEROGENEITY, INFO UNFAIRNESS, and POWER EXP even when assortativity is held fixed (Table 4, Tables 6–10).

Significance. The paper addresses an important and underexplored problem: fairness evaluation in link prediction has focused on homophily, while other structural biases may also affect fairness outcomes. The taxonomy is a useful synthesis of existing measures, and the generator is simple, interpretable, and calibrated to real network statistics. The study covers multiple fairness-aware methods across three distinct use cases, and the fixed-assortativity comparison is a meaningful step beyond homophily. If the main empirical claim were established, this would be a valuable contribution to fair graph learning and would motivate structurally grounded benchmarks. The high R² correlation result is plausible and interesting; however, the causal attribution of 'beyond homophily' sensitivity and the reproducibility of the experiments require substantial strengthening.

major comments (4)

[§5.3, Tables 4, 6–10] The central claim that fairness-aware methods are sensitive to structural biases beyond homophily is not established by the presented analysis. The generator controls only α and β directly; HETEROGENEITY, INFO UNFAIRNESS, POWER EXP, and the other bias measures are emergent and correlated functions of α and β. Appendix C heatmaps show every bias measure varies with both parameters, and Appendix C.1 reports strong inter-measure correlations. Appendix D further shows that SP/EO grow directly with α. Partitioning graphs into low/high ASSORTATIVITY and then splitting on a third measure cannot isolate that measure, because α, degree disparity, density, and other collinear features vary within the bins. The Mann-Whitney tests only establish that the subsets have different metric distributions, not which feature drives the difference. To support the specific attribution, the authors need generat
[§5.1, Table 3] The RQ1 analysis uses Random Forest regressors with all bias measures as features. The reported R² is an in-sample fit, not an independent predictive or explanatory result, and impurity-based feature importance on collinear features is not a reliable attribution. The statement that fairness scores 'can be largely explained by the graph’s topological properties' is therefore overstated. Moreover, the text says 'R² values consistently above 0.8', but Table 3 reports NMF EO Opinion R²=0.74. Please report cross-validated R², error bars across the 5 splits, and clearly distinguish correlation, prediction, and explanation. If 'explainability' is intended, a variance partition or ablations with held-out feature sets would be needed.
[Section 5 and Appendix D] The paper states: 'All models achieve strong predictive performance (see Appendix D), ensuring that observed fairness differences are not confounded by weak predictive quality.' Appendix D actually reports Hit@10 values as low as 0.01–0.09 and AP@10 near 0.00 for the Opinion use case (e.g., Figures 21–22, 25–26, 29–30). If models are near-random or poorly calibrated on these graphs, fairness differences can be driven by very few positive predictions. The manuscript should report AUC or a comparable metric for every model and use case, and either demonstrate strong performance across metrics or restrict the fairness analysis to settings where predictive quality is sufficient.
[§5.3, Tables 4, 6–10] The construction of the compared subsets is underspecified. 'Low/high ASSORTATIVITY' and 'subsets that differ significantly in HETEROGENEITY, INFO UNFAIRNESS, POWER EXP' need precise operational definitions: quantile thresholds, number of graphs, whether the subsets are disjoint, and the corresponding α/β ranges. The tables report percentage changes without raw values, confidence intervals, or effect sizes, and the large number of comparisons in the appendix would require multiple-testing correction. Without this information, the stability and reproducibility of the RQ3 results cannot be assessed.

minor comments (6)

[Appendix A] Typo: 'V ⊂ E × E' should be 'E ⊂ V × V'. Also, 'Fiendship' in Appendix B.1 and 'convoltuonal' in reference [19] should be corrected.
[Table 1] The caption says 'Measures in red are from fairness-oriented works', but the red color is not visible in monochrome print or plain text. Use bold symbols or asterisks instead.
[Figure 4] The caption should explain what the red crosses represent and how the box plots aggregate over the 5 train/test splits and graph realizations.
[§5.1, Table 3] The column '%R² assessed by ASSORTATIVITY' is not defined. Is this the R² of a univariate regression using only assortativity, or a variance partition in the Random Forest? Please clarify in the caption.
[Reproducibility] No code, seeds, or exact graph counts are provided. For a benchmark contribution, please include a reproducibility appendix with generator hyperparameters, random seeds, and code/data availability.
[Tables 4, 6–10] Significance is indicated by color, which is lost in monochrome or text-based versions. Add asterisks and report p-values or effect sizes.

Circularity Check

1 steps flagged · score 2.0 of 10

No definitional circularity; results are empirical. Minor in-sample-fit issue in RQ1, but RQ3's fixed-assortativity comparisons provide independent, non-tautological evidence.

fitted input called prediction [Section 5.1 (RQ1) and Table 3]
"To assess how strongly structural biases influence fairness outcomes, we train Random Forest regressors to predict fairness scores from structural bias measures. ... Table 3 shows the R2 scores ... The results reveal a strong link between structural bias and fairness, with R2 values consistently above 0.8. This indicates that fairness scores can be largely explained by the graph's topological properties."

The high R2 is presented as evidence of a 'strong link' between structural bias and fairness, but it is the in-sample fit of regressors trained on the same fairness scores they are used to explain; no held-out or cross-validated prediction of fairness from structural measures is reported. The explanatory claim therefore partly restates the fitted relationship. This is a minor form of the fitted-input-called-prediction pattern, and it does not affect the independent RQ3 fixed-assortativity comparisons.

full rationale

The paper is an empirical study rather than a derivation, and no central result reduces to its inputs by construction. The taxonomy and bias measures are defined independently of model fairness outcomes; the graph generator varies α and β, and fairness metrics are measured from trained LP models, so the reported correlations and sensitivity results are not definitional. RQ3 partitions graphs by measured assortativity and compares subsets differing in other bias measures, providing a non-tautological comparison even if confounds among the emergent bias measures remain a validity concern. Self-citations (e.g., [21]) appear only in related-work context and are not load-bearing. The sole mild circularity is RQ1's in-sample R2 being framed as evidence of explanation rather than as a predictive validation; this is minor and does not undermine the paper's main empirical claims.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central empirical claims rest on the extended BA generator's α, β, m, γ, and anchor weights, all fitted or swept by hand. No new physical or formal entities are postulated. The main hidden load is the assumption that one generative family covers the structural-bias space relevant to fair link prediction.

free parameters (5)

α (sensitive class imbalance) = 0.52 (Opinion), 0.66 (Friendship), 0.53 (Collab); swept 0.50–0.90
Fitted to real datasets in Table 5 then varied; controls group-size disparity and strongly affects heterogeneity/assortativity in Appendix C.
β (homophily intensity) = swept 0–8 (Opinion/Collab), 0–3.8 (Friendship)
Free control in attachment probability Eq. (1); drives assortativity (Figure 5) and therefore fairness outcomes.
m (expected edges per new node) = 14 (Opinion), 3 (Collab); Friendship uses affine 0.55·deg(u)+3
Standard BA parameter fitted to match real degree distributions in Table 2/Table 5.
γ (Gamma variance parameter) = 0.08 (Opinion), 1 (Collab); not used for Friendship
Controls degree heterogeneity; fitted to real degree distributions.
anchor-node attachment weights = Friendship: 1-hop high, 2-hop 2, 3+hop 1; Collab: 1-hop 1, 2+hop 0
Hand-set in Table 2 to mimic community-driven attachment; affects local structure and heterogeneity.

assumptions (5)

domain assumption Barabási–Albert preferential attachment produces graphs whose structural bias space is representative of real-world social networks for link-prediction fairness.
The entire corpus is generated by the extended BA model (Section 3.2); if BA-family graphs miss topologies where other biases dominate, the general conclusion is unsupported.
domain assumption Measured assortativity is an adequate proxy for homophily when constructing 'fixed homophily' subsets in RQ3.
RQ3 groups by sampled ASSORTATIVITY rather than controlling β; Figure 5 shows monotone but not one-to-one relationship.
domain assumption Random-forest impurity importance is a reliable attribution of fairness variance to individual collinear structural measures.
Section 5.1 uses impurity-based feature importance despite strong correlations between measures (Appendix C.1).
domain assumption Binary sensitive attribute and dyadic/statistical-parity fairness metrics capture the fairness-relevant bias for the studied tasks.
All definitions use S:V→{0,1}; the paper states multivalued attributes as future work (Section 6).
standard math Effective resistance and information-unfairness measures from [31] and [16] are well-defined for the generated graphs.
Used in Appendix A.1/A.2; standard graph-theoretic definitions relying on the Laplacian pseudo-inverse.

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Cite this review

Pith. "Pith review of Structural Bias Beyond Homophily: A Study of Fairness in Link Prediction." pith.science (2026). https://pith.science/paper/MVPUD5AM

@misc{pith2026260211802,
  author       = {Pith},
  title        = {Pith review of: Structural Bias Beyond Homophily: A Study of Fairness in Link Prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MVPUD5AM}},
  note         = {Machine review of arXiv:2602.11802}
}

read the original abstract

Graph link prediction (LP) plays a critical role in socially impactful applications such as job recommendation and friendship formation, making fairness a critical concern in this task. While many fairness-aware methods manipulate graph structures to mitigate prediction disparities, the topological biases inherent to social graphs remain poorly understood and are consistently conflated with homophily alone. In this work, we study the relationship between structural biases and fairness outcomes in LP. To this end, we formalize a taxonomy of topological bias measures and introduce a graph generation method producing a diverse corpus of synthetic graphs with controlled structural properties. Using this corpus, we show empirically that fairness outcomes are strongly correlated with graph topology, and that current fairness-aware methods remain sensitive to structural biases beyond homophily. These findings highlight the need for structurally grounded evaluations in fair graph learning.

Figures

Figures reproduced from arXiv: 2602.11802 by the authors.

**Figure 2.** Examples of structural bias → Fairness regression feature importance scores. From left to right: Opinion SP N2V, Opinion SP SVD, Friendship SP N2V. In addition, the importance scores ( [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** ASSORTATIVITY (top) and HETEROGENEITY (bottom) across class imbalance and homophily parameters, in Opinion (left), Friendship (middle), and Collab (right) use cases. 5.2 Comparing Fairness Approaches in Terms of Structural Bias Dependencies (RQ2) To assess the robustness of fairness-aware LP methods to structural bias, we evaluate them on graphs generated by our framework [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (29 more)

**Figure 4.** Figure 4: Box plots of fair models on generated use cases. The red crosses represent the results on the real datasets: [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: ASSORTATIVITY values of generated graphs with respect to homophily parameter β in the three scenarios (other graph generation parameters are fitted to real datasets) [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

**Figure 7.** Figure 7: BETWEENNESS values in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) -0.40 0.00 0.40 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) -0.14 0.00 0.14 0.00 8.00 homophily ( ) 0…

**Figure 8.** Figure 8: PRESTIGE values in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) -0.33 0.00 0.33 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) -0.09 0.00 0.09 0.00 8.00 homophily ( ) 0.50…

**Figure 9.** Figure 9: DEGREE values in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) -0.42 0.00 0.42 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) -0.10 0.00 0.10 0.00 8.00 homophily ( ) 0.50 0…

**Figure 10.** Figure 10: CONSTRAINT values in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) -0.21 0.00 0.21 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) -0.03 0.00 0.03 0.00 8.00 homophily ( ) 0…

**Figure 11.** Figure 11: DENSITY values in Opinion (left), Friendship (middle), and Collab. (right) use cases. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

**Figure 12.** Figure 12: HETEROGENEITY values in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.11 0.21 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.00 0.01 0.00 8.00 homophily ( ) …

**Figure 13.** Figure 13: ISOLATION values in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.10 0.21 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.00 0.01 0.00 8.00 homophily ( ) 0.50…

**Figure 14.** Figure 14: DIAMETER values in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.22 0.43 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.12 0.24 0.00 8.00 homophily ( ) 0.50 …

**Figure 15.** Figure 15 [PITH_FULL_IMAGE:figures/full_fig_p016_15.png]

**Figure 16.** Figure 16: ASSORTATIVITY in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 3.50 3.81 4.12 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 3.59 3.74 3.88 0.00 8.00 homophily ( ) 0.50 0.…

**Figure 17.** Figure 17: AVG MIXED DIST in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.39 0.73 1.06 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.35 0.81 1.26 0.00 8.00 homophily ( ) 0.50 0…

**Figure 18.** Figure 18: POWER EXP in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 19.77 39.53 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 6.13 12.25 0.00 8.00 homophily ( ) 0.50 0.9…

**Figure 19.** Figure 19 [PITH_FULL_IMAGE:figures/full_fig_p017_19.png]

**Figure 20.** Figure 20: Correlations between structural bias measures in [PITH_FULL_IMAGE:figures/full_fig_p018_20.png]

**Figure 21.** Figure 21 [PITH_FULL_IMAGE:figures/full_fig_p018_21.png]

**Figure 22.** Figure 22: AP@10 for N2V models in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.01 0.49 0.98 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.39 0.78 0.00 8.00 homophily ( ) …

**Figure 23.** Figure 23: SP@10 for N2V models in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.01 0.01 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.07 0.13 0.00 8.00 homophily ( ) …

**Figure 24.** Figure 24: EO@10 for N2V models in Opinion (left), Friendship (middle), and Collab. (right) use cases. D.2 Singular Value Decomposition (SVD) 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.01 0.04 0.06 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) …

**Figure 25.** Figure 25: Hit@10 for SVD models in Opinion (left), Friendship (middle), and Collab. (right) use cases. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_25.png]

**Figure 26.** Figure 26: AP@10 for SVD models in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.01 0.41 0.82 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.01 0.36 0.71 0.00 8.00 homophily ( ) …

**Figure 27.** Figure 27: SP@10 for SVD models in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.00 0.01 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.02 0.04 0.00 8.00 homophily ( ) …

**Figure 28.** Figure 28: EO@10 for SVD models in Opinion (left), Friendship (middle), and Collab. (right) use cases. D.3 Non-Negative Matrix Factorization (NMF) 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.02 0.04 0.06 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e…

**Figure 29.** Figure 29: Hit@10 for NMF models in Opinion (left), Friendship (middle), and Collab. (right) use cases. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_29.png]

**Figure 30.** Figure 30: AP@10 for NMF models in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.39 0.77 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.01 0.36 0.71 0.00 8.00 homophily ( ) …

**Figure 31.** Figure 31: SP@10 for NMF models in Opinion (left), Friendship (middle), and Collab. (right) use cases. 0.00 8.00 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.00 0.01 0.00 3.80 homophily ( ) 0.50 0.90 cla s s im b ala n c e ( ) 0.00 0.02 0.04 0.00 8.00 homophily ( ) …

**Figure 32.** Figure 32: EO@10 for NMF models in Opinion (left), Friendship (middle), and Collab. (right) use cases. E Additional Results for Fairness Methods’ Robustness at Fixed Homophily Model Assor. Heterogeneity Info unfairness Power exp Hit EO SP Hit EO SP Hit EO SP crosswalk high 3.1 0…

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Works this paper leans on

37 extracted references · 1 canonical work pages

[1]

Stochastic blockmodels: First steps

Paul Holland et al. “Stochastic blockmodels: First steps”. In:Social networks5.2 (1983), pp. 109–137. 21 Model Assor. Heterogeneity Info unfairness Power exp Hit EO SP Hit EO SP Hit EO SP crosswalk high -0.50.3 35.8 0.8-0.4 -43 -0.60.4 45.2 low -1.4 0.5 61.2 0.9-0.4 -48.9 -0.80.4 58.1 debayes high -0.3 0.1 10.5 -0.1 -0.1 -13.5 -0.20.4 15.8 low -1.40.6 63....

1983
[2]

Network measures of social capital

Stephen P Borgatti et al. “Network measures of social capital”. In:Connections21.2 (1998), pp. 27–36

1998
[3]

Emergence of scaling in random networks

Albert-L ´aszl´o Barab´asi and R´eka Albert. “Emergence of scaling in random networks”. In:science286.5439 (1999), pp. 509–512

1999
[4]

Birds of a feather: Homophily in social networks

Miller McPherson et al. “Birds of a feather: Homophily in social networks”. In:Annual review of sociology27.1 (2001), pp. 415–444

2001
[5]

The structure and function of complex networks

Mark EJ Newman. “The structure and function of complex networks”. In:SIAM review45.2 (2003), pp. 167–256

2003
[6]

The political blogosphere and the 2004 US election: divided they blog

Lada A Adamic and Natalie Glance. “The political blogosphere and the 2004 US election: divided they blog”. In: Proceedings of the 3rd international workshop on Link discovery. 2005, pp. 36–43. 22

2004
[7]

Finding structure with randomness: Probabilistic algo- rithms for constructing approximate matrix decompositions

Nathan Halko, Per-Gunnar Martinsson, and Joel A Tropp. “Finding structure with randomness: Probabilistic algo- rithms for constructing approximate matrix decompositions”. In:SIAM review53.2 (2011), pp. 217–288

2011
[8]

penguin UK, 2011

Eli Pariser.The filter bubble: What the Internet is hiding from you. penguin UK, 2011

2011

Show all 37 references

[9]

Learning to discover social circles in ego networks

Jure Leskovec and Julian Mcauley. “Learning to discover social circles in ego networks”. In:Advances in neural information processing systems25 (2012)

2012
[10]

node2vec: Scalable feature learning for networks

Aditya Grover and Jure Leskovec. “node2vec: Scalable feature learning for networks”. In:Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining. 2016, pp. 855–864

2016
[11]

Sources of segregation in social networks: A novel approach using Facebook

Bas Hofstra et al. “Sources of segregation in social networks: A novel approach using Facebook”. In:American Sociological Review82.3 (2017), pp. 625–656

2017
[12]

Pitfalls of graph neural network evaluation

Oleksandr Shchur et al. “Pitfalls of graph neural network evaluation”. In:arXiv preprint arXiv:1811.05868(2018)

2018 arXiv
[13]

Algorithmic glass ceiling in social networks: The effects of social recommendations on network diversity

A Stoica et al. “Algorithmic glass ceiling in social networks: The effects of social recommendations on network diversity”. In:Proceedings of the 2018 World Wide Web Conference. 2018, pp. 923–932

2018
[14]

Fairwalk: Towards Fair Graph Embedding

Tahleen Rahman et al. “Fairwalk: Towards Fair Graph Embedding”. In:Proceedings of the Twenty-Eighth Inter- national Joint Conference on Artificial Intelligence, IJCAI-19. International Joint Conferences on Artificial Intelli- gence Organization, July 2019, pp. 3289–3295.DOI: 1...

2019 doi
[15]

DeBayes: a Bayesian method for debiasing network embeddings

Maarten Buyl and Tijl De Bie. “DeBayes: a Bayesian method for debiasing network embeddings”. In:Proceedings of ICML. 2020

2020
[16]

On the information unfairness of social networks

Zeinab S Jalali et al. “On the information unfairness of social networks”. In:Proceedings of the 2020 SIAM Inter- national Conference on Data Mining. SIAM. 2020, pp. 613–521

2020
[17]

Bursting the filter bubble: Fairness-aware network link prediction

Farzan Masrour et al. “Bursting the filter bubble: Fairness-aware network link prediction”. In:Proceedings of the AAAI conference on artificial intelligence. V ol. 34. 2020, pp. 841–848

2020
[18]

Geom-gcn: Geometric graph convolutional networks

Hongbin Pei et al. “Geom-gcn: Geometric graph convolutional networks”. In:arXiv preprint arXiv:2002.05287 (2020)

2002 arXiv
[19]

Investigating and mitigating degree-related biases in graph convoltuional networks

Xianfeng Tang et al. “Investigating and mitigating degree-related biases in graph convoltuional networks”. In:Pro- ceedings of the 29th ACM International Conference on Information & Knowledge Management. 2020, pp. 1435– 1444

2020
[20]

Say no to the discrimination: Learning fair graph neural networks with limited sensitive attribute information

Enyan Dai and Suhang Wang. “Say no to the discrimination: Learning fair graph neural networks with limited sensitive attribute information”. In:Proceedings of the 14th ACM international conference on web search and data mining. 2021, pp. 680–688

2021
[21]

All of the fairness for edge prediction with optimal transport

Charlotte Laclau et al. “All of the fairness for edge prediction with optimal transport”. In:International Conference on Artificial Intelligence and Statistics. PMLR. 2021, pp. 1774–1782

2021
[22]

On dyadic fairness: Exploring and mitigating bias in graph connections

Peizhao Li et al. “On dyadic fairness: Exploring and mitigating bias in graph connections”. In:International Con- ference on Learning Representations. 2021

2021
[23]

Fairdrop: Biased edge dropout for enhancing fairness in graph representation learning

Indro Spinelli et al. “Fairdrop: Biased edge dropout for enhancing fairness in graph representation learning”. In: IEEE Transactions on Artificial Intelligence3.3 (2021), pp. 344–354

2021
[24]

Graph learning with localized neighborhood fairness

April Chen et al. “Graph learning with localized neighborhood fairness”. In:arXiv preprint arXiv:2212.12040 (2022)

2022 arXiv
[25]

Edits: Modeling and mitigating data bias for graph neural networks

Yushun Dong et al. “Edits: Modeling and mitigating data bias for graph neural networks”. In:Proceedings of the ACM web conference 2022. 2022, pp. 1259–1269

2022
[26]

Crosswalk: Fairness-enhanced node representation learning

Ahmad Khajehnejad et al. “Crosswalk: Fairness-enhanced node representation learning”. In:Proceedings of the AAAI Conference on Artificial Intelligence. V ol. 36. 2022

2022
[27]

Fairlp: Towards fair link prediction on social network graphs

Yanying Li et al. “Fairlp: Towards fair link prediction on social network graphs”. In:Proceedings of the interna- tional AAAI conference on web and social media. V ol. 16. 2022, pp. 628–639

2022
[28]

Fairedit: Preserving fairness in graph neural networks through greedy graph editing

Donald Loveland et al. “Fairedit: Preserving fairness in graph neural networks through greedy graph editing”. In: arXiv preprint arXiv:2201.03681(2022)

2022 arXiv
[29]

Beyond real-world benchmark datasets: An empirical study of node classification with GNNs

Seiji Maekawa, Koki Noda, Yuya Sasaki, et al. “Beyond real-world benchmark datasets: An empirical study of node classification with GNNs”. In:Advances in Neural Information Processing Systems35 (2022), pp. 5562–5574

2022
[30]

A survey on deep graph generation: Methods and applications

Yanqiao Zhu et al. “A survey on deep graph generation: Methods and applications”. In:Learning on Graphs Conference. PMLR. 2022, pp. 47–1

2022
[31]

Structural Group Unfairness: Measurement and Mitigation by means of the Effec- tive Resistance

Adrian Arnaiz-Rodriguez et al. “Structural Group Unfairness: Measurement and Mitigation by means of the Effec- tive Resistance”. In:arXiv preprint arXiv:2305.03223(2023). 23

2023 arXiv
[32]

Evaluating graph neural networks for link prediction: Current pitfalls and new benchmarking

Juanhui Li et al. “Evaluating graph neural networks for link prediction: Current pitfalls and new benchmarking”. In:Advances in Neural Information Processing Systems36 (2023), pp. 3853–3866

2023
[33]

GenCAT: Generating attributed graphs with controlled relationships between classes, at- tributes, and topology

Seiji Maekawa et al. “GenCAT: Generating attributed graphs with controlled relationships between classes, at- tributes, and topology”. In:Information Systems115 (2023), p. 102195

2023
[34]

A topology-aware analysis of graph collaborative filtering

Daniele Malitesta et al. “A topology-aware analysis of graph collaborative filtering”. In:arXiv preprint arXiv:2308.10778 (2023)

2023 arXiv
[35]

Link Prediction Without Learning

Simon Delarue et al. “Link Prediction Without Learning”. In:European Conference on Artificial Intelligence. 2024

2024
[36]

Fairgen: Towards fair graph generation

Lecheng Zheng et al. “Fairgen: Towards fair graph generation”. In:2024 IEEE 40th International Conference on Data Engineering (ICDE). IEEE. 2024, pp. 2285–2297

2024
[37]

Fairness amidst non-IID graph data: A literature review

Wenbin Zhang et al. “Fairness amidst non-IID graph data: A literature review”. In:AI Magazine46.1 (2025), e12212. 24

2025

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [1]

Stochastic blockmodels: First steps

Paul Holland et al. “Stochastic blockmodels: First steps”. In:Social networks5.2 (1983), pp. 109–137. 21 Model Assor. Heterogeneity Info unfairness Power exp Hit EO SP Hit EO SP Hit EO SP crosswalk high -0.50.3 35.8 0.8-0.4 -43 -0.60.4 45.2 low -1.4 0.5 61.2 0.9-0.4 -48.9 -0.80.4 58.1 debayes high -0.3 0.1 10.5 -0.1 -0.1 -13.5 -0.20.4 15.8 low -1.40.6 63....

1983

[2] [2]

Network measures of social capital

Stephen P Borgatti et al. “Network measures of social capital”. In:Connections21.2 (1998), pp. 27–36

1998

[3] [3]

Emergence of scaling in random networks

Albert-L ´aszl´o Barab´asi and R´eka Albert. “Emergence of scaling in random networks”. In:science286.5439 (1999), pp. 509–512

1999

[4] [4]

Birds of a feather: Homophily in social networks

Miller McPherson et al. “Birds of a feather: Homophily in social networks”. In:Annual review of sociology27.1 (2001), pp. 415–444

2001

[5] [5]

The structure and function of complex networks

Mark EJ Newman. “The structure and function of complex networks”. In:SIAM review45.2 (2003), pp. 167–256

2003

[6] [6]

The political blogosphere and the 2004 US election: divided they blog

Lada A Adamic and Natalie Glance. “The political blogosphere and the 2004 US election: divided they blog”. In: Proceedings of the 3rd international workshop on Link discovery. 2005, pp. 36–43. 22

2004

[7] [7]

Finding structure with randomness: Probabilistic algo- rithms for constructing approximate matrix decompositions

Nathan Halko, Per-Gunnar Martinsson, and Joel A Tropp. “Finding structure with randomness: Probabilistic algo- rithms for constructing approximate matrix decompositions”. In:SIAM review53.2 (2011), pp. 217–288

2011

[8] [8]

penguin UK, 2011

Eli Pariser.The filter bubble: What the Internet is hiding from you. penguin UK, 2011

2011