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REVIEW 1 major objections 1 minor 67 references

Community detection robustness of graph neural networks

T0 review · 1 major / 1 minor · reviewed 2026-05-18 · grok-4.3

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Pith's one-line read Supervised GNNs start more accurate on community detection but unsupervised models like DMoN hold up better under perturbations and attacks.

desk verdict This paper benchmarks six GNNs on community detection under perturbations and flags unsupervised models like DMoN as more resilient, but the supervised-unsupervised split may not be evaluated under identical protocols. read the letter →

arxiv 2509.24662 v1 submitted 2025-09-29 cs.SI cs.AIphysics.soc-phstat.ML

Jaidev Goel , Pablo Moriano , Ramakrishnan Kannan , Yulia R. Gel This is my paper · ORCID
classification cs.SIcs.AIphysics.soc-phstat.ML
keywords graphneuralnetworkscommunitydetectionrobustnessadversarialattacksnetworkperturbationsunsupervisedmethodssupervisedcitation
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 tests six graph neural network architectures on the task of recovering communities in networks where node attributes or edges have been altered or attacked. It compares performance on both synthetic graphs with controlled community strength and real citation networks, using element-centric similarity to measure how well the detected groups match the true ones. Supervised models post higher scores when data is clean, yet they lose more ground when faced with targeted changes, while unsupervised methods prove steadier especially when communities are clearly separated. The work matters because GNNs are now common tools for grouping nodes in noisy or contested network data, and knowing which architectures survive real-world distortions helps choose the right one.

What carries the argument

Comparative evaluation of six GNN architectures (GCN, GAT, Graph-SAGE, DiffPool, MinCUT, DMoN) across node attribute manipulations, edge topology distortions, and adversarial attacks, scored by element-centric similarity.

What would settle it

A controlled experiment on a new set of networks with stronger community mixing or a different attack type that reverses the resilience pattern, showing unsupervised models degrading faster than supervised ones.

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Extended reading notes

Core claim

Supervised GNNs tend to achieve higher baseline accuracy, while unsupervised methods, particularly DMoN, maintain stronger resilience under targeted and adversarial perturbations. Robustness appears to be strongly influenced by community strength, with well-defined communities reducing performance loss. Across all models, node attribute perturbations associated with targeted edge deletions and shift in attribute distributions tend to cause the largest degradation in community recovery.

Load-bearing premise

The synthetic benchmarks, real citation networks, and three chosen categories of perturbations represent the conditions GNNs face in typical community detection settings.

Editorial extensions

If this is right

  • Unsupervised architectures such as DMoN become preferable when networks may contain adversarial tampering or attribute noise.
  • Stronger inherent community structure in the data lowers the performance drop for every tested model.
  • Targeted changes to node attributes combined with edge deletions inflict more damage than random or uniform perturbations.
  • Designers must weigh initial accuracy against sustained performance when deploying GNNs for real-world grouping tasks.
  • Well-separated communities act as a buffer that preserves detection quality even after moderate attacks.

Reading between the lines

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

  • Adding explicit robustness objectives during training could narrow the accuracy gap between supervised and unsupervised approaches.
  • The same evaluation pattern may appear in other graph tasks such as link prediction or node classification under attack.
  • Testing on time-varying networks would show whether the observed resilience holds when perturbations accumulate over time.
  • Practitioners facing high-stakes grouping decisions might default to DMoN when data integrity cannot be guaranteed.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The paper evaluates the robustness of six GNN models (GCN, GAT, Graph-SAGE, DiffPool, MinCUT, DMoN) for community detection under node attribute manipulations, edge topology distortions, and adversarial attacks on synthetic and real-world networks. It reports that supervised GNNs have higher baseline accuracy, unsupervised methods like DMoN are more resilient, robustness depends on community strength, and node attribute perturbations with targeted edge deletions cause the most degradation, using element-centric similarity.

Significance. If validated, these empirical findings would be significant for understanding accuracy-robustness trade-offs in GNN community detection, aiding model selection in noisy environments. The multi-perturbation analysis and focus on community strength provide actionable insights beyond single-model studies.

major comments (1)
  1. [Experimental Setup] The central claim contrasting supervised GNNs' higher baseline accuracy with unsupervised methods' stronger resilience under perturbations assumes a uniform evaluation protocol. However, if unsupervised models like DMoN are re-optimized on perturbed graphs while supervised models like GCN are applied with parameters fixed from clean training data, the resilience difference may reflect adaptation rather than robustness. The manuscript must specify this protocol explicitly in the experimental setup to support the claim.
minor comments (1)
  1. [Abstract] The abstract presents qualitative findings without including any quantitative results, error bars, or specific parameter values for perturbations, making it difficult to assess the practical significance of the reported differences.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We have carefully considered the major comment regarding the experimental setup and protocol for evaluating robustness. We address this point below and will make the necessary revisions to enhance clarity.

read point-by-point responses

  1. Referee: [Experimental Setup] The central claim contrasting supervised GNNs' higher baseline accuracy with unsupervised methods' stronger resilience under perturbations assumes a uniform evaluation protocol. However, if unsupervised models like DMoN are re-optimized on perturbed graphs while supervised models like GCN are applied with parameters fixed from clean training data, the resilience difference may reflect adaptation rather than robustness. The manuscript must specify this protocol explicitly in the experimental setup to support the claim.

    Authors: We appreciate the referee pointing out the need for explicit clarification on our evaluation protocol. To address this, we confirm that in our experiments, the supervised GNNs (GCN, GAT, Graph-SAGE) are trained exclusively on the clean, unperturbed graphs using their standard training procedures. These trained models are then directly applied to the perturbed graphs for evaluation, without any re-optimization or adaptation to the perturbations. This setup tests the models' robustness to changes in input data. For the unsupervised models (DiffPool, MinCUT, DMoN), which do not involve a separate training phase on clean data, they are optimized or run directly on each perturbed graph as input. This is the natural and standard way to apply unsupervised community detection methods. We believe this protocol fairly compares the robustness, as it reflects real-world usage where supervised models are deployed after training and unsupervised ones process the available (possibly noisy) data. We will add a detailed description of this protocol in the Experimental Setup section of the revised manuscript to support our claims more robustly. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: empirical evaluation of GNN robustness

full rationale

The paper performs a direct computational comparison of six existing GNN architectures on community detection tasks under node, edge, and adversarial perturbations, reporting results via element-centric similarity on synthetic benchmarks and citation networks. No mathematical derivations, first-principles claims, or parameter-fitting steps are present that could reduce to the inputs by construction. All reported findings on accuracy-robustness trade-offs and the influence of community strength follow from the experimental protocol and external benchmarks rather than any self-definitional or self-citation load-bearing steps.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The central empirical claims rest on the representativeness of the chosen benchmarks and perturbations plus standard assumptions about GNN message-passing behavior; no new free parameters or invented entities are introduced in the abstract.

assumptions (2)
  • domain assumption Synthetic benchmarks and citation networks constitute a sufficient testbed for generalizing robustness observations.
    The abstract invokes these datasets without discussing their limitations or external validation.
  • domain assumption Element-centric similarity is an appropriate metric for comparing community recovery under perturbation.
    The abstract uses this metric as the sole evaluation criterion without justifying alternatives.

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Cite this review

Pith. "Pith review of Community detection robustness of graph neural networks." pith.science (2026). https://pith.science/paper/2509.24662

@misc{pith2026250924662,
  author       = {Pith},
  title        = {Pith review of: Community detection robustness of graph neural networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2509.24662}},
  note         = {Machine review of arXiv:2509.24662}
}
read the original abstract

Graph neural networks (GNNs) are increasingly widely used for community detection in attributed networks. They combine structural topology with node attributes through message passing and pooling. However, their robustness or lack of thereof with respect to different perturbations and targeted attacks in conjunction with community detection tasks is not well understood. To shed light into latent mechanisms behind GNN sensitivity on community detection tasks, we conduct a systematic computational evaluation of six widely adopted GNN architectures: GCN, GAT, Graph-SAGE, DiffPool, MinCUT, and DMoN. The analysis covers three perturbation categories: node attribute manipulations, edge topology distortions, and adversarial attacks. We use element-centric similarity as the evaluation metric on synthetic benchmarks and real-world citation networks. Our findings indicate that supervised GNNs tend to achieve higher baseline accuracy, while unsupervised methods, particularly DMoN, maintain stronger resilience under targeted and adversarial perturbations. Furthermore, robustness appears to be strongly influenced by community strength, with well-defined communities reducing performance loss. Across all models, node attribute perturbations associated with targeted edge deletions and shift in attribute distributions tend to cause the largest degradation in community recovery. These findings highlight important trade-offs between accuracy and robustness in GNN-based community detection and offer new insights into selecting architectures resilient to noise and adversarial attacks.

Figures

Figures reproduced from arXiv: 2509.24662 by the authors.

Figure 1
Figure 1. FIG. 1: GNN based community detection approach [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: ECS scores for GCN-based community [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: ECS scores for GAT-based community [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: FIG. 4: ECS scores for SAGE-based community [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: ECS scores for MinCut-based community [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: ECS scores for DiffPool-based community [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: ECS scores for DMoN-based community [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: ECS scores for Cora dataset. Under node [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: ECS scores for Citeseer dataset. Under node [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 11
Figure 11. Figure 11: FIG. 11: ECS scores for GCN-based community detec [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: ECS scores for GAT-based community [PITH_FULL_IMAGE:figures/full_fig_p020_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: ECS scores for GraphSAGE-based community [PITH_FULL_IMAGE:figures/full_fig_p021_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14: ECS scores for Diffpool-based community [PITH_FULL_IMAGE:figures/full_fig_p022_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15: ECS scores for Mincut-based community [PITH_FULL_IMAGE:figures/full_fig_p023_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16: ECS scores for DMoN-based community [PITH_FULL_IMAGE:figures/full_fig_p024_16.png]

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Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages

  1. [1]

    LFR benchmark The Lancichinetti–Fortunato–Radicchi (LFR) bench- mark has emerged as a popular tool for generating graphs with known community structures [32, 39]. Its primary strength lies in its ability to create networks where both degree and community size distributions follow power- laws, mirroring the characteristics of many real-world networks. Key ...

    work page

  2. [2]

    We vary the mixing parameter µ ranging between 0.1 to 0.5 to investigate the effects of perturbations at different initial community strengths

    to generate undirected, unweighted LFR benchmark graphs with 1,000 nodes. We vary the mixing parameter µ ranging between 0.1 to 0.5 to investigate the effects of perturbations at different initial community strengths

    work page

  3. [3]

    In the SBM, a graph with n vertices is partitioned into K different communities

    Stochastic block model (SBM) The standard (degree-free) SBM is a probabilistic framework for generating random graphs with planted community structure [41]. In the SBM, a graph with n vertices is partitioned into K different communities. Each vertex is assigned to one of these K communi- ties, and the probability of an edge existing between any two vertic...

    work page

  4. [4]

    Node attribute perturbation Here, we perturb node attributes by first, altering the location and then scale of their distribution. We add random Gaussian noise generated by varying location parameter and keeping scale parameter fixed and then varying the scale parameter, but keeping the location parameter fixed, similar to [22]. By doing this, we per- tur...

    work page

  5. [5]

    We follow the procedure outlined by [31]

    Graph topology perturbation We explore how removing edges affects network struc- ture through two approaches, random and targeted edge deletions. We follow the procedure outlined by [31]. In the random approach, which emulates real-world network failures, we randomly select some percentage of nodes ranging between 10% to 70% of the nodes in increments of ...

    work page

  6. [6]

    Adversarial attacks for community detection We also evaluate GNN robustness under more sophis- ticated attacks that target the overall learning process to degrade community detection performance. Specifically, we use Nettack [23] and Metattack [24] schemes, which represent advanced adversarial techniques designed to compromise graph-based machine learning...

    work page

  7. [7]

    They allow the learning of node representations based on both node features and graph structure

    GCN GCNs are a type of GNN designed to work with graph structured data, extending the concept of convolutional neural networks to graphs. They allow the learning of node representations based on both node features and graph structure. The core operation in a GCN is the graph convolution, where for a single GCN layer, the output features H(l+1) are compute...

    work page

  8. [8]

    GAT GAT uses attention mechanism enabling structural learning on networks. In this GNN, the node features are updated as h(l+1) i = σ(P j∈N(i) αijW(l)h(l) j ), with atten- tion coefficients αij = softmax j(eij) = exp(eij)P k∈N (i) exp(eik), where eij = LeakyReLU(aT [W(l)H(l) i ∥W(l)H(l) j ]) and ∥ denotes concatenation. This allows the network to assign d...

    work page

Show all 67 references
  1. [9]

    The key innovation is the sampling of a fixed-size neighborhood and the combination of the node’s own features with the aggregated neighborhood features

    GraphSAGE GraphSAGE generalizes the neighborhood ag- gregation approach with h(l+1) i = σ(W(l) · CONCAT(h(l) i , AGG({h(l) j , ∀j ∈ N(i)}))), where AGG is a permutation-invariant aggregation function such as mean, max, or LSTM, applied to the neighbor set. The key innovation i...

  2. [10]

    The key idea is to formulate a continuous relaxation of the normalized MinCut problem and train- ing a GNN to compute optimal cluster assignments

    MinCut MinCutPool is differentiable graph pooling layer that performs hierarchical clustering based on spectral clus- tering [21]. The key idea is to formulate a continuous relaxation of the normalized MinCut problem and train- ing a GNN to compute optimal cluster assignments....

  3. [11]

    Given a graph with adjacency matrix A ∈ [0, 1]n×n and node features X ∈ Rn×p

    DiffPool DiffPool introduces hierarchical graph representation learning through differentiable pooling layers that enable end-to-end training of deep GNNs [20]. Given a graph with adjacency matrix A ∈ [0, 1]n×n and node features X ∈ Rn×p. DiffPool learns to cluster nodes at ea...

  4. [12]

    DMoN DMoN introduces an unsupervised clustering approach that leverages a differentiable modularity objective for graph pooling [22]. The key idea is to encode commu- nity assignments using GNNs and a modularity based objective function to optimize to make a learnable graph cl...

  5. [13]

    For average drop acrossµi values for a specific model and perturbation type, we compute: ∆ECSµi = 1 |Mi| X Mi |ECSinitial(µi) − ECSfinal(µi)| ECSinitial(µi) ×100%, where Mi is the set of all perturbations levels for all values µi

  6. [14]

    ∆ECSpert = 1 |P| X p∈P |ECSinitial(p) − ECSfinal(p)| ECSinitial(p) ×100%, where P is the set of all perturbation types (mean, scale, random edge, targeted edge)

    For average drop across perturbation types for a specific model, we compute. ∆ECSpert = 1 |P| X p∈P |ECSinitial(p) − ECSfinal(p)| ECSinitial(p) ×100%, where P is the set of all perturbation types (mean, scale, random edge, targeted edge). Table IV shows results av- eraged for ...

  7. [15]

    Nettack Network perturbation attacks, specifically Nettack and Metattack, represent sophisticated approaches to com- promising graph-based learning systems through struc- tural perturbations. Nettack operates as a targeted at- tack mechanism that modifies the graph structure a...

  8. [16]

    Fortunato, Community detection in graphs, Phys

    S. Fortunato, Community detection in graphs, Phys. Rep 486, 75 (2010)

    2010

  9. [17]

    M. E. Newman, Modularity and community structure in networks, Proc. Natl. Acad. Sci. U. S. A 103, 8577 (2006)

    2006

  10. [18]

    Girvan and M

    M. Girvan and M. E. Newman, Community structure in social and biological networks, Proc. Natl. Acad. Sci, U. S. A 99, 7821 (2002)

    2002

  11. [19]

    Wandelt, X

    S. Wandelt, X. Shi, and X. Sun, Estimation and improve- ment of transportation network robustness by exploiting communities, Reliab. Eng. Syst. Saf 206, 107307 (2021)

    2021

  12. [20]

    Lancichinetti and S

    A. Lancichinetti and S. Fortunato, Community detection algorithms: a comparative analysis, Phys. Rev. E 80, 056117 (2009)

    2009

  13. [21]

    Moriano, J

    P. Moriano, J. Finke, and Y.-Y. Ahn, Community-based event detection in temporal networks, Sci. Rep 9, 4358 (2019)

    2019

  14. [22]

    Aref and M

    S. Aref and M. Mostajabdaveh, Analyzing modularity maximization in approximation, heuristic, and graph neural network algorithms for community detection, J. Comput. Sci 78, 102283 (2024)

    2024

  15. [23]

    Schuurman and E

    T. Schuurman and E. Bruner, Modularity and commu- nity detection in human brain morphology, Anat. Rec 307, 345 (2024)

    2024

  16. [24]

    F. R. Khawaja, Z. Zhang, Y. Memon, and A. Ullah, Ex- ploring community detection methods and their diverse applications in complex networks: a comprehensive re- view, Soc. Netw. Anal. Min 14, 115 (2024)

    2024

  17. [25]

    Scarselli, M

    F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Monfardini, The graph neural network model, IEEE. Trans. Neural. Netw 20, 61 (2008)

    2008

  18. [26]

    Z. Wu, S. Pan, F. Chen, G. Long, C. Zhang, and P. S. Yu, A comprhensive survey on graph neural networks, IEEE. Trans. Neural. Netw. Learning. Syst 32, 4 (2020)

    2020

  19. [27]

    K. Xu, W. Hu, J. Leskovec, and S. Jegelka, How powerful are graph neural networks?, arXiv preprint arXiv:1810.00826 (2018)

    2018 arXiv

  20. [28]

    Veliˇ ckovi´ c, Everything is connected: Graph neural net- works, Curr

    P. Veliˇ ckovi´ c, Everything is connected: Graph neural net- works, Curr. Opin. Struct. Biol 79, 102538 (2023)

    2023

  21. [29]

    T. N. Kipf and M. Welling, Semi-supervised classifica- tion with graph convolutional networks, arXiv preprint arXiv:1609.02907 (2016)

    2016 arXiv

  22. [30]

    Veliˇ ckovi´ c, G

    P. Veliˇ ckovi´ c, G. Cucurull, A. Casanova, A. Romero, P. Lio, and Y. Bengio, Graph attention networks, arXiv preprint arXiv:1710.10903 (2017)

    2017 arXiv

  23. [31]

    Hamilton, Z

    W. Hamilton, Z. Ying, and J. Leskovec, Inductive rep- resentation learning on large graphs, Advances in neural information processing systems 30 (2017)

    2017

  24. [32]

    X. Su, S. Xue, F. Liu, J. Wu, J. Yang, C. Zhou, W. Hu, C. Paris, S. Nepal, D. Jin, et al., A comprehensive survey on community detection with deep learning, IEEE Trans. Neural. Netw. Learn. Syst (2022)

    2022

  25. [33]

    Y. Ren, J. Pu, Z. Yang, J. Xu, G. Li, X. Pu, S. Y. Philip, and L. He, Deep clustering: A comprehensive survey, IEEE. Trans. Neural. Netw. Learn. Syst (2024)

    2024

  26. [34]

    Y. Liu, J. Xia, S. Zhou, X. Yang, K. Liang, C. Fan, Y. Zhuang, S. Z. Li, X. Liu, and K. He, A survey of deep graph clustering: Taxonomy, challenge, application, and open resource, arXiv preprint arXiv:2211.12875 (2022)

    2022

  27. [35]

    Z. Ying, J. You, C. Morris, X. Ren, W. Hamilton, and J. Leskovec, Hierarchical graph representation learning with differentiable pooling, Advances in neural informa- tion processing systems 31 (2018)

    2018

  28. [36]

    F. M. Bianchi, D. Grattarola, and C. Alippi, Spectral clustering with graph neural networks for graph pool- ing, in International Conference on Machine Learning (PMLR, 2020) pp. 874–883

    2020

  29. [37]

    Tsitsulin, J

    A. Tsitsulin, J. Palowitch, B. Perozzi, and E. M¨ uller, Graph clustering with graph neural networks, J. Mach. Learn. Res 24, 1 (2023)

    2023

  30. [38]

    Z¨ ugner, A

    D. Z¨ ugner, A. Akbarnejad, and S. G¨ unnemann, Adver- sarial attacks on neural networks for graph data, in Pro- ceedings of the 24th ACM SIGKDD International Con- ference on Knowledge Discovery & Data Mining (2018) pp. 2847–2856

    2018

  31. [39]

    Z¨ ugner and S

    D. Z¨ ugner and S. G¨ unnemann, Adversarial attacks on graph neural networks via meta learning (2024), arXiv:1902.08412 [cs.LG]

    2024

  32. [40]

    B. Wang, J. Jia, X. Cao, and N. Z. Gong, Certified ro- bustness of graph neural networks against adversarial structural perturbation, in Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining (2021) pp. 1645–1653

    2021

  33. [41]

    G¨ unnemann, Graph neural networks: Adversarial ro- bustness, in Graph neural networks: foundations, fron- tiers, and applications (Springer, 2022) pp

    S. G¨ unnemann, Graph neural networks: Adversarial ro- bustness, in Graph neural networks: foundations, fron- tiers, and applications (Springer, 2022) pp. 149–176

    2022

  34. [42]

    Zhang, X

    B. Zhang, X. Guo, Z. Tu, and J. Zhang, Graph alter- nate learning for robust graph neural networks in node classification, Neural. Comput. Appl 34, 8723 (2022)

    2022

  35. [43]

    Zhang, B

    H. Zhang, B. Wu, X. Yuan, S. Pan, H. Tong, and J. Pei, Trustworthy graph neural networks: Aspects, methods, and trends, Proceedings of the IEEE 112, 97 (2024)

    2024

  36. [44]

    L. Sun, Y. Dou, C. Yang, K. Zhang, J. Wang, S. Y. Philip, L. He, and B. Li, Adversarial attack and defense on graph data: A survey, IEEE. Trans. Knowl. Data. Eng 35, 7693 (2022)

    2022

  37. [45]

    Tian and P

    M. Tian and P. Moriano, Robustness of community struc- ture under edge addition, Phys. Rev. E 108, 054302 (2023)

    2023

  38. [46]

    Z.-F. Wei, P. Moriano, and R. Kannan, Robustness of graph embedding methods for community detection, arXiv preprint arXiv:2405.00636 (2024)

    2024

  39. [47]

    Lancichinetti, S

    A. Lancichinetti, S. Fortunato, and F. Radicchi, Bench- mark graphs for testing community detection algorithms, Phys. Rev. E 78, 046110 (2008)

    2008

  40. [48]

    Karrer and M

    B. Karrer and M. E. Newman, Stochastic blockmodels and community structure in networks, Phys. Rev. E 83, 016107 (2011)

    2011

  41. [49]

    A. K. Dey, Y. Tian, and Y. R. Gel, Community detec- tion in complex networks: From statistical foundations to data science applications, Wiley Interdisciplinary Re- views: Computational Statistics 14, e1566 (2022)

    2022

  42. [50]

    Y. Zhao, E. Levina, and J. Zhu, Consistency of com- munity detection in networks under degree-corrected stochastic block models, Ann. Stat 40, 2266–2292 (2012)

    2012

  43. [51]

    Tsitsulin, B

    A. Tsitsulin, B. Rozemberczki, J. Palowitch, and B. Per- ozzi, Synthetic graph generation to benchmark graph learning, arXiv preprint arXiv:2204.01376 (2022)

    2022

  44. [52]

    A. J. Gates, I. B. Wood, W. P. Hetrick, and Y.-Y. Ahn, Element-centric clustering comparison unifies overlaps and hierarchy, Sci. Rep 9, 8574 (2019). 17

    2019

  45. [53]

    Goel, Robust graph neural networks, https://github.com/jdg-stat/robustgnn (2025), gitHub repository

    J. Goel, Robust graph neural networks, https://github.com/jdg-stat/robustgnn (2025), gitHub repository

    2025

  46. [54]

    Lancichinetti and S

    A. Lancichinetti and S. Fortunato, Benchmarks for test- ing community detection algorithms on directed and weighted graphs with overlapping communities, Phys. Rev. E 80, 016118 (2009)

    2009

  47. [55]

    Hagberg, P

    A. Hagberg, P. J. Swart, and D. A. Schult, Exploring net- work structure, dynamics, and function using NetworkX , Tech. Rep. (Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2008)

    2008

  48. [56]

    P. W. Holland, K. B. Laskey, and S. Leinhardt, Stochastic blockmodels: First steps, Social networks 5, 109 (1983)

    1983

  49. [57]

    Z. Yang, W. Cohen, and R. Salakhudinov, Revisiting semi-supervised learning with graph embeddings, in In- ternational Conference on Machine Learning (PMLR,

  50. [58]

    Y. Xu, M. Lanier, A. Sarkar, and Y. Vorobeychik, At- tacks on node attributes in graph neural networks, arXiv preprint arXiv:2402.12426 (2024)

    2024

  51. [59]

    Souravlas, S

    S. Souravlas, S. Anastasiadou, and S. Katsavounis, A sur- vey on the recent advances of deep community detection, Appl. Sci 11, 7179 (2021)

    2021

  52. [60]

    Sobolevsky and A

    S. Sobolevsky and A. Belyi, Graph neural network in- spired algorithm for unsupervised network community detection, Appl. Netw. Sci 7, 63 (2022)

    2022

  53. [61]

    Leeney and R

    W. Leeney and R. McConville, Uncertainty in gnn learn- ing evaluations: A comparison between measures for quantifying randomness in gnn community detection, En- tropy 26, 78 (2024)

    2024

  54. [62]

    V. D. Kumar, S. Sreesankar, K. Dinesan, P. B. Nair, and L. Deepthi, Analyzing gnn models for commu- nity detection using graph embeddings: A comparative study, in 2024 15th International Conference on Comput- ing Communication and Networking Technologies (ICC- CNT) (IEEE, 2024...

    2024

  55. [63]

    Merkwirth and T

    C. Merkwirth and T. Lengauer, Automatic generation of complementary descriptors with molecular graph net- works, J. Chem. Inf. Model 45, 1159 (2005)

    2005

  56. [64]

    X. Su, S. Xue, F. Liu, J. Wu, J. Yang, C. Zhou, W. Hu, C. Paris, S. Nepal, D. Jin, et al. , A comprehensive sur- vey on community detection with deep learning, IEEE. Trans. Neural. Netw. Learning. Syst (2022)

    2022

  57. [65]

    Budel, M

    G. Budel, M. Kitsak, R. Aldecoa, K. Zuev, and D. Kri- oukov, Random hyperbolic graphs in d+1 dimensions, Physical Review E 109, 054131 (2024)

    2024

  58. [66]

    D´ esy, P

    B. D´ esy, P. Desrosiers, and A. Allard, Dimension mat- ters when modeling network communities in hyperbolic spaces, PNAS nexus 2, pgad136 (2023)

    2023

  59. [67]

    M. Yang, M. Zhou, Z. Li, J. Liu, L. Pan, H. Xiong, and I. King, Hyperbolic graph neural networks: A review of methods and applications, arXiv:2202.13852 (2025). 18 APPENDIX A. Theoretical details Cut-based metrics Let {Ci}K i=1 be disjoint partitions of V. We can define a cut ...

    2025

Pith tools

Reviewed May 18, 2026 · model on record in the stance chip above.