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REVIEW 2 major objections 55 references

Nonparametric Inference for Balance in Signed Networks

T0 review · 2 major / 0 minor · reviewed 2026-05-23 · grok-4.3

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Pith's one-line read A nonparametric method using graphons finds strong evidence for balance theory in real signed networks across domains.

desk verdict The paper gives a new nonparametric sparse signed graphon plus higher-order CIs for balance parameters, but the node exchangeability assumption is the clear weak point for real networks. read the letter →

arxiv 2409.06172 v2 submitted 2024-09-10 stat.ME

Xuyang Chen , Yinjie Wang , Weijing Tang This is my paper · ORCID
classification stat.ME
keywords networkssignedbalancefriendtheoryinferencenonparametricreal-world
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 develops a way to test whether real signed networks follow social balance theory, the idea that positive and negative links tend to form consistent triads such as friend-of-friend or enemy-of-enemy. It starts from the assumption that networks are generated exchangeably and represents them with a nonparametric sparse signed graphon that lets edge signs depend on latent node positions. From this model the authors derive confidence intervals for the population quantities that quantify balance, intervals that achieve higher-order accuracy yet remain as simple to compute as a normal approximation. When applied to empirical networks the intervals support the theory in multiple fields. A reader would care because the approach turns a long-standing qualitative claim into a testable statistical statement that can be checked on data rather than assumed.

What carries the argument

the nonparametric sparse signed graphon model, a latent-position representation that assigns probabilities to positive and negative edges without parametric restrictions and supports inference on balance quantities

What would settle it

A large signed network in which the constructed confidence intervals for the balance parameters exclude the values implied by balance theory would falsify the reported evidence.

Watch

Extended reading notes

Core claim

Under the nonparametric sparse signed graphon model justified by node exchangeability, the authors construct valid confidence intervals for the population parameters associated with balance theory; these intervals, when applied to real-world signed networks, supply strong empirical evidence that the theory holds across domains beyond social psychology.

Load-bearing premise

Signed networks are generated by a process that admits a node-exchangeable characterization, which in turn justifies the sparse signed graphon model used for inference.

Editorial extensions

If this is right

  • The inference procedure yields valid confidence intervals for balance parameters that can be computed for any exchangeable signed network.
  • The method achieves higher-order accuracy while remaining computationally comparable to a normal approximation.
  • Empirical application across domains produces intervals consistent with balance theory, indicating the pattern is not confined to social psychology.
  • The same modeling and interval construction can be used to quantify balance in any new signed network that satisfies the exchangeability condition.

Reading between the lines

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

  • The graphon-based intervals could be extended to test balance in temporal or multilayer signed networks if an analogous exchangeability condition can be stated.
  • If the exchangeability premise holds only approximately, the method might still give useful diagnostics for the degree of deviation from balance in networks with community structure.
  • The same nonparametric construction could be repurposed to test other local motif hypotheses, such as the prevalence of particular four-node configurations, by redefining the target population parameters.
  • Application to biological or technological signed networks might reveal whether balance is a general organizing principle or domain-specific.
  • keywords:[
  • signed networks
  • balance theory
  • nonparametric inference
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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

2 major / 0 minor

Summary. The manuscript proposes a nonparametric inference procedure for assessing balance theory in signed networks. It characterizes signed-network generation via node exchangeability, introduces a nonparametric sparse signed graphon model, derives confidence intervals for population balance parameters (e.g., triangle sign probabilities) that are claimed to be theoretically valid with higher-order accuracy while remaining computationally simple, and applies the procedure to real-world signed networks to report strong empirical evidence for balance theory across domains.

Significance. If the node-exchangeability assumption and the attendant theoretical results hold, the work supplies a statistically grounded, higher-order-accurate yet practical tool for testing structural balance in signed networks outside social psychology, with potential to strengthen empirical claims in network science.

major comments (2)
  1. [Abstract] Abstract: the central empirical claim of 'strong real-world evidence for balance theory' rests on the nonparametric sparse signed graphon model being justified by node exchangeability. Real signed networks frequently exhibit non-exchangeable features (community structure, degree heterogeneity, block-model dependence) that cannot be captured by a single graphon of latent positions; if exchangeability fails, the population parameters lose their limiting interpretation and the reported CIs do not transfer to the data-generating process. The manuscript provides no diagnostics, sensitivity checks, or justification for this assumption in the applications, rendering it load-bearing for the main conclusion.
  2. [Abstract] Abstract: the claims of 'theoretical validity' and 'higher-order accuracy' for the confidence intervals are asserted, yet the full derivation, explicit error-bar construction, and data-exclusion rules are not supplied in the provided text. Without these, the soundness of the inference procedure cannot be verified (soundness assessment 4.0).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central empirical claim of 'strong real-world evidence for balance theory' rests on the nonparametric sparse signed graphon model being justified by node exchangeability. Real signed networks frequently exhibit non-exchangeable features (community structure, degree heterogeneity, block-model dependence) that cannot be captured by a single graphon of latent positions; if exchangeability fails, the population parameters lose their limiting interpretation and the reported CIs do not transfer to the data-generating process. The manuscript provides no diagnostics, sensitivity checks, or justification for this assumption in the applications, rendering it load-bearing for the main conclusion.

    Authors: Node exchangeability is the modeling foundation that permits the sparse signed graphon representation and the associated limiting parameters. While the referee correctly notes that certain network features (e.g., strong block structure) may require careful specification of the latent-position distribution, the nonparametric graphon framework can accommodate degree heterogeneity and community structure through appropriate choices of the position measure and the graphon function W. Nevertheless, we agree that explicit justification and robustness checks are desirable. In the revision we will add a dedicated subsection discussing the exchangeability assumption, together with sensitivity diagnostics applied to the real-data examples. revision: yes

  2. Referee: [Abstract] Abstract: the claims of 'theoretical validity' and 'higher-order accuracy' for the confidence intervals are asserted, yet the full derivation, explicit error-bar construction, and data-exclusion rules are not supplied in the provided text. Without these, the soundness of the inference procedure cannot be verified (soundness assessment 4.0).

    Authors: The full asymptotic derivations establishing validity and higher-order accuracy, the explicit construction of the studentized intervals, and the data-exclusion criteria used in the applications appear in Sections 3–4 and the supplementary material. We acknowledge that these elements may not have been sufficiently highlighted in the version sent for review. In the revision we will add a concise summary subsection that collects the error-bar formula, the Edgeworth-type expansion justifying the higher-order accuracy, and the precise data-filtering rules, thereby making verification straightforward. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

Derivation is self-contained under modeling assumptions with no reduction to inputs

full rationale

The paper begins by assuming node exchangeability to characterize signed network generation and define a nonparametric sparse signed graphon model, then derives CIs for balance-related population parameters (e.g., triangle sign probabilities) under that model. These steps are conditional on the posited model without any fitted quantities being relabeled as predictions, self-definitional loops, or load-bearing self-citations that reduce the central claims to their own inputs. The empirical application follows directly from the model-based inference, which remains independent of the target results by construction.

Assumptions & free parameters 0 free parameters · 1 assumptions · 1 invented entities

The central claim rests on node exchangeability as the modeling foundation and on the existence of a nonparametric sparse signed graphon representation for signed networks; no free parameters or invented entities with independent evidence are stated in the abstract.

assumptions (1)
  • domain assumption The generating process of signed networks is characterized by node exchangeability.
    Invoked to justify the nonparametric sparse signed graphon model.
invented entities (1)
  • nonparametric sparse signed graphon model
    purpose: To represent the link probabilities in signed networks under exchangeability for balance inference.
    New modeling framework introduced to enable the confidence-interval construction.

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Cite this review

Pith. "Pith review of Nonparametric Inference for Balance in Signed Networks." pith.science (2026). https://pith.science/paper/2409.06172

@misc{pith2026240906172,
  author       = {Pith},
  title        = {Pith review of: Nonparametric Inference for Balance in Signed Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2409.06172}},
  note         = {Machine review of arXiv:2409.06172}
}
read the original abstract

In many real-world networks, relationships often go beyond simple dyadic presence or absence; they can be positive, like friendship, alliance, and mutualism, or negative, characterized by enmity, disputes, and competition. To understand the formation mechanism of such signed networks, the social balance theory sheds light on the dynamics of positive and negative connections. In particular, it characterizes the proverbs, "a friend of my friend is my friend" and "an enemy of my enemy is my friend". In this work, we propose a nonparametric inference approach for assessing empirical evidence for the balance theory in real-world signed networks. We first characterize the generating process of signed networks with node exchangeability and propose a nonparametric sparse signed graphon model. Under this model, we construct confidence intervals for the population parameters associated with balance theory and establish their theoretical validity. Our inference procedure is as computationally efficient as a simple normal approximation but offers higher-order accuracy. By applying our method, we find strong real-world evidence for balance theory in signed networks across various domains, extending its applicability beyond social psychology.

Figures

Figures reproduced from arXiv: 2409.06172 by the authors.

Figure 1
Figure 1. Four types of different triangles, where the green solid line represents a positive [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The true CDF of the studentized ratio of network moments, along with its [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. The length and coverage proportion of 95% confidence intervals for (weakly) [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The length and coverage proportion of 95% confidence intervals for (weakly) [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: The length and coverage proportion of 95% confidence intervals of (weakly) [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: (a) The network size and the number of positive and negative edges for each five [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Visualization of two networks: (a) the functional similarity network among [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

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Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    Mixed membership stochastic blockmodels

    Edo M Airoldi, David Blei, Stephen Fienberg, and Eric Xing. Mixed membership stochastic blockmodels. Advances in Neural Information Processing Systems, 21, 2008

    work page 2008

  2. [2]

    Representations for partially exchangeable arrays of random variables

    David J Aldous. Representations for partially exchangeable arrays of random variables. Journal of Multivariate Analysis, 11 0 (4): 0 581--598, 1981

    work page 1981

  3. [3]

    An edgeworth expansion for symmetric statistics

    Vidmantas Bentkus, Friedrich G \"o tze, and Willem R van Zwet. An edgeworth expansion for symmetric statistics. The Annals of Statistics, 25 0 (2): 0 851--896, 1997

    work page 1997

  4. [4]

    Sharmodeep Bhattacharyya and Peter J. Bickel. Subsampling bootstrap of count features of networks . The Annals of Statistics, 43 0 (6): 0 2384 -- 2411, 2015. doi:10.1214/15-AOS1338. URL https://doi.org/10.1214/15-AOS1338

    work page doi:10.1214/15-aos1338 2015

  5. [5]

    PJ Bickel, Friedrich G¨ otze, and WR Van Zwet

    Peter J. Bickel, Aiyou Chen, and Elizaveta Levina. The method of moments and degree distributions for network models . The Annals of Statistics, 39 0 (5): 0 2280 -- 2301, 2011. doi:10.1214/11-AOS904. URL https://doi.org/10.1214/11-AOS904

    work page doi:10.1214/11-aos904 2011

  6. [6]

    The edgeworth expansion for u-statistics of degree two

    PJ Bickel, Friedrich G \"o tze, and WR Van Zwet. The edgeworth expansion for u-statistics of degree two. The Annals of Statistics, pages 1463--1484, 1986

    work page 1986

  7. [7]

    The order of the normal approximation for a studentized u-statistic

    Herman Callaert and Noel Veraverbeke. The order of the normal approximation for a studentized u-statistic. The Annals of Statistics, pages 194--200, 1981

    work page 1981

  8. [8]

    An edgeworth expansion for u-statistics

    Herman Callaert, Paul Janssen, and Noel Veraverbeke. An edgeworth expansion for u-statistics. The Annals of Statistics, pages 299--312, 1980

    work page 1980

Show all 55 references
  1. [9]

    Structural balance: a generalization of heider's theory

    Dorwin Cartwright and Frank Harary. Structural balance: a generalization of heider's theory. Psychological Review, 63 0 (5): 0 277, 1956

    1956

  2. [10]

    A bootstrap method for goodness of fit and model selection with a single observed network

    Sixing Chen and Jukka-Pekka Onnela. A bootstrap method for goodness of fit and model selection with a single observed network. Scientific Reports, 9 0 (1): 0 16674, 2019

    2019

  3. [11]

    Prediction and clustering in signed networks: a local to global perspective

    Kai-Yang Chiang, Cho-Jui Hsieh, Nagarajan Natarajan, Inderjit S Dhillon, and Ambuj Tewari. Prediction and clustering in signed networks: a local to global perspective. Journal of Machine Learning Research, 15 0 (1): 0 1177--1213, 2014

    2014

  4. [12]

    Clustering and structural balance in graphs

    James A Davis. Clustering and structural balance in graphs. Human Relations, 20 0 (2): 0 181--187, 1967

    1967

  5. [13]

    Signed network modeling based on structural balance theory

    Tyler Derr, Charu Aggarwal, and Jiliang Tang. Signed network modeling based on structural balance theory. In Proceedings of the 27th ACM International Conference on Information and Knowledge Management, pages 557--566, 2018

    2018

  6. [14]

    FY Edgeworth. Xlii. the law of error. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 16 0 (100): 0 300--309, 1883

  7. [15]

    Computing global structural balance in large-scale signed social networks

    Giuseppe Facchetti, Giovanni Iacono, and Claudio Altafini. Computing global structural balance in large-scale signed social networks. Proceedings of the National Academy of Sciences, 108 0 (52): 0 20953--20958, 2011

    2011

  8. [16]

    Testing for balance in social networks

    Derek Feng, Randolf Altmeyer, Derek Stafford, Nicholas A Christakis, and Harrison H Zhou. Testing for balance in social networks. Journal of the American Statistical Association, 117 0 (537): 0 156--174, 2022

    2022

  9. [17]

    Legislative cosponsorship networks in the us house and senate

    James H Fowler. Legislative cosponsorship networks in the us house and senate. Social Networks, 28 0 (4): 0 454--465, 2006

    2006

  10. [18]

    International military alliances, 1648-2008

    Douglas M Gibler. International military alliances, 1648-2008. CQ Press, 2008

    2008

  11. [19]

    Bootstrapping exchangeable random graphs

    Alden Green and Cosma Rohilla Shalizi. Bootstrapping exchangeable random graphs. Electronic Journal of Statistics, 16 0 (1): 0 1058--1095, 2022

    2022

  12. [20]

    Understanding multicellular function and disease with human tissue-specific networks

    Casey S Greene, Arjun Krishnan, Aaron K Wong, Emanuela Ricciotti, Rene A Zelaya, Daniel S Himmelstein, Ran Zhang, Boris M Hartmann, Elena Zaslavsky, Stuart C Sealfon, et al. Understanding multicellular function and disease with human tissue-specific networks. Nature Genetics, ...

    2015

  13. [21]

    The bootstrap and Edgeworth expansion

    Peter Hall. The bootstrap and Edgeworth expansion. Springer Science & Business Media, 2013

    2013

  14. [22]

    On the notion of balance of a signed graph

    Frank Harary. On the notion of balance of a signed graph. Michigan Mathematical Journal, 2 0 (2): 0 143--146, 1953

    1953

  15. [23]

    Attitudes and cognitive organization

    Fritz Heider. Attitudes and cognitive organization. The Journal of Psychology, 21 0 (1): 0 107--112, 1946

    1946

  16. [24]

    On the edgeworth expansion and the bootstrap approximation for a studentized u-statistic

    Roelof Helmers. On the edgeworth expansion and the bootstrap approximation for a studentized u-statistic. The Annals of Statistics, pages 470--484, 1991

    1991

  17. [25]

    A class of statistics with asymptotically normal distribution

    Wassily Hoeffding. A class of statistics with asymptotically normal distribution. Breakthroughs in Statistics: Foundations and Basic Theory, pages 308--334, 1992

    1992

  18. [26]

    Latent space approaches to social network analysis

    Peter D Hoff, Adrian E Raftery, and Mark S Handcock. Latent space approaches to social network analysis. Journal of the American Statistical Association, 97 0 (460): 0 1090--1098, 2002

    2002

  19. [27]

    Relations on probability spaces and arrays of random variables

    Douglas N Hoover. Relations on probability spaces and arrays of random variables. Institute for Advanced Study, 1979

    1979

  20. [28]

    Low rank modeling of signed networks

    Cho-Jui Hsieh, Kai-Yang Chiang, and Inderjit S Dhillon. Low rank modeling of signed networks. In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 507--515, 2012

    2012

  21. [29]

    The bioplex network: a systematic exploration of the human interactome

    Edward L Huttlin, Lily Ting, Raphael J Bruckner, Fana Gebreab, Melanie P Gygi, John Szpyt, Stanley Tam, Gabriela Zarraga, Greg Colby, Kurt Baltier, et al. The bioplex network: a systematic exploration of the human interactome. Cell, 162 0 (2): 0 425--440, 2015

    2015

  22. [30]

    Dual proteome-scale networks reveal cell-specific remodeling of the human interactome

    Edward L Huttlin, Raphael J Bruckner, Jose Navarrete-Perea, Joe R Cannon, Kurt Baltier, Fana Gebreab, Melanie P Gygi, Alexandra Thornock, Gabriela Zarraga, Stanley Tam, et al. Dual proteome-scale networks reveal cell-specific remodeling of the human interactome. Cell, 184 0 (1...

    2021

  23. [31]

    Mixed membership estimation for social networks

    Jiashun Jin, Zheng Tracy Ke, and Shengming Luo. Mixed membership estimation for social networks. Journal of Econometrics, 239 0 (2): 0 105369, 2024 a

    2024

  24. [32]

    Optimal network pairwise comparison

    Jiashun Jin, Zheng Tracy Ke, Shengming Luo, and Yucong Ma. Optimal network pairwise comparison. Journal of the American Statistical Association, 0 0 (ja): 0 1--25, 2024 b . doi:10.1080/01621459.2024.2393471

    2024 doi

  25. [33]

    Balance in signed networks

    Alec Kirkley, George T Cantwell, and Mark EJ Newman. Balance in signed networks. Physical Review E, 99 0 (1): 0 012320, 2019

    2019

  26. [34]

    Network representation using graph root distributions

    Jing Lei. Network representation using graph root distributions . The Annals of Statistics, 49 0 (2): 0 745--768, April 2021. ISSN 0090-5364,2168-8966. doi:10.1214/20-aos1976

    2021 doi

  27. [35]

    Signed networks in social media

    Jure Leskovec, Daniel Huttenlocher, and Jon Kleinberg. Signed networks in social media. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pages 1361--1370, 2010

    2010

  28. [36]

    Bootstrapping networks with latent space structure

    Keith Levin and Elizaveta Levina. Bootstrapping networks with latent space structure. arXiv preprint arXiv:1907.10821, 2019

    1907

  29. [37]

    Subsampling sparse graphons under minimal assumptions

    Robert Lunde and Purnamrita Sarkar. Subsampling sparse graphons under minimal assumptions . Biometrika, 110 0 (1): 0 15--32, 06 2022. ISSN 1464-3510. doi:10.1093/biomet/asac032. URL https://doi.org/10.1093/biomet/asac032

    2022 doi

  30. [38]

    Computational correction of copy number effect improves specificity of CRISPR -- C as9 essentiality screens in cancer cells

    Robin M Meyers, Jordan G Bryan, James M McFarland, Barbara A Weir, Ann E Sizemore, Han Xu, Neekesh V Dharia, Phillip G Montgomery, Glenn S Cowley, Sasha Pantel, et al. Computational correction of copy number effect improves specificity of CRISPR -- C as9 essentiality screens i...

    2017

  31. [39]

    Random dot product graphs a model for social networks

    Christine Leigh Myers Nickel. Random dot product graphs a model for social networks. PhD thesis, Johns Hopkins University, 2008

    2008

  32. [40]

    Estimation and prediction for stochastic blockstructures

    Krzysztof Nowicki and Tom A B Snijders. Estimation and prediction for stochastic blockstructures. Journal of the American Statistical Association, 96 0 (455): 0 1077--1087, 2001

    2001

  33. [41]

    Bayesian models of graphs, arrays and other exchangeable random structures

    Peter Orbanz and Daniel M Roy. Bayesian models of graphs, arrays and other exchangeable random structures. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37 0 (2): 0 437--461, 2014

    2014

  34. [42]

    The MID 5 D ataset, 2011--2014: Procedures, coding rules, and description

    Glenn Palmer, Roseanne W McManus, Vito D’Orazio, Michael R Kenwick, Mikaela Karstens, Chase Bloch, Nick Dietrich, Kayla Kahn, Kellan Ritter, and Michael J Soules. The MID 5 D ataset, 2011--2014: Procedures, coding rules, and description. Conflict Management and Peace Science, ...

    2011

  35. [43]

    Empirical edgeworth expansions for symmetric statistics

    Hein Putter and Willem R van Zwet. Empirical edgeworth expansions for symmetric statistics. The Annals of Statistics, 26 0 (4): 0 1540--1569, 1998

    1998

  36. [44]

    Evidence of structural balance in spatial ecological networks

    Hugo Saiz, Jes \'u s G \'o mez-Garde \ n es, Paloma Nuche, Andrea Gir \'o n, Yolanda Pueyo, and Concepci \'o n L Alados. Evidence of structural balance in spatial ecological networks. Ecography, 40 0 (6): 0 733--741, 2017

    2017

  37. [45]

    Higher-order accurate two-sample network inference and network hashing

    Meijia Shao, Dong Xia, Yuan Zhang, Qiong Wu, and Shuo Chen. Higher-order accurate two-sample network inference and network hashing. arXiv preprint arXiv:2208.07573, 2022

    2022

  38. [46]

    Population-level balance in signed networks

    Weijing Tang and Ji Zhu. Population-level balance in signed networks. Journal of the American Statistical Association, 0 0 (ja): 0 1--22, 2024. doi:10.1080/01621459.2024.2356894. URL https://doi.org/10.1080/01621459.2024.2356894

    2024 doi

  39. [47]

    Using the bootstrap for statistical inference on random graphs

    Mary E Thompson, Lilia L Ramirez Ramirez, Vyacheslav Lyubchich, and Yulia R Gel. Using the bootstrap for statistical inference on random graphs. Canadian Journal of Statistics, 44 0 (1): 0 3--24, 2016

    2016

  40. [48]

    Asymptotic approximations to distributions

    David L Wallace. Asymptotic approximations to distributions. The Annals of Mathematical Statistics, 29 0 (3): 0 635--654, 1958

    1958

  41. [49]

    Network enhancement as a general method to denoise weighted biological networks

    Bo Wang, Armin Pourshafeie, Marinka Zitnik, Junjie Zhu, Carlos D Bustamante, Serafim Batzoglou, and Jure Leskovec. Network enhancement as a general method to denoise weighted biological networks. Nature Communications, 9 0 (1): 0 3108, 2018

    2018

  42. [50]

    All of Nonparametric Statistics

    Larry Wasserman. All of Nonparametric Statistics. Springer Science & Business Media , 2006

    2006

  43. [51]

    Brainnet viewer: a network visualization tool for human brain connectomics

    Mingrui Xia, Jinhui Wang, and Yong He. Brainnet viewer: a network visualization tool for human brain connectomics. PLoS One, 8 0 (7): 0 e68910, 2013

    2013

  44. [52]

    Connectivity differences in brain networks

    Andrew Zalesky, Luca Cocchi, Alex Fornito, Micah M Murray, and ED Bullmore. Connectivity differences in brain networks. Neuroimage, 60 0 (2): 0 1055--1062, 2012

    2012

  45. [53]

    Signed network embedding with application to simultaneous detection of communities and anomalies

    Haoran Zhang and Junhui Wang. Signed network embedding with application to simultaneous detection of communities and anomalies. arXiv preprint arXiv:2207.09324, 2022

    2022

  46. [54]

    Edgeworth expansions for network moments

    Yuan Zhang and Dong Xia. Edgeworth expansions for network moments. The Annals of Statistics, 50 0 (2): 0 726--753, 2022

    2022

  47. [55]

    Detecting overlapping communities in networks using spectral methods

    Yuan Zhang, Elizaveta Levina, and Ji Zhu. Detecting overlapping communities in networks using spectral methods. SIAM Journal on Mathematics of Data Science, 2 0 (2): 0 265--283, 2020

    2020

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