A Hierarchical Scale-free Graph Generator under Limited Resources

Xiaojie Yuan; Xiaorui Qi; Yanlong Wen

REVIEW 5 major objections 4 minor 55 references

A Hierarchical Scale-free Graph Generator under Limited Resources

T0 review · 5 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A non-learned hierarchical generator using a Poisson degree prior and degree-mixing preferential attachment fits real graph distributions better than classical and untrained deep generators across 12 datasets.

desk verdict A sensible non-learned generator recipe, but the headline comparison to baselines is not yet reproducible; the paper needs a fixed hyperparameter rule, released code, and variance estimates before the empirical claims carry weight. read the letter →

arxiv 2411.13888 v2 pith:3CM2ERJM submitted 2024-11-21 cs.DM cs.SI

Xiaorui Qi , Yanlong Wen , Xiaojie Yuan This is my paper · ORCID

classification cs.DMcs.SI MSC 05C8005C82

keywords graphgenerationscale-freenon-learnedgeneratorlimitedresourceshierarchicalPoissondegreedistributionpreferentialattachmentMMD

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 argues that when training data is unavailable and only the node count N and edge count M are known, graph generation can still be performed well by relying on the scale-free property instead of learned models. The proposed generator works in two stages: it samples anchor-node degrees from a Poisson distribution with mean equal to the average degree $\bar{D}=2M/N$ and builds star substructures around those anchors, then adds the remaining edges by sampling node pairs with probabilities that combine a substructure-preferential factor with a next-degree Poisson factor. Two thresholds, the maximum degree $d_{\max}$ and a truncation value $k$, regulate how much deviation from the scale-free ideal the generator tolerates. The paper claims that this non-learned method fits the ground-truth distribution better than classical generators (ER, BA, WS, MMSB, Kronecker) and better than untrained or briefly trained deep generative models, measured by MMD on average degree, clustering coefficient, and orbit counts over 12 datasets. If right, it means useful graph generation does not require learning when the target graphs are approximately scale-free.

What carries the argument

The load-bearing object is the two-stage hierarchical construction. In stage one, the algorithm samples a degree sequence for anchor nodes from the Poisson distribution $P(\bar{D})$ with $\bar{D}=2M/N$, turns each anchor into a star substructure $G^{(i)}_{\rm sub}$, and partitions the node set into such substructures. In stage two, it draws the remaining edges by sampling endpoint pairs $u,v$, where each node's selection probability is $\Pr(v^{(i)}_j)=s^{(i)}_{\rm sub}\cdot P(\mathrm{Lent}[i][j]+1\mid \bar{D})$: the substructure's node fraction $s^{(i)}_{\rm sub}=N^{(i)}_{\rm sub}/N$ acts as a preferential-attachment weight, and the Poisson term is the probability of moving to the next degree. Two thresholds, the maximum degree $d_{\max}$ and the truncation $k$ (smallest positive integer with $P(k\mid\bar{D})<P(0\mid\bar{D})$), mask out nodes or substructures that would produce exotic structures, controlling the generator's tolerance. The authors prove that the expected degree of non-anchor nodes remains $\bar{D}$, so the scale-free observation is preserved in expectation.

What would settle it

Run the same two-stage algorithm on a deliberately non-scale-free target, such as a regular lattice or a uniform-degree random graph, and compute the MMD on degree and orbit counts; the paper's own GRID results already suggest the method degrades there, pinpointing the boundary of the claim. Sharper still: replace the Poisson prior with the empirical degree distribution of the target dataset and rerun the generator; if the MMD improves substantially, the Poisson assumption is the bottleneck, whereas little change would show the hierarchy, not the prior, does the work.

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Extended reading notes

Core claim

The paper's central claim is that a hierarchical generator built entirely on the scale-free invariant—Poisson degree sampling with mean $\bar{D}$, degree-mixing preferential attachment, and two tolerance thresholds—can outperform classical random-graph models and deep generative models when the ground-truth distribution is unknown and only $N$ and $M$ are available. The authors report that on 12 datasets spanning bioinformatics, social networks, and synthetic graphs, their method reaches the best or second-best MMD score on average degree, clustering coefficient, and orbit counts in nearly every configuration, and they state that their method is 'one of the optimal choices in the scenario of unknown distribution.'

Load-bearing premise

The load-bearing premise is that the degree distribution of real-world graphs is well approximated by a Poisson distribution whose mean is the graph's average degree, so that anchor degrees sampled from this prior lead, after the second-stage edge additions, to graphs whose degree and clustering statistics match the unknown ground truth.

Editorial extensions

If this is right

In resource-limited settings, this generator offers a strong, interpretable default baseline that deep generative models must outperform.
The two thresholds give practitioners direct control over how far the generated graphs may deviate from the scale-free ideal, allowing adaptation to categories with high clustering or regular structures.
Because the construction is hierarchical, the generated graph comes with explicit anchor nodes and substructures, making the process and output interpretable.
The distribution-ablation results indicate that alternative heavy-tailed priors (Gamma, Pareto) remain competitive under the same hierarchy, so the two-stage design itself, not the exact Poisson choice, is the main robustness driver.

Reading between the lines

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

A natural extension is to replace the fixed Poisson prior with a degree distribution estimated from a small handful of observed graphs in a semi-limited setting; the hierarchy would likely remain the workhorse while the empirical prior could close the gap on clustered or structured graphs.
The paper's LLM comparison, where language models tended to emit Barabási-Albert-style generation code, suggests that learned priors may not exceed this explicit algorithm; a direct test would be to prompt an LLM with the two-stage algorithm itself and compare MMD scores.
The appendix's connectivity thresholds connect the method to classical random-graph phase transitions; one could test whether generated graphs exhibit the predicted giant-component and connectivity transitions as $M$ grows, potentially extending the generator to dynamic network growth simulation.

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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

Let me cut to it: the method is a sensible combination of known ideas—hierarchical star substructures, a Poisson degree prior with mean set to 2M/N, degree-mixing selection, and two thresholds—and it makes sense as a fallback when you only have N and M. The paper does a decent job of testing it across three graph categories and is honest about the cases where it fails (REDDIT-BINARY, GRID). The threshold ablation and the distribution ablation are genuinely informative, even if the distribution results undercut the claim that Poisson is the uniquely right prior.

The problem is that the central empirical claim—that the method beats ER, BA, WS, MMSB, Kronecker, and untrained deep models on MMD—is not yet controlled. The stress-test note is on target: dmax and k are treated as tunable in Section 5.3, and the main results never state how they are set per dataset. If they are chosen with knowledge of the target graphs or by optimizing the reported MMD, the limited-resource premise is violated and the comparison is not fair. The point estimates themselves are unstable: the same 'Ours' row differs substantially between Table 1 and Table 5 for several datasets (e.g., ENZYMES degree MMD 0.1811 vs 0.3274; deezer 0.0371 vs 0.1401). Without error bars or a fixed protocol, those numbers don't yet support the 'optimal choice' conclusion. The appendix proof in Eq. (2) is also not valid—expectation does not commute with the Poisson PMF—so the theoretical backing should be read as intuition, not a guarantee.

Where does that leave the paper? As a proposal, it is worth taking seriously. The recipe is new enough as a combination, the method is simple and cheap, and the problem setting is real—this is for people working on graph generation in data-scarce or privacy-sensitive scenarios. But the current manuscript does not make a reproducible case for superiority. I would send it to peer review, not desk-reject it, because the idea has merit and the experiments can be fixed. The authors need to release code, specify a hyperparameter rule that uses only N and M or a validation split, report variance across generated graphs, and temper the claims accordingly. If those fixes land, I would cite it as a baseline. As it stands, I would not rely on the quantitative claims, but I would be interested to see a revision.

Referee Report

5 major / 4 minor

Summary. The paper proposes a non-learned, hierarchical graph generator for the limited-resource setting in which only the number of nodes N and the number of edges M are known. The first stage samples anchor-node degrees from a Poisson distribution with mean λ = 2M/N and builds star-shaped substructures; the second stage connects substructures and then adds remaining edges by sampling node pairs from a degree-mixing distribution that combines substructure size with the next-degree Poisson probability, subject to thresholds dmax and k. The authors claim theoretical guarantees for the hierarchical process and evaluate the method on 12 datasets from bioinformatics, social networks, and synthetic graphs, reporting MMD scores on average degree, clustering coefficient, and orbit counts and comparing with ER, BA, WS, MMSB, Kronecker, deep generative models, and LLM-based generation.

Significance. If the central empirical claim were established, the paper would make a useful contribution: an interpretable, parameter-light generator for settings where training data are unavailable or sensitive, with explicit algorithmic pseudocode and a broad comparison across several baseline families. The paper also deserves credit for attempting to justify the generator with an expectation calculation and for including distribution ablations. However, the current evidence is not yet reliable: the parameter-selection protocol for dmax and k is unspecified, the same 'Ours' method gives inconsistent MMD values across tables, and the appendix proof contains an invalid independence step. These issues are load-bearing for the main claim that the method fits ground-truth distributions better than existing generators.

major comments (5)

[§5.3 and Table 2; main results in Table 1]
[Appendix C.2, Eq. (2)]
[§5.2 Table 1 vs §E.3 Table 5]
[§3, Observation 1 and Eq. (1)]
[Appendix C.1, Algorithm 2, lines 2-7]

minor comments (4)

[§4.2, after Eq. (2)]
[§5.2, discussion of Table 1]
[Appendix C.1, Algorithm 2, line 21]
[Appendix D.2]

Circularity Check

1 steps flagged · score 2.0 of 10

One tautological 'theoretical guarantee' (expected degree equals the input average degree) is circular, but the central MMD comparison retains independent content.

self definitional [Section 4.2 and Appendix C.2, Eq. (1)]
"Given (N, M), we leverage the available information to estimate the average degree expectation, where lambda = 2M/N = Dbar. ... E(Vna) = ... = E[d~P(Dbar)] * 1 = Dbar."

The Poisson prior parameter lambda is set to the target's average degree 2M/N, and the appendix then 'proves' that the expected degree of generated non-anchor nodes equals the same Dbar. This equality is an identity for any generation process that outputs M edges over N nodes; it is not a consequence of the hierarchical design and does not establish the heavy-tailed scale-free conclusion of Observation 1. The claimed theoretical guarantee is therefore equivalent to its own input (the average degree), not a first-principles prediction. That said, the degree MMD used in the evaluation compares degree distributions, not just their mean, and the baselines also operate from the same N and M, so this circular identity does not by itself force the reported superiority.

full rationale

The paper contains no load-bearing self-citation chain, no uniqueness theorem imported from the authors, and no ansatz smuggled in via self-citation. The only reduction-by-construction I can exhibit is in Appendix C.2: lambda is set to the input average degree 2M/N (Section 4.2), and then Eq. (1) of C.2 derives that the expected degree of generated nodes equals the same Dbar. That is a tautology of edge-count conservation rather than a substantive derivation, so I flag it as a minor self-definitional step. The main empirical claim, however, is not reduced by this identity: the evaluation uses MMD over degree distributions, clustering coefficients, and orbit counts, and all compared generators (ER, BA, WS, MMSB, Kronecker) also receive N and M, so matching the average degree is not a unique advantage that explains the reported margins. The tuning of dmax and k is a legitimate reproducibility concern, but the paper states no selection rule and I cannot infer without speculation that they were fitted to the evaluation metric, so it does not meet the evidentiary bar for circularity. The overall circularity is therefore minor and non-load-bearing, consistent with a score of 2.

Assumptions & free parameters 3 free parameters · 5 assumptions · 2 invented entities

The paper's central claim rests on three main free inputs: the Poisson prior with mean set to the observed average degree, the two ad hoc thresholds dmax and k, and the hierarchical substructure design. The Poisson choice is the most consequential: the authors show in Table 3 that several alternative priors work reasonably on different categories, which means the method's success is tied to an empirical choice. The theoretical guarantees are elementary expectations about the sampling process, not theorems that validate the generator against all graph families. The invented entities are internal algorithmic components with no external falsifiable predictions.

free parameters (3)

lambda (Poisson mean) = 2M/N (average degree of the input graph)
The degree prior for anchor sampling and node selection is set to the average degree computed from the only available information (N, M). It is a free parameter in the sense that it encodes the entire degree-distribution assumption, and the method's performance depends critically on this choice.
dmax (maximum degree threshold) = Not specified globally, reported as 'dmax = 3' in one example
The max degree threshold controls anchor degree sampling and edge generation. The ablation study shows it has a strong effect, but the paper does not provide the mechanism for choosing it across datasets.
k (Poisson truncation threshold) = Smallest positive integer with P(k|lambda) < P(0|lambda)
The truncation threshold removes low-probability high-degree nodes. Though it is defined from lambda, its application to different datasets is an ad hoc modeling choice that affects the generated degree distribution.

assumptions (5)

domain assumption Real-world graphs are approximately scale-free (Observation 1)
The method's foundation is the claim that most real-world systems have heavy-tailed degree distributions. The paper cites prior literature and shows empirical fits, but this is a modeling assumption that fails for several datasets, as the authors acknowledge.
domain assumption The Poisson distribution with mean equal to the average degree is a valid generative model for the degree distribution
Section 3 uses the Poisson distribution (Equation 1) and Section 4.2 sets lambda to the average degree. This substitutes a known distribution for the unknown ground truth, and the paper's own ablation (Table 3) shows that Gamma and Pareto priors also perform competitively; hence the Poisson choice is not justified by theory but by empirical preference.
domain assumption The number of edges M and nodes N are known (the only available information)
The problem statement assumes that the generator receives only N and M. This is the definition of the limited-resources setting, and it is consistent throughout the paper.
domain assumption Maximum degree and truncation thresholds are valid controls for avoiding exotic structures
The paper introduces dmax and k to 'adjust the algorithm tolerance towards exotic structures' without a principled justification for their values. These parameters are fitted empirically in the ablation study.
domain assumption Connectivity threshold from Erdos-Renyi applies to this hierarchical generator
Appendix C.2 cites the classical random-graph connectivity threshold M = [0.5 N log N + epsilon N] and applies it to the proposed generator, but the hierarchical degree-mixing process is not an Erdos-Renyi model, so the applicability of this bound is not established.

invented entities (2)

Substructure (star graph led by an anchor node)
purpose: Hierarchical decomposition of the node set to guide edge formation and enhance local clustering
This is a structural device used by the generator, similar to BTER's blocks and Kronecker's recursive partitions. It is not independently verified, and its properties are defined by the algorithm itself.
Degree mixing distribution (Equation 3)
purpose: Node selection probability that combines substructure size and Poisson next-degree mass
This is the algorithm's sampling rule; it is a design choice that produces the reported empirical behavior, but it is not independently validated as a universal law of graphs.

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Cite this review

Pith. "Pith review of A Hierarchical Scale-free Graph Generator under Limited Resources." pith.science (2026). https://pith.science/paper/3CM2ERJM

@misc{pith2026241113888,
  author       = {Pith},
  title        = {Pith review of: A Hierarchical Scale-free Graph Generator under Limited Resources},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3CM2ERJM}},
  note         = {Machine review of arXiv:2411.13888}
}

read the original abstract

Graph generation is one of the most challenging tasks in recent years, and its core is to learn the ground truth distribution hiding in the training data. However, training data may not be available due to security concerns or unaffordable costs, which severely blows the learning models, especially the deep generative models. The dilemma leads us to rethink non-learned generation methods based on graph invariant features. Based on the observation of scale-free property, we propose a hierarchical scale-free graph generation algorithm. Specifically, we design a two-stage generation strategy. In the first stage, we sample multiple anchor nodes to further guide the formation of substructures, splitting the initial node set into multiple ones. Next, we progressively generate edges by sampling nodes through a degree mixing distribution, adjusting the tolerance towards exotic structures via two thresholds. We provide theoretical guarantees for hierarchical generation and verify the effectiveness of our method under 12 datasets of three categories. Experimental results show that our method fits the ground truth distribution better than various generation strategies and other distribution observations.

Figures

Figures reproduced from arXiv: 2411.13888 by the authors.

**Figure 1.** An illustration of deep learning models with limited/no training data failing to generate graphs due to safety propose or high price (in red). However, with invariant features dragging from observation on universal data available, we can generate graphs fitting ground truth distribution well without learning (in blue). in restricted scenarios by learning invariant features in other training data that can be easily o… view at source ↗

**Figure 2.** Generation strategy comparison between several baselines and our method. 3 Preliminary Definition 1 (Graph). A graph can form as G = {V, E}, where V and E represent nodes and edges set, and N and M are the number of nodes the edges, respectively. A[u, v] ∈ {0, 1} N×N , u, v ∈ V is the adjacency matrix, where A[u, v] = 1 shows there is an edge between node u and node v. We use du to represent the degree of node u. … view at source ↗

**Figure 3.** Illustration of the edge generation. (A) connection to plain nodes. (B) connection to anchor nodes. node with the dmax to fit the ground truth situation. And that is why we sample anchors first and build the star graph instead of any other structures. The second parameter is a truncation against Equation 1. For large degrees much greater than the average, denoted by d∞ ≫ D¯, it shows that P(d∞|D¯) ≃ 0 < P(0|D¯). (2… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Generation steps with/without dmax limitation. Anchor nodes and edges to add in each step are in red. that both parameters are positive to the performance, and dmax shows a more competitive contribution than k. 5.4 Graph Generation under Various Distributions We conduc…

**Figure 5.** Figure 5: Degree distribution comparisons between generated and real-world graphs. to the ground truth distribution. Despite the differences between categories, we can see the scale-free characteristics of all datasets in [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]

**Figure 6.** Figure 6: Visualization of graphs of all categories. They are (from left to right, each consisting of three columns) bioinformatics & molecules, social networks, and synthetic graphs. Within each category, the first column is from the dataset, and the third is from baselines ach…

**Figure 1.** Figure 1: Detailed Runtime Analysis. T1: the parse phase. T2: connecting sub-structures. T3: rebuilding the rest edges. exhibits superior time complexity, with an average runtime second only to BA. The theoretical worst-case time complexity of our method is O(N2 ), which aligns …

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Reference graph

Works this paper leans on

55 extracted references · 51 canonical work pages

[1]

C. Wang, B. Wang, B. Huang, S. Song, and Z. Li, ``FastSGG: Efficient Social Graph Generation Using a Degree Distribution Generation Model,'' in ICDE, 2021

work page 2021
[2]

Xiang, D

S. Xiang, D. Cheng, J. Zhang, Z. Ma, X. Wang, and Y. Zhang, ``Efficient Learning-based Community-Preserving Graph Generation,'' in ICDE, 2022

work page 2022
[3]

Zhang, D

L. Zhang, D. Zhou, H. Tong, J. Xu, Y. Zhu, and J. He, ``FairGen: Towards Fair Graph Generation,'' in ICDE, 2024

work page 2024
[4]

Huang, L

H. Huang, L. Sun, B. Du, and W. Lv, ``Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation,'' in AAAI, 2023

work page 2023
[5]

Y. Zhu, Z. Ouyang, B. Liao, J. Wu, Y. Wu, C. Hsieh, T. Hou, and J. Wu, ``MolHF: A Hierarchical Normalizing Flow for Molecular Graph Generation,'' in IJCAI, 2023

work page 2023
[6]

G. Wei, Y. Huang, C. Duan, Y. Song, and Y. Du, ``Navigating Chemical Space with Latent Flows,'' in NeurIPS, 2024

work page 2024
[7]

Huang, L

H. Huang, L. Sun, B. Du, Y. Fu, and W. Lv, ``GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generation,'' in ICDM, 2022

work page 2022
[8]

Gruver, S

N. Gruver, S. D. Stanton, N. C. Frey, T. G. J. Rudner, I. Hotzel, J. L. Vanasse, A. Rajpal, K. Cho, and A. G. Wilson, ``Protein Design with Guided Discrete Diffusion,'' in NeurIPS, 2023

work page 2023

Show all 55 references

[9]

Y. Du, M. Plainer, R. Brekelmans, C. Duan, F. No\'e, C. P. Gomes, A. A. Guzik, and K. Neklyudov, ``Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling,'' in NeurIPS, 2024

2024
[10]

X. Guo, Y. Du, and L. Zhao, ``Deep Generative Models for Spatial Networks,'' in KDD, 2021

2021
[11]

Zhang, X

C. Zhang, X. Lyu, and Z. Tang, ``TGG: Transferable Graph Generation for Zero-shot and Few-shot Learning,'' in MM, 2019

2019
[12]

Zhang, T

S. Zhang, T. Li, S. Hui, G. Li, Y. Liang, L. Yu, D. Jin, and Y. Li, ``Deep Transfer Learning for City-scale Cellular Traffic Generation through Urban Knowledge Graph,'' in KDD, 2023

2023
[13]

J. Yang, X. Jiang, Y. Guo, L. T. Yang, and J. Yang, ``Generalize to Fully Unseen Graphs: Learn Transferable Hyper-Relation Structures for Inductive Link Prediction,'' in MM, 2024

2024
[14]

Bernardino Romera-Paredes and Philip Torr, ``An embarrassingly simple approach to zero-shot learning,'' in ICML, 2015

2015
[15]

T. G. Armstrong, V. Ponnekanti, D. Borthakur, and M. Callaghan, ``LinkBench: A database benchmark based on the Facebook social graph,'' in SIGMOD, 2013

2013
[16]

A. K. Joshi, P. Hitzler, and G. Dong, ``LinkGen: Multipurpose linked data generator,'' in ISWC, 2016

2016
[17]

Bagan, A

G. Bagan, A. Bonifati, R. Ciucanu, G. Fletcher, A. Lemay, and N. Advokaat, ``gMark: Schema-driven generation of graphs and queries,'' in TKDE, 2016

2016
[18]

Samanta, A

B. Samanta, A. De, G. Jana, V. Gomez, P. K. Chattaraj, N. Ganguly, and M. G. Rodriguez, ``NeVAE: A Deep Generative Model for Molecular Graphs,'' in JMLR, 2020

2020
[19]

Y. Du, Y. Wang, F. Alam, Y. Lu, X. Guo, L. Zhao, and A. Shehu, ``Deep Latent-Variable Models for Controllable Molecule Generation,'' in BIBM, 2021

2021
[20]

Y. Du, X. Guo, A. Shehu, and L. Zhao, ``Interpretable Molecular Graph Generation via Monotonic Constraints,'' in SDM, 2022

2022
[21]

Y. Liu, X. Ao, F. Feng, Y. Ma, K. Li, T. Chua, and Q. He, ``FLOOD: A Flexible Invariant Learning Framework for Out-of-Distribution Generalization on Graphs,'' in KDD, 2023

2023
[22]

Y. Liu, L. Zou, and Z. Wei, ``Building Graphs at Scale via Sequence of Edges: Model and Generation Algorithms (Extended Abstract),'' in ICDE, 2022

2022
[23]

Zheng, C

S. Zheng, C. Wang, C. Wu, Y. Lou, H. Feng, and X. Yang, ``Temporal Graph Generation Featuring Time-Bound Communities,'' in ICDE, 2024

2024
[24]

Clement Vignac and Pascal Frossard, ``Top-N: Equivariant Set and Graph Generation without Exchangeability,'' in ICLR, 2022

2022
[25]

Qiang, Y

B. Qiang, Y. Song, M. Xu, J. Gong, B. Gao, H. Zhou, W. Ma, and Y. Lan, ``Coarse-to-Fine: a Hierarchical Diffusion Model for Molecule Generation in 3D,'' in ICML, 2023

2023
[26]

T. Jia, H. Li, C. Yang, T. Tao, and C. Shi, ``Graph Invariant Learning with Subgraph Co-mixup for Out-of-Distribution Generalization,'' in AAAI, 2024

2024
[27]

Martin Simonovsky and Nikos Komodakis, ``Graphvae: Towards generation of small graphs using variational autoencoders,'' in ICANN, 2018

2018
[28]

Nicola De Cao and Thomas Kipf, ``MolGAN: An implicit generative model for small molecular graphs,'' in ICML, 2018

2018
[29]

Y. Luo, K. Yan, and S. Ji, ``Graphdf: A discrete flow model for molecular graph generation,'' in ICML, 2021

2021
[30]

H. Cao, C. Tan, Z. Gao, G. Chen, P. A. Heng, and S. Z. Li, ``A survey on generative diffusion model,'' arXiv preprint arXiv:2209.02646, 2022

2022 arXiv
[31]

Eijkelboom, G

F. Eijkelboom, G. Bartosh, C. A. Naesseth, M. Welling, and J. van de Meent, ``Variational Flow Matching for Graph Generation,'' in NeurIPS, 2024

2024
[32]

Bonifati, I

A. Bonifati, I. Holubov\'a, A. P. P\'erez, and S. Sakr, ``Graph Generators: State of the Art and Open Challenges,'' in CSUR, 2020

2020
[33]

Xiaojie Guo and Liang Zhao, ``A Systematic Survey on Deep Generative Models for Graph Generation,'' in TPAMI, 2022

2022
[34]

C. Liu, W. Fan, Y. Liu, J. Li, H. Li, H. Liu, J. Tang, and Q. Li, ``Generative Diffusion Models on Graphs: Methods and Applications,'' in IJCAI, 2023

2023
[35]

Chakrabarti, Y

D. Chakrabarti, Y. Zhan, and C. Faloutsos, ``R-MAT: A recursive model for graph mining,'' in ICDM, 2004

2004
[36]

T. G. Kolda, A. Pinar, T. Plantenga, and C. Seshadhri, ``A scalable generative graph model with community structure,'' in SISC, 2014

2014
[37]

Edunov, D

S. Edunov, D. Logothetis, C. Wang, A. Ching, and M. Kabiljo, ``Darwini: Generating realistic large-scale social graphs,'' in arXiv preprint arXiv:1610.00664, 2016

2016 arXiv
[38]

T. N. Kipf and M. Welling, ``Semi-supervised classification with graph convolutional networks,'' in ICLR, 2017

2017
[39]

Aiello, F

W. Aiello, F. Chung, and L. Lu, ``A Random Graph Model for Power Law Graphs,'' in Experimental Mathematics, 2001

2001
[40]

Morris, N

C. Morris, N. M. Kriege, F. Bause, K. Kersting, P. Mutzel, and M. Neumann, ``TUDataset: A collection of benchmark datasets for learning with graphs,'' arXiv preprint arXiv:2007.08663, 2020

2007 arXiv
[41]

Erd o s, P\'al and R\'enyi, Alfr\'ed, ``On Random Graphs I,'' in Publicationes Mathematicae, 1959

1959
[42]

and Barab\'asi, L., ``Statistical mechanics of complex networks,'' in Reviews of Modern Physics, 2002

Albert, R. and Barab\'asi, L., ``Statistical mechanics of complex networks,'' in Reviews of Modern Physics, 2002

2002
[43]

D. J. Watts and S. H. Strogatz, ``Collective dynamics of small-world networks,'' in Nature, 1998

1998
[44]

E. M. Airoldi, D. M. Blei, S. E. Fienberg, and E. P. Xing, ``Mixed Membership Stochastic Blockmodels,'' in JMLR, 2008

2008
[45]

Leskovec, D

J. Leskovec, D. Chakrabarti, J. M. Kleinberg, C. Faloutsos, and Z. Ghahramani, ``Kronecker Graphs: An Approach to Modeling Networks,'' in JMLR, 2010

2010
[46]

J. You, R. Ying, X. Ren, W. L. Hamilton, and J. Leskovec, ``GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models,'' in ICML, 2018

2018
[47]

L. Kong, J. Cui, H. Sun, Y. Zhuang, B. A. Prakash, and C. Zhang, ``Autoregressive Diffusion Model for Graph Generation,'' in ICML, 2023

2023
[48]

Bergmeister, K

A. Bergmeister, K. Martinkus, N. Perraudin, and R. Wattenhofer, ``Efficient and Scalable Graph Generation through Iterative Local Expansion,'' in ICLR, 2024

2024
[49]

M., Rasch, M

Gretton, A., Borgwardt, K. M., Rasch, M. J., Sch\"olkopf, B., and Smola, A., ``A kernel two-sample test,'' in JMLR, 2012

2012
[50]

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[51]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...
[52]

R. Milo, S. S. Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, ``Network Motifs: Simple Building Blocks of Complex Networks,'' in Science, 2002

2002
[53]

Leskovec, ``Stanford CS224W: Machine Learning with Graphs,'' in cs224w.stanford.edu

J. Leskovec, ``Stanford CS224W: Machine Learning with Graphs,'' in cs224w.stanford.edu
[54]

Holme and B

P. Holme and B. J. Kim, ``Growing scale-free networks with tunable clustering,'' in Pysical Review E, 2002

2002
[55]

A. A. Hagberg, D. A. Schult, and P. J. Swart, ``Exploring network structure, dynamics, and function using NetworkX,'' in SciPy2008, 2008

2008

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

C. Wang, B. Wang, B. Huang, S. Song, and Z. Li, ``FastSGG: Efficient Social Graph Generation Using a Degree Distribution Generation Model,'' in ICDE, 2021

work page 2021

[2] [2]

Xiang, D

S. Xiang, D. Cheng, J. Zhang, Z. Ma, X. Wang, and Y. Zhang, ``Efficient Learning-based Community-Preserving Graph Generation,'' in ICDE, 2022

work page 2022

[3] [3]

Zhang, D

L. Zhang, D. Zhou, H. Tong, J. Xu, Y. Zhu, and J. He, ``FairGen: Towards Fair Graph Generation,'' in ICDE, 2024

work page 2024

[4] [4]

Huang, L

H. Huang, L. Sun, B. Du, and W. Lv, ``Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation,'' in AAAI, 2023

work page 2023

[5] [5]

Y. Zhu, Z. Ouyang, B. Liao, J. Wu, Y. Wu, C. Hsieh, T. Hou, and J. Wu, ``MolHF: A Hierarchical Normalizing Flow for Molecular Graph Generation,'' in IJCAI, 2023

work page 2023

[6] [6]

G. Wei, Y. Huang, C. Duan, Y. Song, and Y. Du, ``Navigating Chemical Space with Latent Flows,'' in NeurIPS, 2024

work page 2024

[7] [7]

Huang, L

H. Huang, L. Sun, B. Du, Y. Fu, and W. Lv, ``GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generation,'' in ICDM, 2022

work page 2022

[8] [8]

Gruver, S

N. Gruver, S. D. Stanton, N. C. Frey, T. G. J. Rudner, I. Hotzel, J. L. Vanasse, A. Rajpal, K. Cho, and A. G. Wilson, ``Protein Design with Guided Discrete Diffusion,'' in NeurIPS, 2023

work page 2023