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Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithms

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper claims that graph coarsening can strictly preserve a graph's topological features—connected components, rings, and higher-order voids—by repeatedly deleting dominated nodes and dominated edges, without ever enumerating cliques, a

desk verdict Solid, practical coarsening paper with a real proof gap in the central homotopy lemma; worth refereeing, but the authors need to cite or properly prove the edge-collapse theorem. read the letter →

arxiv 2601.22943 v2 pith:2TCMPGNR submitted 2026-01-30 cs.LG

Xiang Wu , Rong-Hua Li , Xunkai Li , Kangfei Zhao , Hongchao Qin , Guoren Wang This is my paper
classification cs.LG MSC 05C8555U1068R10
keywords graphcoarseningtopologicalfeatureshomotopyequivalencestrongcollapseedgeneuralnetworksBettinumberscliquecomplex
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 tries to establish that two local graph operations—graph strong collapse and graph edge collapse—reduce a graph while leaving its homotopy type unchanged. Because the homotopy type is unchanged, the coarsened graph keeps the same connected components, cycles, and higher-dimensional cavities (the Betti numbers) as the original, and this is exactly what graph neural networks seem to need. The paper packages these operations into three algorithms (GStrongCollapse, GEdgeCollapse, NeighborhoodConing) that avoid the exponential clique enumeration of earlier topology-preserving coarsening, and proves shortest-path distance bounds that tie the operations to GNN receptive-field preservation. Experiments show STPGC matches or beats prior topology-preserving coarsening on node classification while running up to 37x faster.

What carries the argument

The load-bearing machinery is the pair of local deletion rules plus a homotopy-equivalence guarantee. A node u is dominated by v when N[u]⊆N[v]; deleting it is a graph strong collapse. An edge (x,y) is dominated by v (with v not an endpoint) when N[x,y]⊆N[v]; deleting it is a graph edge collapse. Lemma 2.5 asserts that both operations preserve the homotopy type of the clique complex, so connected components, rings, and higher-order voids survive exact coarsening. NeighborhoodConing works as an inverse of edge collapse: insert dominated edges so the target node becomes dominated, then strong-collapse it, preserving homotopy equivalence while enabling further reduction.

What would settle it

Take a small graph (for example, an octahedron graph or a 4-cycle with a chord), compute the first Betti number of its clique complex, delete one dominated edge—an edge (x,y) where N[x,y]⊆N[v] for some non-endpoint v—and recompute the first Betti number. Any change in the Betti number would falsify Lemma 2.5 and collapse the topological-preservation guarantee.

Watch

Extended reading notes

Core claim

The central claim is Lemma 2.5: if Gc is obtained from G by any sequence of graph strong collapses (delete a node whose closed neighborhood is contained in another's) and graph edge collapses (delete an edge whose common-closed-neighborhood is contained in a third node's closed neighborhood), then the clique complex of Gc is homotopy equivalent to the clique complex of G. Therefore every homotopy invariant—connected components, cycles/rings, higher voids, Betti numbers—is identical in the exact phase. The key distinction from the earlier GEC method is that STPGC identifies reducible nodes and edges directly by neighborhood inclusion rather than listing all cliques, removing the exponential b

Load-bearing premise

The entire topological guarantee rests on the claim that deleting a dominated edge from the graph's 1-skeleton is a homotopy-preserving collapse of the full clique complex—a correspondence the paper states via Lemma 2.5 but does not fully derive.

Editorial extensions

If this is right

  • Topology-preserving coarsening no longer requires clique enumeration; total amortized complexity is near-linear for sparse graphs, so graphs with millions of nodes can be coarsened in practice.
  • Exact coarsening keeps Betti numbers unchanged until no dominated nodes or edges remain; experiments show STPGC's Betti count stays flat while spectral/spatial baselines lose topological features immediately.
  • Shortest-path distances do not increase under strong collapse or neighborhood coning and increase by at most 1 under edge collapse, which the paper uses to argue that GNN receptive fields—and thus node-classification performance—are preserved.
  • On five node-classification benchmarks, STPGC outperforms the prior topology-preserving GEC method by an average of 1.73% and delivers up to a 37x runtime speedup on large-scale graphs.
  • When exact preservation is impossible or a target coarsening ratio requires further reduction, the r-relaxed strong collapse provides a controlled approximate phase that still yields strong GNN accuracy.

Reading between the lines

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

  • Editorial inference: The same neighborhood-inclusion tests could be reused for homotopy-preserving sparsification, not just coarsening: deleting dominated edges alone gives a smaller edge set while preserving the graph's homotopy type, which may be cheaper for downstream GNN sampling or spectral computation.
  • Editorial inference: The r-relaxed strong collapse creates a smooth trade-off between topological fidelity and compression; a natural extension the paper does not pursue is to measure, via persistent homology of intermediate graphs, how topology degrades as r increases.
  • Editorial inference: Since homotopy equivalence preserves the fundamental group but not graph isomorphism, many locally different graphs can coarsen to the same reduced form; this suggests a canonical minimal homotopy-type representative that could serve as a graph fingerprint or a preprocessing step for graph matching.
  • Editorial inference: The receptive-field argument relies on shortest-path distances, so the method should transfer to any message-passing GNN whose propagation respects path length; the paper's experiments cover GCN, APPNP, GraphSAGE, and GraphSAINT, leaving higher-order topological layers (e.g., persistent-homology-enhanced GNNs) untested.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes Scalable Topology-Preserving Graph Coarsening (STPGC), a framework for reducing graph size while preserving topological features. It introduces two graph-level operations, graph strong collapse and graph edge collapse, and a third operation, neighborhood coning, all defined by neighborhood-inclusion conditions rather than clique enumeration. The authors claim that any graph obtained by these operations is homotopy equivalent to the original (Lemma 2.5), that the three algorithms preserve the GNN receptive field up to small distance distortion (Lemmas 3.3 and 3.4), and that an approximate phase with relaxed dominance conditions can reach arbitrary coarsening ratios. Experiments on node classification and scalability compare STPGC with spectral/spatial coarsening baselines and with the topology-preserving GEC method, reporting higher accuracy and large speedups.

Significance. If the central homotopy-preservation lemma is established, the paper makes a useful algorithmic contribution: it replaces clique enumeration in topology-preserving coarsening with efficient neighborhood-inclusion checks, leading to near-linear amortized complexity on sparse graphs. The GNN receptive-field analysis is a thoughtful addition that connects topological coarsening to practical GNN training. The experimental study is broad, covering five labeled benchmarks and four large unlabeled graphs, and the reported speedups over GEC are substantial. However, the paper's main theoretical guarantee rests on a proof that is currently incomplete, and the full STPGC pipeline used in the experiments includes an approximate phase that does not preserve topology. The contribution is therefore promising but not yet fully substantiated.

major comments (3)
  1. [Appendix A.1, Lemma 2.5] The proof of Lemma 2.5 does not establish the claim. It states that if the clique complexes Kc and K are homotopy equivalent, then Gc and G are homotopy equivalent, but Kc ≃ K is precisely what the lemma must prove. The nontrivial step is graph edge collapse (Definition 2.3): deleting an edge (x,y) with N[x,y] ⊆ N[v] removes, in the clique complex, all cliques containing (x,y) simultaneously. Since (x,y) may belong to multiple maximal cliques (all containing v), this is not an elementary collapse as defined in Section 2.1, and no deformation retraction or sequence of collapses is constructed. This gap affects both GEdgeCollapse and NeighborhoodConing, which relies on the inverse of edge collapse. The authors should either supply a complete proof or cite a precise theorem showing that dominated-edge deletion in a flag complex preserves homotopy type (e.g., the edge-collapse results of Boi
  2. [Section 3.4, Algorithm 4] The full STPGCForGNN procedure applies ApproximateCoarsening after ExactCoarsening, and the approximate phase uses r-relaxed strong collapse (Definition 3.5), which does not preserve homotopy type or Betti numbers in general. The abstract's statement that STPGC 'rigorously preserves topological features' therefore applies only to the exact phase, not to the final output used in the node-classification experiments. In addition, Appendix C describes a DropEdge post-processing step on coarsened graphs, which can further change topology. The paper should qualify all topology-preservation claims, state explicitly that the exact phase is topology-preserving while the full pipeline is not, and clarify whether the Betti-number measurements in Figure 4 are taken before or after DropEdge and after the approximate phase.
  3. [Appendix A.2, Lemma 3.2] The proof that neighborhood coning does not create new dominated nodes is incomplete and contains undefined notation. The set N[v,w] is not defined, and the phrase 'u dominates (v,w)' mixes the edge-dominance definition (Definition 2.3) with node dominance. The argument that N[v] ⊆ N[u] follows from the common neighbors being adjacent to u does not rule out neighbors of v outside N[v,w]. Since Lemma 3.2 is used to justify termination of the NeighborhoodConing procedure, it needs a correct proof or should be stated as an empirical observation with the termination argument revised.
minor comments (5)
  1. [Section 3.3 / Algorithm 4] The text says the exact phase runs GStrongCollapse and GEdgeCollapse for δ1 iterations (lines 6-8), but Algorithm 4 uses δ2 in the loop condition. The parameter δ3 appears only in the complexity formula and is not defined in the pseudocode. Please unify the notation.
  2. [Figure 3] The legend and caption contain the typo 'SPTGC'; it should be 'STPGC'.
  3. [Appendix A.2] Please define N[v,w] or restate the proof using the already-defined open neighborhood of an edge, N(x,y). The current notation is confusing.
  4. [Section 4, Betti Number] The experiments report only the 1-Betti number. Since the paper claims preservation of connectivity, rings, and higher-order voids, please clarify whether β0 and β2 were also measured, or state that only β1 was evaluated.
  5. [Appendix C] The DropEdge step is described only briefly. Please state in the main text how it interacts with the topological guarantees, and whether the reported Betti numbers are computed before or after this step.

Circularity Check

1 steps flagged · score 4.0 of 10

Lemma 2.5's proof assumes the homotopy equivalence it must prove; the exact-phase topology guarantee is not fully derived, though the result has external algebraic-topology support.

  1. other [Appendix A.1, proof of Lemma 2.5]
    "If Gc is derived from a series of graph strong collapse and graph edge collapse from G, and Kc is the clique complex derived through reducing the same nodes and edges via strong collapse and edge collapse, then Gc is also the 1-skeleton of Kc, as Kc and K are homotopy equivalent, we have Gc and G are homotopy equivalent."

    The lemma to be proved is Gc ≃ G. Under the paper's own definition of graph homotopy equivalence (Section 2.2), this is exactly Kc ≃ K. The proof's only bridge is the phrase 'as Kc and K are homotopy equivalent' — no deformation retraction is constructed, no external strong/edge-collapse theorem is invoked at this step, and no argument shows that deleting a dominated node/edge in the 1-skeleton is a homotopy-preserving collapse on the clique complex. Thus the proof's premise is the conclusion of the lemma. This is a circular proof step (or at minimum an unproved assumption) in the central topological guarantee, although the statement itself is likely repairable by the cited algebraic-topology literature.

full rationale

The rest of the derivation chain is not circular. Lemmas 3.3 and 3.4 are direct distance arguments, not fits. ApproximateCoarsening explicitly relaxes the topological guarantee, so it does not masquerade as exact. No parameter is fitted and then reported as a prediction; Betti-number curves and node-classification accuracies are genuine validations of the implementation rather than definitions of the output. Self-citations (Meng et al. 2024a/b) are used as a baseline and motivation, not as the load-bearing proof of STPGC's collapse rules; the intended support is the external strong/edge-collapse literature (Boissonnat & Pritam; Barmak & Minian). The one significant flaw is Appendix A.1's proof of Lemma 2.5, which assumes Kc ≃ K rather than deriving it. Because Lemma 2.5 is the basis for all exact-coarsening topology preservation, this is a partial circularity/proof gap; it does not make the paper vacuous because independent external results and experiments support the claim.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

Central claims rest on standard simplicial-collapse theorems and on an unproved correspondence between graph edge deletion and simplicial collapse; several hyperparameters control the algorithm. No invented physical entities.

free parameters (5)
  • θ1 (degree threshold) = 15 (Cora, Citeseer), 25 (DBLP), 50 (ogbn-arXiv), 100 (ogbn-products), 50 in scalability runs
    Caps which nodes/edges are checked for dominance; set per-dataset by hand and varied in Fig. 5; controls the exact-phase scope and complexity.
  • θ2 (relaxation trigger) = 1% of node count
    If fewer than θ2 nodes are reduced in an iteration, the relaxation parameter r increments; hand-chosen.
  • r (relaxation parameter) = 0,1,2,... incremented by trigger
    Trades topology preservation for coarsening ratio in ApproximateCoarsening; starts at 0 (exact).
  • δ2, δ3 (iteration caps) = not reported
    Bound the Exact and Approximate loops in Algorithm 4; appear in complexity but no concrete values are given.
  • DropEdge ratio = 0.1
    Randomly removes heterophilic edges from coarsened graphs in experiments; affects reported GNN accuracy, not topological theory.
assumptions (4)
  • standard math Simplicial strong collapse and edge collapse preserve homotopy type.
    Used implicitly in Lemma 2.5; results cited from Boissonnat & Pritam 2019/2020 and Barmak & Minian 2012.
  • domain assumption Graph topology is captured by the clique complex; graph homotopy equivalence is defined as homotopy equivalence of clique complexes.
    Section 2.2; necessary to connect graph operations to topological features.
  • ad hoc to paper Graph strong collapse (N[u]⊆N[v]) and graph edge collapse (N[x,y]⊆N[v]) act on the clique complex as the simplicial collapses that preserve homotopy.
    Appendix A.1 asserts 'as Kc and K are homotopy equivalent' without proving the edge-deletion-to-collapse correspondence; load-bearing and unverified.
  • ad hoc to paper Shortest-path distance non-increase (or +1) implies preservation of the GNN receptive field.
    Section 3.4 uses this to claim receptive-field preservation; no formal definition of receptive field or proof of equivalence.

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Cite this review

Pith. "Pith review of Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithms." pith.science (2026). https://pith.science/paper/2TCMPGNR

@misc{pith2026260122943,
  author       = {Pith},
  title        = {Pith review of: Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2TCMPGNR}},
  note         = {Machine review of arXiv:2601.22943}
}
read the original abstract

Graph coarsening reduces the size of a graph while preserving certain properties. Most existing methods preserve either spectral or spatial characteristics. Recent research shows that topology-preserving coarsening methods maintain GNN performance on coarsened graphs but suffer from exponential time complexity. To address these problems, we propose Scalable Topology-Preserving Graph Coarsening (STPGC) by introducing the concepts of graph strong collapse and graph edge collapse extended from algebraic topology. STPGC comprises three new algorithms, GStrongCollapse, GEdgeCollapse, and NeighborhoodConing based on these two concepts, which eliminate dominated nodes and edges while rigorously preserving topological features. We further prove that STPGC preserves the GNN receptive field and develop approximate algorithms to accelerate GNN training. Experiments on node classification with GNNs demonstrate the efficiency and effectiveness of STPGC.

Figures

Figures reproduced from arXiv: 2601.22943 by the authors.

Figure 1
Figure 1. Examples of graph strong collapse and graph edge collapse. The dominated nodes and edges are shown in red. Example 2.4. An example of dominated edges is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Examples of neighborhood coning. The inserted edges and newly created dominated nodes are shown in red. of a graph edge collapse. Here, the inverse means that after adding a dominated edge to the graph, we can obtain the original graph through a graph edge collapse, thereby guar￾anteeing homotopy equivalence. The red nodes can then be reduced through graph strong collapse. This approach is not restricted to creating… view at source ↗
Figure 3
Figure 3. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Betti number preserved by different methods. illustrates the impact of varying θ1 on GCN node classifica￾tion accuracy and runtime across different target coarsening ratios (c ∈ {0.1, 0.3, 0.5}). As observed in the figure, in￾creasing θ1 generally leads to improved cla…
Figure 6
Figure 6. Figure 6: Scalability analysis of STPGC. in this range than in previous intervals. Compared to GEC, STPGC achieves an order-of-magnitude speedup in most configurations, and delivers up to a 37x acceleration on the cit-Patent dataset. These results validate superior scalability o…
Figure 8
Figure 8. Figure 8: Results with varying coarsening ratios. others. In maximum independent set computation (Chang et al., 2017; Piao et al., 2020), a node can be safely removed if its closed neighborhood fully contains another’s. In short￾est distance queries, neighborhood inclusion helps…
Figure 9
Figure 9. Figure 9: An example in the proof. B. Complexity Analysis B.1. Complexity analysis for GStrongCollapse (Algorithm 1) In Algorithm 1, we iterate through all nodes. For a specific node u, we check its dominance only if deg(u) ≤ θ1. The dominance check involves verifying whether N[…
Figure 10
Figure 10. Figure 10: Training time and GPU memory usage of GNNs. Additional experimental details. All GNNs are implemented using the PyTorch Geometric framework, following the standard benchmarking protocol established by (Huang et al., 2021). Regarding the STPGC hyperparameters, we set t…

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Reference graph

Works this paper leans on

50 extracted references · 4 linked inside Pith

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    and Periwal, V

    Aggarwal, M. and Periwal, V. Tight basis cycle representatives for persistent homology of large biological data sets. PLOS Computational Biology, 19 0 (5): 0 e1010341, 2023

    2023

  3. [3]

    Barmak, J. A. and Minian, E. G. Strong homotopy types, nerves and collapses. Discrete & Computational Geometry, 47: 0 301--328, 2012

    2012

  4. [4]

    and Pritam, S

    Boissonnat, J.-D. and Pritam, S. Computing persistent homology of flag complexes via strong collapses. In SoCG 2019-International Symposium on Computational geometry, 2019

    2019

  5. [5]

    and Pritam, S

    Boissonnat, J.-D. and Pritam, S. Edge collapse and persistence of flag complexes. In 36th International Symposium on Computational Geometry (SoCG 2020). Schloss-Dagstuhl-Leibniz Zentrum f \"u r Informatik, 2020

    2020

  6. [6]

    Positional dominance: Concepts and algorithms

    Brandes, U., Heine, M., M \"u ller, J., and Ortmann, M. Positional dominance: Concepts and algorithms. In Algorithms and Discrete Applied Mathematics: Third International Conference, CALDAM 2017, Sancoale, Goa, India, February 16-18, 2017, Proceedings 3, pp.\ 60--71. Springer, 2017

    2017

  7. [7]

    and Gunderson, L

    Bravo Hermsdorff, G. and Gunderson, L. A unifying framework for spectrum-preserving graph sparsification and coarsening. NeurIPS, 32, 2019

    2019

  8. [8]

    Graph coarsening with neural networks

    Cai, C., Wang, D., and Wang, Y. Graph coarsening with neural networks. arXiv preprint arXiv:2102.01350, 2021

    arXiv 2021

Show all 50 references
  1. [9]

    Computing a near-maximum independent set in linear time by reducing-peeling

    Chang, L., Li, W., and Zhang, W. Computing a near-maximum independent set in linear time by reducing-peeling. In Proceedings of the 2017 ACM International Conference on Management of Data, pp.\ 1181--1196, 2017

    2017

  2. [10]

    and Safro, I

    Chen, J. and Safro, I. Algebraic distance on graphs. SIAM Journal on Scientific Computing, 33 0 (6): 0 3468--3490, 2011

    2011

  3. [11]

    A unified lottery ticket hypothesis for graph neural networks

    Chen, T., Sui, Y., Chen, X., Zhang, A., and Wang, Z. A unified lottery ticket hypothesis for graph neural networks. In ICML, pp.\ 1695--1706. PMLR, 2021 a

    2021

  4. [12]

    Topological relational learning on graphs

    Chen, Y., Coskunuzer, B., and Gel, Y. Topological relational learning on graphs. NeurIPS, 34: 0 27029--27042, 2021 b

    2021

  5. [13]

    Dey, T. K. and Wang, Y. Computational topology for data analysis. Cambridge University Press, 2022

    2022

  6. [14]

    Graph coarsening via convolution matching for scalable graph neural network training

    Dickens, C., Huang, E., Reganti, A., Zhu, J., Subbian, K., and Koutra, D. Graph coarsening via convolution matching for scalable graph neural network training. In Companion Proceedings of the ACM on Web Conference 2024, pp.\ 1502--1510, 2024

    2024

  7. [15]

    and Gonzalez, T

    E g ecio g lu, \"O . and Gonzalez, T. F. A computationally intractable problem on simplicial complexes. Computational Geometry, 6 0 (2): 0 85--98, 1996

    1996

  8. [16]

    and Steenrod, N

    Eilenberg, S. and Steenrod, N. Foundations of algebraic topology, volume 2193. Princeton University Press, 2015

    2015

  9. [17]

    Exgc: Bridging efficiency and explainability in graph condensation

    Fang, J., Li, X., Sui, Y., Gao, Y., Zhang, G., Wang, K., Wang, X., and He, X. Exgc: Bridging efficiency and explainability in graph condensation. In Proceedings of the ACM Web Conference 2024, pp.\ 721--732, 2024

    2024

  10. [18]

    Efficient computation of the characteristic polynomial of a threshold graph

    F \"u rer, M. Efficient computation of the characteristic polynomial of a threshold graph. Theoretical Computer Science, 657: 0 3--10, 2017

    2017

  11. [19]

    Predict then propagate: Graph neural networks meet personalized pagerank

    Gasteiger, J., Bojchevski, A., and G \"u nnemann, S. Predict then propagate: Graph neural networks meet personalized pagerank. arXiv preprint arXiv:1810.05997, 2018

    2018 arXiv

  12. [20]

    Inductive representation learning on large graphs

    Hamilton, W., Ying, Z., and Leskovec, J. Inductive representation learning on large graphs. Advances in neural information processing systems, 30, 2017

    2017

  13. [21]

    A topology-aware graph coarsening framework for continual graph learning

    Han, X., Feng, Z., and Ning, Y. A topology-aware graph coarsening framework for continual graph learning. In Globersons, A., Mackey, L., Belgrave, D., Fan, A., Paquet, U., Tomczak, J. M., and Zhang, C. (eds.), Advances in Neural Information Processing Systems 38: Annual Confer...

    2024

  14. [22]

    Topological node2vec: Enhanced graph embedding via persistent homology

    Hiraoka, Y., Imoto, Y., Lacombe, T., Meehan, K., and Yachimura, T. Topological node2vec: Enhanced graph embedding via persistent homology. Journal of Machine Learning Research, 25 0 (134): 0 1--26, 2024

    2024

  15. [23]

    Topological graph neural networks

    Horn, M., De Brouwer, E., Moor, M., Moreau, Y., Rieck, B., and Borgwardt, K. Topological graph neural networks. In ICLR

  16. [24]

    Scaling up graph neural networks via graph coarsening

    Huang, Z., Zhang, S., Xi, C., Liu, T., and Zhou, M. Scaling up graph neural networks via graph coarsening. In KDD, pp.\ 675--684, 2021

    2021

  17. [25]

    Rethinking graph lottery tickets: Graph sparsity matters

    Hui, B., Yan, D., Ma, X., and Ku, W.-S. Rethinking graph lottery tickets: Graph sparsity matters. arXiv preprint arXiv:2305.02190, 2023

    2023 arXiv

  18. [26]

    Going beyond persistent homology using persistent homology

    Immonen, J., Souza, A., and Garg, V. Going beyond persistent homology using persistent homology. NeurIPS, 36: 0 63150--63173, 2023

    2023

  19. [27]

    Graph condensation for graph neural networks

    Jin, W., Zhao, L., Zhang, S., Liu, Y., Tang, J., and Shah, N. Graph condensation for graph neural networks. arXiv preprint arXiv:2110.07580, 2021

    2021 arXiv

  20. [28]

    Kipf, T. N. and Welling, M. Semi-supervised classification with graph convolutional networks. In ICLR, 2017

    2017

  21. [29]

    Featured graph coarsening with similarity guarantees

    Kumar, M., Sharma, A., Saxena, S., and Kumar, S. Featured graph coarsening with similarity guarantees. In ICML, pp.\ 17953--17975. PMLR, 2023

    2023

  22. [30]

    and Terzi, E

    LeFevre, K. and Terzi, E. Grass: Graph structure summarization. In Proceedings of the SIAM International Conference on Data Mining, SDM 2010, April 29 - May 1, 2010, Columbus, Ohio, USA , pp.\ 454--465. SIAM , 2010. doi:10.1137/1.9781611972801.40

    2010 doi

  23. [31]

    Scaling distance labeling on small-world networks

    Li, W., Qiao, M., Qin, L., Zhang, Y., Chang, L., and Lin, X. Scaling distance labeling on small-world networks. In Proceedings of the 2019 International Conference on Management of Data, pp.\ 1060--1077, 2019

    2019

  24. [32]

    Graph reduction with spectral and cut guarantees

    Loukas, A. Graph reduction with spectral and cut guarantees. Journal of Machine Learning Research, 20 0 (116): 0 1--42, 2019

    2019

  25. [33]

    and Vandergheynst, P

    Loukas, A. and Vandergheynst, P. Spectrally approximating large graphs with smaller graphs. In ICML, pp.\ 3237--3246. PMLR, 2018

    2018

  26. [34]

    Improving graph neural networks with structural adaptive receptive fields

    Ma, X., Wang, J., Chen, H., and Song, G. Improving graph neural networks with structural adaptive receptive fields. In Proceedings of the web conference 2021, pp.\ 2438--2447, 2021

    2021

  27. [35]

    Mahadev, N. V. and Peled, U. N. Threshold graphs and related topics. Elsevier, 1995

    1995

  28. [36]

    Topology-preserving graph coarsening: An elementary collapse-based approach

    Meng, Y., Li, R.-H., Lin, L., Li, X., and Wang, G. Topology-preserving graph coarsening: An elementary collapse-based approach. Proceedings of the VLDB Endowment, 17 0 (13): 0 4760--4772, 2024 a

    2024

  29. [37]

    Encoding group interests with persistent homology for personalized search

    Meng, Y., Li, R.-H., Qin, H., Wu, X., Duan, H., Lu, Y., and Wang, G. Encoding group interests with persistent homology for personalized search. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 54 0 (9): 0 5606--5616, 2024 b

    2024

  30. [38]

    Nikolopoulos, S. D. and Papadopoulos, C. The number of spanning trees in k n-complements of quasi-threshold graphs. Graphs and Combinatorics, 20: 0 383--397, 2004

    2004

  31. [39]

    Topological machine learning for low data medical imaging

    Nuwagira, B., Korkmaz, C., Koung, P., and Coskunuzer, B. Topological machine learning for low data medical imaging. In Hegselmann, S., Zhou, H., Healey, E., Chang, T., Ellington, C., Mhasawade, V., Tonekaboni, S., Argaw, P., and Zhang, H. (eds.), Proceedings of the 4th Machine...

    2025

  32. [40]

    Maximizing the reduction ability for near-maximum independent set computation

    Piao, C., Zheng, W., Rong, Y., and Cheng, H. Maximizing the reduction ability for near-maximum independent set computation. Proceedings of the VLDB Endowment, 13 0 (12): 0 2466--2478, 2020

    2020

  33. [41]

    A., Kang, C., Zhang, Y., and Subrahmanian, V

    Purohit, M., Prakash, B. A., Kang, C., Zhang, Y., and Subrahmanian, V. Fast influence-based coarsening for large networks. In KDD, pp.\ 1296--1305, 2014

    2014

  34. [42]

    P., Hymel, J

    Townsend, J., Micucci, C. P., Hymel, J. H., Maroulas, V., and Vogiatzis, K. D. Representation of molecular structures with persistent homology for machine learning applications in chemistry. Nature communications, 11 0 (1): 0 3230, 2020

    2020

  35. [43]

    Whitehead, J. H. C. Simplicial spaces, nuclei and m-groups. Proceedings of the London mathematical society, 2 0 (1): 0 243--327, 1939

    1939

  36. [44]

    Link prediction with persistent homology: An interactive view

    Yan, Z., Ma, T., Gao, L., Tang, Z., and Chen, C. Link prediction with persistent homology: An interactive view. In ICML, pp.\ 11659--11669. PMLR, 2021

    2021

  37. [45]

    Cycle representation learning for inductive relation prediction

    Yan, Z., Ma, T., Gao, L., Tang, Z., and Chen, C. Cycle representation learning for inductive relation prediction. In Chaudhuri, K., Jegelka, S., Song, L., Szepesv \' a ri, C., Niu, G., and Sabato, S. (eds.), ICML, ICML 2022, 17-23 July 2022, Baltimore, Maryland, USA , volume 1...

    2022

  38. [46]

    Neural approximation of graph topological features

    Yan, Z., Ma, T., Gao, L., Tang, Z., Wang, Y., and Chen, C. Neural approximation of graph topological features. NeurIPS, 35: 0 33357--33370, 2022 b

    2022

  39. [47]

    Cycle invariant positional encoding for graph representation learning

    Yan, Z., Ma, T., Gao, L., Tang, Z., Chen, C., and Wang, Y. Cycle invariant positional encoding for graph representation learning. In Villar, S. and Chamberlain, B. (eds.), Learning on Graphs Conference, 27-30 November 2023, Virtual Event, volume 231 of Proceedings of Machine L...

    2023

  40. [48]

    Graphsaint: Graph sampling based inductive learning method

    Zeng, H., Zhou, H., Srivastava, A., Kannan, R., and Prasanna, V. Graphsaint: Graph sampling based inductive learning method. In International Conference on Learning Representations

  41. [49]

    Neighborhood skyline on graphs: Concepts, algorithms and applications

    Zhang, Q., Li, R.-H., Qin, H., Dai, Y., Yuan, Y., and Wang, G. Neighborhood skyline on graphs: Concepts, algorithms and applications. In 2023 IEEE 39th International Conference on Data Engineering (ICDE), pp.\ 585--598. IEEE, 2023

    2023

  42. [50]

    Gnn: incorporating ring priors into molecular modeling

    Zhu, J., Wu, K., Wang, B., Xia, Y., Xie, S., Meng, Q., Wu, L., Qin, T., Zhou, W., Li, H., and Liu, T. Gnn: incorporating ring priors into molecular modeling. In The Eleventh ICLR, ICLR 2023, Kigali, Rwanda, May 1-5, 2023 , 2023

    2023

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.