Pith. sign in

REVIEW 4 major objections 6 minor 108 references

HIT-Leiden maintains Leiden communities incrementally with work bounded by the affected region, not the whole graph, and reports speedups of up to five orders of magnitude.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 10:48 UTC pith:YGV5TU5Q

load-bearing objection HIT-Leiden is a credible, carefully built incremental-Leiden engineering result with plausible large speedups, but the headline relative-boundedness claim rests on an unproven empirical observation and the artifact is not verifiable as submitted. the 4 major comments →

arxiv 2601.08554 v5 pith:YGV5TU5Q submitted 2026-01-13 cs.SI cs.DBcs.GR

Maintaining Leiden Communities in Large Dynamic Graphs

Chunxu Lin , Yumao Xie , Yixiang Fang , Yongmin Hu , Yingqian Hu , Cheng Chen This is my paper
classification cs.SI cs.DBcs.GR
keywords community detectiondynamic graphsLeiden algorithmincremental maintenancemodularityhierarchical clusteringconnected componentsrelative boundedness
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper addresses the practical problem of keeping Leiden community partitions up to date as large graphs evolve. It argues that existing incremental Leiden methods can require essentially full recomputation even for tiny updates, and presents HIT-Leiden, which bounds the work to the two-hop neighborhood of the changed vertex set and the affected region. The central move is to explicitly maintain the hierarchical supergraph Leiden builds across iterations and to use a dynamic connected-component index to preserve the gamma-connectivity that gives Leiden its quality guarantee. If the claims hold, community refreshes at billion-edge scale drop from hours to minutes while preserving modularity comparable to recomputing from scratch.

Core claim

The paper claims that Leiden communities can be maintained incrementally with total time O(|N2(CHANGED)|+|N2(AFF)|), making the algorithm relatively bounded with respect to the static Leiden algorithm, whereas prior incremental Leiden methods are unbounded and cost O(P*(|V|+|E|)) per update. The discovery is that by explicitly maintaining the tree-like hierarchy Leiden builds across iterations and by treating each connected component of a split sub-community as a new sub-community (Observation 5), the cascade of membership changes stays local. On five large real-world dynamic graphs the method reports modularity within 0.01 of full recomputation, subpartition gamma-density proportions essent

What carries the argument

The load-bearing piece is the hierarchical supergraph (the tree-like structure of supervertices across Leiden's P iterations) combined with a connected-component index (CC-index) that tracks intra-sub-community edges. Inc-movement, inc-refinement, and inc-aggregation operate level by level on this hierarchy. The gamma-order and gamma-connectivity definitions from Leiden provide the theoretical hook: Observations 1-5 say which edge updates can affect community and sub-community memberships, and Observation 5 justifies treating connected components of a split sub-community as new gamma-connected sub-communities. The CC-index lets the algorithm detect when a deletion disconnects a sub-community

Load-bearing premise

Observation 5 says that after treating each connected component of a sub-community as a new sub-community, most maintained communities are still subpartition gamma-dense; this is an unproven empirical assertion, and if a real update batch violates it, the affected region can escape the two-hop bound and the algorithm degrades toward full recomputation.

What would settle it

Run HIT-Leiden on a dynamic graph constructed so that an intra-sub-community edge deletion splits a sub-community into two connected components that have no valid gamma-order (each is not gamma-dense). If the proportion of maintained communities that are subpartition gamma-dense falls substantially below the over-99% figure reported on real workloads, or if runtime on such updates scales with the full graph rather than with |N2(CHANGED)|+|N2(AFF)|, Observation 5 and the boundedness claim would be falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If correct, dynamic community refreshes at billion-edge scale drop from hours to minutes, enabling near-real-time features and retrieval indices.
  • Graph-RAG pipelines can update hierarchical communities and only regenerate LLM summaries for changed communities, reducing token cost to roughly 0.8% of full recomputation per the paper's experiment.
  • Fraud-ring discovery on evolving financial graphs gets a 7.7x speedup with comparable recall, as demonstrated in the paper's production study.
  • The relative-boundedness result gives a principled complexity statement: maintenance cost is polynomial in the size of the affected region, not the whole graph.
  • The hierarchy Leiden builds is explicitly preserved across updates, so downstream consumers that rely on the supergraph structure do not need to rebuild it.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The boundedness guarantee is heuristic: Observation 5 is an empirical 'most of the time' statement, so the O(|N2(CHANGED)|+|N2(AFF)|) bound holds only while connected components of split sub-communities remain gamma-dense; an adversarial update that violates this could push the affected region toward full recomputation.
  • The same hierarchical-maintenance recipe might transfer to other iterative refinement-based clustering heuristics (e.g., Louvain variants with connectivity constraints), since the key is maintaining the component structure rather than the specific gamma-order.
  • A testable extension would be to measure the proportion of maintained communities that are subpartition gamma-dense under edge deletions specifically engineered to split sub-communities into non-gamma-connected pieces; the paper reports over 99% on its workloads but gives no worst-case construction.
  • The paper leaves directed graphs and parallel execution as future work; a parallel version of HIT-Leiden would be the natural next step for even larger deployments.

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

4 major / 6 minor

Summary. The paper proposes HIT-Leiden, an incremental algorithm for maintaining Leiden communities in dynamic graphs. The algorithm maintains the hierarchical supergraph structure produced by Leiden across iterations and uses dynamic connectivity indices to restrict recomputation to an affected region. It consists of three phases—inc-movement, inc-refinement, and inc-aggregation—plus a deferred-update step to synchronize community memberships across levels. The paper also gives a boundedness analysis claiming that prior incremental Leiden methods (ND-, DS-, DF-Leiden) require O(P(|V|+|E|)) work per update, and claims that HIT-Leiden achieves O(|N2(CHANGED)|+|N2(AFF)|) cost, hence is relatively bounded. Experiments on five large real-world graphs report modularity comparable to competitors, a high percentage of subpartition γ-dense communities, and speedups up to five orders of magnitude, together with two production application studies.

Significance. If the algorithmic claims hold, this is a practically significant contribution: it addresses a real industrial need for low-latency community maintenance in billion-edge graphs, and the empirical evaluation is extensive and consistent with the qualitative story. The paper also includes detailed pseudocode, a full-version reference, and deployment results, which are strengths. However, the central theoretical claim—relative boundedness and preservation of Leiden's connectivity guarantees—rests on an unproven empirical observation (Observation 5) and on a definition of AFF that makes the complexity statement close to tautological. The practical algorithm may well be useful, but the theoretical framing is substantially overstated as written.

major comments (4)
  1. [§4.2, Observation 5; used in §5.1/Alg. 2 and §5.2/Alg. 3] Observation 5 is the load-bearing assumption of the paper, but it is presented as an empirical observation with no proof. It states that most maintained communities are subpartition γ-dense when connected components are treated as new sub-communities, and it is used to ignore intra-sub-community edge deletions that break γ-connectivity without disconnecting the component. If Observation 5 fails, a vertex whose sub-community is no longer γ-dense will never be added to K and never re-mapped, so the output will violate the Leiden subpartition γ-density property that the paper claims to preserve in §7. Figure 14 reports only 'over 99%' density, which is not 100%, and the evaluation method re-finds γ-orders heuristically, so the reported rate may be optimistic. The paper needs either a proof of Observation 5 under Assumption 1 or an explicit downgrade of the guarantee to 'empirically preserve
  2. [§4.1, Definitions 4–5; §5.4 Complexity analysis] The total-time claim O(|N2(CHANGED)|+|N2(AFF)|) is partly circular because AFF is defined in Definition 4 as the set of vertices/supervertices that actually change communities or sub-communities. With this output-dependent definition, an algorithm that touches only vertices it later labels as changed is 'relatively bounded' by construction. The complexity paragraph in §5.4 introduces Γ_p (supervertices involved in superedge changes) and states per-level costs O(|N2(Γ_p)|+h_p|Γ_p|+|N2(Λ_p)|+h_p|Λ_p|), but no proof is given that Γ_p ⊆ CHANGED∪AFF, that the two-hop neighborhoods can be aggregated in this way, or that h_p terms are dominated by the N2 terms. The non-trivial content—that AFF is small and that the algorithm never touches vertices outside this output-defined set—is not established. The paper should define CHANGED and AFF as input-dependent predicates (or accept the circularity)
  3. [§4.1, Theorem 1 and Table 2] Theorem 1 states that all three prior incremental Leiden algorithms cost O(P(|V|+|E|)) per update and are hence neither bounded nor relatively bounded. No proof is given in the paper or appendix; the appendix proves only Lemmas 2–4 for Observations 2–4. Moreover, an upper bound of O(P(|V|+|E|)) does not itself establish unboundedness with respect to CHANGED under Definition 3: the algorithm could still have cost polynomial in |CHANGED| in the cases that matter. To make the motivating 'unbounded work' claim rigorous, the authors need either witness updates where the actual work is Ω(c(|CHANGED|)) for an unbounded function c, or a per-algorithm affected-region analysis proving that the cost is not polynomially bounded in |CHANGED| for some family of updates. As it stands, the comparison with prior work is not proved.
  4. [§6.2, Figure 14 and §6.3, Figures 18–19] The empirical support for Observation 5 and for the complexity claim is thinner than the text suggests. Figure 14 reports an aggregate 'almost 1' proportion of γ-dense communities for all algorithms, but this does not specifically validate HIT-Leiden's conditional pruning rule, and no error bars or run-to-run variance are given even though the text notes that ST-Leiden modularity fluctuates by about 0.02 due to randomness. The speedup claim varies between 'up to three orders of magnitude' (Figure 16) and 'up to five orders' (Figure 18 and Abstract), and the main comparative experiment uses only 9 update batches with the first two excluded. The 999-batch long-term experiment is on one dataset only. I would like to see repeated runs/confidence intervals, and a batch-by-batch or update-type breakdown of γ-density failures for HIT-Leiden, since the theoretical claim depends on the failure ra
minor comments (6)
  1. [Alg. 4, line 6] The inner loop is written 'for v_j ∈ N(v_j)', which must be 'for v_j ∈ N(v_i)'.
  2. [Alg. 6, Output and signature] The output list contains '{f^P(·)}' twice; one of these should presumably be '{s^P_cur(·)}' or '{s^P_pre(·)}'.
  3. [Alg. 5, line 7] The notation s^{-p}(·) is used for the inverse of s^p(·) but is not defined in Table 1 or in the text; please define it explicitly.
  4. [Table 2] The HIT-Leiden row lists 'Relative boundedness ✓' but no derivation is provided; given the circularity concern in §5.4, this checkmark should be qualified or accompanied by the missing proof.
  5. [Figure 14 and Figure 21(b)] The y-axis label '% community' should state that this is the percentage of subpartition γ-dense communities; also the caption for Figure 21(b) is missing.
  6. [Throughout] The text uses 'superparameter' in Section 3.1; the standard term is 'hyperparameter' or 'resolution parameter'.

Circularity Check

0 steps flagged

No significant circularity: the main complexity and quality claims depend on an explicit empirical heuristic (Observation 5), not on a self-referential derivation.

full rationale

No significant circularity is present. The central complexity claim O(|N2(CHANGED)|+|N2(AFF)|) is stated in Section 5.4 and rests on the pruning validity of Observations 1-5, but it is not a definitional identity. In Algorithm 2, the initial affected set A is seeded from the endpoints in ΔG (essentially CHANGED) and expands only through neighbors of vertices that actually change community (the set B, which is contained in AFF); Algorithms 3 and 4 process split connected components and changed sub-community memberships (also AFF); Algorithm 5 processes B and R level by level. Thus the stated bound is a structural consequence of the algorithm's loop structure conditional on the observations. The genuinely load-bearing premise is Observation 5 (Section 4.2): that treating each connected component of a sub-community as a new sub-community leaves most maintained communities subpartition γ-dense, so intra-sub-community edge deletions that break γ-connectivity without disconnecting a component can be ignored. This is an unproven empirical heuristic, and if it fails the quality guarantee and the AFF bound would both degrade; that is a correctness/complexity risk, not circularity. The support cited for Observation 5 (Figure 14 and Section 6.2) is an empirical check on HIT-Leiden's outputs, not a reduction of the conclusion to the premise. Self-citations ([1], and related work by Y. Fang et al. [47,78,99]) are not load-bearing: the proofs for Lemma 1 and Observations 2-4 are included in the appendix, and related-work citations do not support the central derivation. External comparisons against ST-Leiden and the [65] methods give the empirical claims independent content. No step equates an output to an input by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 0 invented entities

The paper introduces no new physical or conceptual entities; the maintained hierarchy and CC-index are algorithmic structures composed from existing techniques. The real axiomatic load is carried by Observations 5 and 6, which are empirical/asserted rather than proven, plus Assumption 1 about update sizes.

free parameters (2)
  • γ (resolution parameter) = 1
    Set to 1 by default; controls community granularity per [62]. Chosen by hand, not fitted to the evaluation data.
  • P (number of Leiden iterations) = 10
    Iteration cap set to 10; affects hierarchical depth and runtime. Chosen by hand, not tuned per dataset.
axioms (6)
  • domain assumption Assumption 1: the sum of weights of updated edges is sufficiently small relative to total edge weight m.
    Used in §4.2 to derive Observations 2–4 and to justify ignoring many update cases. Fails for large batches or dense local changes.
  • domain assumption Observation 1 [64]: intra-community edge deletions and inter-community edge insertions affect community memberships; other edge changes can be ignored.
    Borrowed from prior Louvain maintenance work [64,93] and used to seed inc-movement; the paper does not prove it for Leiden.
  • ad hoc to paper Observation 5: most maintained communities are subpartition γ-dense when connected components are treated as new sub-communities.
    Empirically validated only on the paper's datasets; load-bearing for inc-refinement and for the claimed relative boundedness. Without it, the affected region may not stay local.
  • ad hoc to paper Observation 6: in refinement, vertices merge into sub-communities with larger edge weight and smaller degree, making the threshold conditions in Lemmas 2–4 unlikely to hold.
    Asserted without proof in Appendix A and used to ignore most removal cases in Lemmas 2–4. Not a theorem; restricts inc-refinement to connected-component splits.
  • standard math Leiden outputs satisfy vertex optimality and subpartition γ-density when s^P(·)=f^P(·).
    Known from [9,75]; serves as the maintenance target but is not re-derived here.
  • domain assumption A CC-index such as DND-Tree [86] supports dynamic connectivity updates and queries with the stated h_p cost.
    HIT-Leiden relies on this external data structure; no proof or implementation artifact is provided.

pith-pipeline@v1.3.0-alltime-deepseek · 32119 in / 10197 out tokens · 97816 ms · 2026-08-03T10:48:00.332446+00:00 · methodology

0 comments
read the original abstract

Community detection is a foundational capability in large-scale industrial graph analytics, powering applications such as fraud-ring discovery, recommendation systems, and hierarchical indexing for retrieval-augmented generation. Among modularity-based methods, the Leiden algorithm has been widely adopted in production because it delivers high-quality communities with connectivity guarantees. However, real-world graphs evolve continuously, and timely community updates are needed to keep downstream features and retrieval indices fresh. Meanwhile, existing dynamic Leiden approaches recompute the communities whenever their vertices and edges change, thereby almost degrading to near-full recomputation under frequent updates. To alleviate the efficiency issue, we study the efficient maintenance of Leiden communities in large dynamic graphs and present a novel algorithm, called Hierarchical Incremental Tree Leiden (HIT-Leiden). We first provide a boundedness analysis showing that prior incremental Leiden methods can incur essentially unbounded work even for small updates. Guided by this analysis, we propose HIT-Leiden which effectively reduces the range of affected vertices by maintaining connected components and hierarchical community structures. Extensive experiments on large real-world dynamic graphs demonstrate that HIT-Leiden achieves community quality comparable to the state-of-the-art competitors while delivering speedups of up to five orders of magnitude over existing solutions. The production deployment results show that HIT-Leiden meets stringent latency requirements under high-rate updates at scale.

Figures

Figures reproduced from arXiv: 2601.08554 by Cheng Chen, Chunxu Lin, Yingqian Hu, Yixiang Fang, Yongmin Hu, Yumao Xie.

Figure 1
Figure 1. Figure 1: Illustrating the Louvain and Leiden algorithms. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An example of the movement and refinement [PITH_FULL_IMAGE:figures/full_fig_p001_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustrating community maintenance, where ( [PITH_FULL_IMAGE:figures/full_fig_p002_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: Algorithms for maintaining Leiden communities. [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The process of Leiden for the graph 𝐺 in [PITH_FULL_IMAGE:figures/full_fig_p003_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The process of hierarchical partitions in Figure 5 at level 1 under the Leiden algorithm. [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: An example illustrating subpartition 𝛾-density. Lemma 1. When a vertex 𝑣 changes its community to 𝐶, then the community memberships of its neighbors not in 𝐶 in the updated graph could be affected. Proof. For lack of space, the proof of the lemma is given in the appendix of the full version [1] of this paper. □ Based on these analyses, we develop a novel movement phase, called inc-movement in HIT-Leiden to… view at source ↗
Figure 8
Figure 8. Figure 8: An example of HIT-Leiden. 𝑣!" " 𝑣!# " 𝑣! ! 𝑣$ ! 𝑣% ! 𝑣& ! 𝑣' ! 𝑣( ! 𝑣# ! 𝑣" ! 𝑣) $ 𝑣!! $ 𝑣!$ $ 𝑣!* $ (a) Before maintenance. 𝑣!" " 𝑣!# " 𝑣! ! 𝑣$ ! 𝑣% ! 𝑣& ! 𝑣' ! 𝑣( ! 𝑣# ! 𝑣" ! 𝑣) $ 𝑣!! $ 𝑣!$ $ 𝑣!% $ (b) After maintenance [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: The design rationale for inc-movement and inc-refinement. In this section, we propose HIT-Leiden, which updates commu￾nity memberships by restricting computation to the affected region, motivated by the analysis in Section 4.2. We first introduce the [PITH_FULL_IMAGE:figures/full_fig_p006_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Illustrating the process that a sub-community [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Modularity values on dynamic graphs. ST-Leiden ND-Leiden DS-Leiden DF-Leiden HIT-Leiden 0 1 2 3 4 5 6 7 8 9 0.74 0.75 0.76 0.77 0.78 batch Modularity (a) DC 0 1 2 3 4 5 6 7 8 9 0.360 0.365 0.370 batch (b) YS 0 1 2 3 4 5 6 7 8 9 0.445 0.450 0.455 batch (c) SS 0 1 2 3 4 5 6 7 8 9 0.971 0.972 0.973 batch (d) IT 0 1 2 3 4 5 6 7 8 9 0.355 0.360 0.365 batch (e) RS [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Modularity changes w.r.t. the number of update batches. [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Percentage of subpartition 𝛾-dense communities. 𝛾-dense communities for their returned communities. We also eval￾uate the long-term effectiveness of community maintenance. • Modularity [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The effectiveness and efficiency of HIT-Leiden [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Efficiency of all Leiden algorithms on all datasets. [PITH_FULL_IMAGE:figures/full_fig_p011_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Proportion of time cost of each component for the Leiden algorithms on all datasets. [PITH_FULL_IMAGE:figures/full_fig_p012_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Runtime on dynamic graphs. ST-Leiden ND-Leiden DS-Leiden DF-Leiden HIT-Leiden 0 1 2 3 4 5 6 7 8 9 102 103 104 105 batch Runtime (ms) (a) DC 0 1 2 3 4 5 6 7 8 9 103 105 107 batch (b) YS 0 1 2 3 4 5 6 7 8 9 101 103 105 107 batch (c) SS 0 1 2 3 4 5 6 7 8 9 101 103 105 107 batch (d) IT 0 1 2 3 4 5 6 7 8 9 104 105 106 107 108 batch (e) RS [PITH_FULL_IMAGE:figures/full_fig_p012_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Runtime w.r.t. the number of update batches. [PITH_FULL_IMAGE:figures/full_fig_p012_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: Compare ST-Leiden-RAG and HIT-Leiden-RAG over 9 update batches on Graph-RAG. ST-Leiden HIT-Leiden 0 9 18 26 104 105 106 batch Runtime (ms) (a) Runtime 0 9 18 26 0.36 0.39 0.42 batch Recall (b) Recall [PITH_FULL_IMAGE:figures/full_fig_p012_21.png] view at source ↗
Figure 23
Figure 23. Figure 23: Modularity values w.r.t. 𝛾. ST-Leiden ND-Leiden DS-Leiden DF-Leiden HIT-Leiden 0.5 2 8 32 102 103 104 105 𝛾 Runtime (ms) (a) DC 0.5 2 8 32 103 105 107 𝛾 (b) YS 0.5 2 8 32 101 103 105 107 𝛾 (c) SS 0.5 2 8 32 101 103 105 107 𝛾 (d) IT 0.5 2 8 32 104 105 106 107 108 𝛾 (e) RS [PITH_FULL_IMAGE:figures/full_fig_p017_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Runtime w.r.t. 𝛾. DC YS SS IT RS 10 104 107 1010 |AFF| ST-Leiden ND-Leiden DS-Leiden DF-Leiden HIT-Leiden [PITH_FULL_IMAGE:figures/full_fig_p017_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Effect of |AFF| on all datasets. B.4 Proof of Lemma 4 Proof. First, we analyze the insertion of intra-sub-community edges. We adopt the same notations as in the proof of Lemma 2. Based on this setup, the modularity gain after the edge insertion is shown as follows. Case 1: Consider the endpoint 𝑣𝑖 , which is the latter merged endpoint: Δ𝑀𝑛𝑒𝑤 (𝑣𝑖 → ∅,𝛾) = − 𝑤(𝑣𝑖 ,𝑈𝑖) + 2𝛼 2(𝑚 + 𝛼) + 𝛾 · (𝑑 (𝑣𝑖) + 𝛼) · (𝑑 (… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

108 extracted references · 7 linked inside Pith

  1. [1]

    Efficient Maintenance of Leiden Communities in Large Dynamic Graphs (full version)

    2026. Efficient Maintenance of Leiden Communities in Large Dynamic Graphs (full version). https://github.com/swordzlim/HIT-Leiden

    2026

  2. [2]

    Edo M Airoldi, David Blei, Stephen Fienberg, and Eric Xing. 2008. Mixed membership stochastic blockmodels.Advances in neural information processing systems21 (2008)

    2008

  3. [3]

    Arash A Amini, Aiyou Chen, Peter J Bickel, and Elizaveta Levina. 2013. Pseudo- likelihood methods for community detection in large sparse networks. (2013)

    2013

  4. [4]

    Abdelouahab Amira, Abdelouahid Derhab, Elmouatez Billah Karbab, and Omar Nouali. 2023. A survey of malware analysis using community detection algo- rithms.Comput. Surveys56, 2 (2023), 1–29

    2023

  5. [5]

    LN Fred Ana and Anil K Jain. 2003. Robust data clustering. In2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Maintaining Leiden Communities in Large Dynamic Graphs Proceedings., Vol. 2. IEEE, II–II

    2003

  6. [6]

    Thomas Aynaud and Jean-Loup Guillaume. 2010. Static community detection algorithms for evolving networks. In8th international symposium on modeling and optimization in mobile, ad hoc, and wireless networks. IEEE, 513–519

    2010

  7. [7]

    Thomas Aynaud and Jean-Loup Guillaume. 2011. Multi-step community detec- tion and hierarchical time segmentation in evolving networks. InProceedings of the 5th SNA-KDD workshop, Vol. 11

    2011

  8. [8]

    Vandana Bhatia and Rinkle Rani. 2018. Dfuzzy: a deep learning-based fuzzy clustering model for large graphs.Knowledge and Information Systems57 (2018), 159–181

    2018

  9. [9]

    Vincent D Blondel, Jean-Loup Guillaume, Renaud Lambiotte, and Etienne Lefeb- vre. 2008. Fast unfolding of communities in large networks.Journal of statistical mechanics: theory and experiment2008, 10 (2008), P10008

    2008

  10. [10]

    Stefan Boettcher and Allon G Percus. 2002. Optimization with extremal dynam- ics.complexity8, 2 (2002), 57–62

    2002

  11. [11]

    Biao Cai, Yanpeng Wang, Lina Zeng, Yanmei Hu, and Hongjun Li. 2020. Edge classification based on convolutional neural networks for community detection in complex network.Physica A: statistical mechanics and its applications556 (2020), 124826

    2020

  12. [12]

    Jiangxia Cao, Jiawei Sheng, Xin Cong, Tingwen Liu, and Bin Wang. 2022. Cross- domain recommendation to cold-start users via variational information bot- tleneck. In2022 IEEE 38th International Conference on data engineering (ICDE). IEEE, 2209–2223

    2022

  13. [13]

    Tanmoy Chakraborty, Ayushi Dalmia, Animesh Mukherjee, and Niloy Ganguly

  14. [14]

    Qing Chen, Sven Helmer, Oded Lachish, and Michael Bohlen. 2022. Dynamic spanning trees for connectivity queries on fully-dynamic undirected graphs. (2022)

    2022

  15. [15]

    Jiafeng Cheng, Qianqian Wang, Zhiqiang Tao, Deyan Xie, and Quanxue Gao

  16. [16]

    Yun Chi, Xiaodan Song, Dengyong Zhou, Koji Hino, and Belle L Tseng. 2007. Evolutionary spectral clustering by incorporating temporal smoothness. In Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining. 153–162

    2007

  17. [17]

    Yun Chi, Xiaodan Song, Dengyong Zhou, Koji Hino, and Belle L Tseng. 2009. On evolutionary spectral clustering.ACM Transactions on Knowledge Discovery from Data (TKDD)3, 4 (2009), 1–30

    2009

  18. [18]

    Wen Haw Chong and Loo Nin Teow. 2013. An incremental batch technique for community detection. InProceedings of the 16th international conference on information fusion. IEEE, 750–757

    2013

  19. [19]

    Aaron Clauset, Mark EJ Newman, and Cristopher Moore. 2004. Finding commu- nity structure in very large networks.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics70, 6 (2004), 066111

    2004

  20. [20]

    Mário Cordeiro, Rui Portocarrero Sarmento, and Joao Gama. 2016. Dynamic community detection in evolving networks using locality modularity optimiza- tion.Social Network Analysis and Mining6 (2016), 1–20

    2016

  21. [21]

    Ganqu Cui, Jie Zhou, Cheng Yang, and Zhiyuan Liu. 2020. Adaptive graph encoder for attributed graph embedding. InProceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining. 976–985

    2020

  22. [22]

    Siemon C de Lange, Marcel A de Reus, and Martijn P van den Heuvel. 2014. The Laplacian spectrum of neural networks.Frontiers in computational neuroscience 7 (2014), 189

    2014

  23. [23]

    Martin Ester, Hans-Peter Kriegel, Jörg Sander, Xiaowei Xu, et al. 1996. A density- based algorithm for discovering clusters in large spatial databases with noise. Inkdd, Vol. 96. 226–231

    1996

  24. [24]

    Shaohua Fan, Xiao Wang, Chuan Shi, Emiao Lu, Ken Lin, and Bai Wang. 2020. One2multi graph autoencoder for multi-view graph clustering. Inproceedings of the web conference 2020. 3070–3076

    2020

  25. [25]

    Wenfei Fan, Chunming Hu, and Chao Tian. 2017. Incremental graph compu- tations: Doable and undoable. InProceedings of the 2017 ACM International Conference on Management of Data. 155–169

    2017

  26. [26]

    Xinyu Fu, Jiani Zhang, Ziqiao Meng, and Irwin King. 2020. Magnn: Metapath aggregated graph neural network for heterogeneous graph embedding. In Proceedings of the web conference 2020. 2331–2341

    2020

  27. [27]

    László Gadár and János Abonyi. 2024. Explainable prediction of node labels in multilayer networks: a case study of turnover prediction in organizations. Scientific Reports14, 1 (2024), 9036

    2024

  28. [28]

    Paul W Holland, Kathryn Blackmond Laskey, and Samuel Leinhardt. 1983. Stochastic blockmodels: First steps.Social networks5, 2 (1983), 109–137

    1983

  29. [29]

    Jacob Holm, Kristian De Lichtenberg, and Mikkel Thorup. 2001. Poly- logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity.Journal of the ACM (JACM)48, 4 (2001), 723–760

    2001

  30. [30]

    Ruiqi Hu, Shirui Pan, Guodong Long, Qinghua Lu, Liming Zhu, and Jing Jiang

  31. [31]

    Xiao Huang, Jundong Li, and Xia Hu. 2017. Accelerated attributed network embedding. InProceedings of the 2017 SIAM international conference on data mining. SIAM, 633–641

    2017

  32. [32]

    Yuting Jia, Qinqin Zhang, Weinan Zhang, and Xinbing Wang. 2019. Commu- nitygan: Community detection with generative adversarial nets. InThe world wide web conference. 784–794

    2019

  33. [33]

    Baoyu Jing, Chanyoung Park, and Hanghang Tong. 2021. Hdmi: High-order deep multiplex infomax. InProceedings of the web conference 2021. 2414–2424

    2021

  34. [34]

    Ravi Kannan, Santosh Vempala, and Adrian Vetta. 2004. On clusterings: Good, bad and spectral.Journal of the ACM (JACM)51, 3 (2004), 497–515

    2004

  35. [35]

    Brian Karrer and Mark EJ Newman. 2011. Stochastic blockmodels and commu- nity structure in networks.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics83, 1 (2011), 016107

    2011

  36. [36]

    Scott Kirkpatrick, C Daniel Gelatt Jr, and Mario P Vecchi. 1983. Optimization by simulated annealing.science220, 4598 (1983), 671–680

    1983

  37. [37]

    Sadamori Kojaku, Giacomo Livan, and Naoki Masuda. 2021. Detecting anoma- lous citation groups in journal networks.Scientific Reports11, 1 (2021), 14524

    2021

  38. [38]

    Andrea Lancichinetti and Santo Fortunato. 2009. Community detection algo- rithms: a comparative analysis.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics80, 5 (2009), 056117

    2009

  39. [39]

    Ron Levie, Federico Monti, Xavier Bresson, and Michael M Bronstein. 2018. Cay- leynets: Graph convolutional neural networks with complex rational spectral filters.IEEE Transactions on Signal Processing67, 1 (2018), 97–109

    2018

  40. [40]

    Bentian Li, Dechang Pi, Yunxia Lin, and Lin Cui. 2021. DNC: A deep neural network-based clustering-oriented network embedding algorithm.Journal of Network and Computer Applications173 (2021), 102854

    2021

  41. [41]

    Zhangtao Li and Jing Liu. 2016. A multi-agent genetic algorithm for commu- nity detection in complex networks.Physica A: Statistical Mechanics and its Applications449 (2016), 336–347

    2016

  42. [42]

    Xujian Liang and Zhaoquan Gu. 2025. Fast think-on-graph: Wider, deeper and faster reasoning of large language model on knowledge graph. InProceedings of the AAAI Conference on Artificial Intelligence, Vol. 39. 24558–24566

    2025

  43. [43]

    Yu-Ru Lin, Yun Chi, Shenghuo Zhu, Hari Sundaram, and Belle L Tseng. 2008. Facetnet: a framework for analyzing communities and their evolutions in dy- namic networks. InProceedings of the 17th international conference on World Wide Web. 685–694

    2008

  44. [44]

    Fanzhen Liu, Zhao Li, Baokun Wang, Jia Wu, Jian Yang, Jiaming Huang, Yiqing Zhang, Weiqiang Wang, Shan Xue, Surya Nepal, et al . 2022. eRiskCom: an e-commerce risky community detection platform.The VLDB Journal31, 5 (2022), 1085–1101

    2022

  45. [45]

    Fanzhen Liu, Jia Wu, Chuan Zhou, and Jian Yang. 2019. Evolutionary community detection in dynamic social networks. In2019 International Joint Conference on Neural Networks (IJCNN). IEEE, 1–7

    2019

  46. [46]

    Yanbei Liu, Xiao Wang, Shu Wu, and Zhitao Xiao. 2020. Independence promoted graph disentangled networks. InProceedings of the AAAI Conference on Artificial Intelligence, Vol. 34. 4916–4923

    2020

  47. [47]

    Linhao Luo, Yixiang Fang, Xin Cao, Xiaofeng Zhang, and Wenjie Zhang. 2021. Detecting communities from heterogeneous graphs: A context path-based graph neural network model. InProceedings of the 30th ACM international conference on information & knowledge management. 1170–1180

    2021

  48. [48]

    Aaron F McDaid, Derek Greene, and Neil Hurley. 2011. Normalized mutual information to evaluate overlapping community finding algorithms.arXiv preprint arXiv:1110.2515(2011)

    Pith/arXiv arXiv 2011

  49. [49]

    Xiangfeng Meng, Yunhai Tong, Xinhai Liu, Shuai Zhao, Xianglin Yang, and Shaohua Tan. 2016. A novel dynamic community detection algorithm based on modularity optimization. In2016 7th IEEE international conference on software engineering and service science (ICSESS). IEEE, 72–75

    2016

  50. [50]

    Microsoft. 2025. GraphRAG: A Structured, Hierarchical Approach to Retrieval Augmented Generation. https://microsoft.github.io/graphrag/. Accessed: 2026- 02-17

    2025

  51. [51]

    Jennifer Neumann and Peter M Fischer. [n.d.]. Shape-Aware, Scale-Agnostic Representation of Dynamic DAGs.Proceedings of the VLDB Endowment. ISSN 2150 ([n. d.]), 8097

  52. [52]

    Mark EJ Newman. 2004. Fast algorithm for detecting community structure in networks.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics69, 6 (2004), 066133

    2004

  53. [53]

    Mark EJ Newman. 2006. Finding community structure in networks using the eigenvectors of matrices.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics74, 3 (2006), 036104

    2006

  54. [54]

    Mark EJ Newman. 2006. Modularity and community structure in networks. Proceedings of the national academy of sciences103, 23 (2006), 8577–8582

    2006

  55. [55]

    Mark EJ Newman. 2013. Spectral methods for community detection and graph partitioning.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 88, 4 (2013), 042822

    2013

  56. [56]

    Nam P Nguyen, Thang N Dinh, Sindhura Tokala, and My T Thai. 2011. Overlap- ping communities in dynamic networks: their detection and mobile applications. InProceedings of the 17th annual international conference on Mobile computing and networking. 85–96

    2011

  57. [57]

    Nam P Nguyen, Thang N Dinh, Ying Xuan, and My T Thai. 2011. Adaptive algorithms for detecting community structure in dynamic social networks. In Chunxu Lin, Yumao Xie, Yixiang Fang, Yongmin Hu, Yingqian Hu, and Cheng Chen 2011 Proceedings IEEE INFOCOM. IEEE, 2282–2290

    2011

  58. [58]

    Alexandru Oarga, Matthew Hart, Andres M Bran, Magdalena Lederbauer, and Philippe Schwaller. 2024. Scientific knowledge graph and ontology generation using open large language models. InAI for Accelerated Materials Design-NeurIPS 2024

    2024

  59. [59]

    Shashank Pandit, Duen Horng Chau, Samuel Wang, and Christos Faloutsos

  60. [60]

    Songtao Peng, Jiaqi Nie, Xincheng Shu, Zhongyuan Ruan, Lei Wang, Yunxuan Sheng, and Qi Xuan. 2022. A multi-view framework for BGP anomaly detection via graph attention network.Computer Networks214 (2022), 109129

    2022

  61. [61]

    Ganesan Ramalingam and Thomas Reps. 1996. On the computational complexity of dynamic graph problems.Theoretical Computer Science158, 1-2 (1996), 233– 277

    1996

  62. [62]

    Jörg Reichardt and Stefan Bornholdt. 2006. Statistical mechanics of community detection.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics74, 1 (2006), 016110

    2006

  63. [63]

    Boyu Ruan, Junhao Gan, Hao Wu, and Anthony Wirth. 2021. Dynamic structural clustering on graphs. InProceedings of the 2021 International Conference on Management of Data. 1491–1503

    2021

  64. [64]

    Subhajit Sahu. 2024. DF Louvain: Fast Incrementally Expanding Approach for Community Detection on Dynamic Graphs.arXiv preprint arXiv:2404.19634 (2024)

    Pith/arXiv arXiv 2024

  65. [65]

    Subhajit Sahu. 2024. A Starting Point for Dynamic Community Detection with Leiden Algorithm.arXiv preprint arXiv:2405.11658(2024)

    Pith/arXiv arXiv 2024

  66. [66]

    Subhajit Sahu, Kishore Kothapalli, and Dip Sankar Banerjee. 2024. Fast Leiden Algorithm for Community Detection in Shared Memory Setting. InProceedings of the 53rd International Conference on Parallel Processing. 11–20

    2024

  67. [67]

    Arindam Sarkar, Nikhil Mehta, and Piyush Rai. 2020. Graph representation learning via ladder gamma variational autoencoders. InProceedings of the AAAI Conference on Artificial Intelligence, Vol. 34. 5604–5611

    2020

  68. [68]

    Jiaxing Shang, Lianchen Liu, Xin Li, Feng Xie, and Cheng Wu. 2016. Targeted revision: A learning-based approach for incremental community detection in dynamic networks.Physica A: Statistical Mechanics and its Applications443 (2016), 70–85

    2016

  69. [69]

    Jiaxing Shang, Lianchen Liu, Feng Xie, Zhen Chen, Jiajia Miao, Xuelin Fang, and Cheng Wu. 2014. A real-time detecting algorithm for tracking community structure of dynamic networks.arXiv preprint arXiv:1407.2683(2014)

    Pith/arXiv arXiv 2014

  70. [70]

    Oleksandr Shchur and Stephan Günnemann. 2019. Overlapping community detection with graph neural networks.arXiv preprint arXiv:1909.12201(2019)

    Pith/arXiv arXiv 2019

  71. [71]

    Stanislav Sobolevsky, Riccardo Campari, Alexander Belyi, and Carlo Ratti. 2014. General optimization technique for high-quality community detection in com- plex networks.Physical Review E90, 1 (2014), 012811

    2014

  72. [72]

    Xing Su, Shan Xue, Fanzhen Liu, Jia Wu, Jian Yang, Chuan Zhou, Wenbin Hu, Cecile Paris, Surya Nepal, Di Jin, et al. 2022. A comprehensive survey on community detection with deep learning.IEEE transactions on neural networks and learning systems35, 4 (2022), 4682–4702

    2022

  73. [73]

    Wenwen Sun, Zhicheng Pan, Zirui Hu, Yu Liu, Chengcheng Yang, Rong Zhang, and Xuan Zhou. 2025. Rabbit: Retrieval-augmented generation enables better automatic database knob tuning. In2025 IEEE 41st International Conference on Data Engineering (ICDE). IEEE, 3807–3820

    2025

  74. [74]

    2019.Tencent Graph Computing (TGraph) Officially Open Sourced High-Performance Graph Computing Framework: Plato

    Tencent. 2019.Tencent Graph Computing (TGraph) Officially Open Sourced High-Performance Graph Computing Framework: Plato. Accessed: 2026-02-17

    2019

  75. [75]

    Vincent A Traag, Ludo Waltman, and Nees Jan Van Eck. 2019. From Louvain to Leiden: guaranteeing well-connected communities.Scientific reports9, 1 (2019), 1–12

    2019

  76. [76]

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention is all you need.Advances in neural information processing systems30 (2017)

    2017

  77. [77]

    Lewen Wang, Haozhe Zhao, Cunguang Feng, Weiqing Liu, Congrui Huang, Marco Santoni, Manuel Cristofaro, Paola Jafrancesco, and Jiang Bian. 2023. Removing camouflage and revealing collusion: Leveraging gang-crime pattern in fraudster detection. InProceedings of the 29th ACM SIGKDD conference on knowledge discovery and data mining. 5104–5115

    2023

  78. [78]

    Shu Wang, Yixiang Fang, and Wensheng Luo. 2025. Searching and Detect- ing Structurally Similar Communities in Large Heterogeneous Information Networks.Proceedings of the VLDB Endowment18, 5 (2025), 1425–1438

    2025

  79. [79]

    Xiao Wang, Nian Liu, Hui Han, and Chuan Shi. 2021. Self-supervised hetero- geneous graph neural network with co-contrastive learning. InProceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining. 1726–1736

    2021

  80. [80]

    Wei Xia, Qianqian Wang, Quanxue Gao, Xiangdong Zhang, and Xinbo Gao

Showing first 80 references.