pith. sign in

arxiv: 2606.29651 · v1 · pith:UURLCDTXnew · submitted 2026-06-28 · 💻 cs.DC

NI-ORCA: A Parallel Algorithm for Counting the Orbits of Non-Induced Graphlets up to K4

Syed Ibtisam Tauhidi , Arindam Karmakar , Thai Son Mai , Hans Vandierendonck This is my paper

Pith reviewed 2026-06-30 07:27 UTC · model grok-4.3

classification 💻 cs.DC
keywords non-induced graphletsorbit countingparallel graph algorithmstriangle counting4-clique enumerationgraph analyticslinear system reformulation
0
0 comments X

The pith

NI-ORCA extends the ORCA framework with a reformulated linear system to count non-induced graphlet orbits up to size four in parallel.

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

The paper presents NI-ORCA as a parallel algorithm that computes exact orbits of non-induced graphlets up to four vertices. It builds on the ORCA framework by reformulating the linear equations that relate orbit counts, then splits the work into triangle counting, 4-clique enumeration, and orbit solving stages. Each stage receives its own parallelization using thread-local and vertex-local data structures to reduce contention and balance load. Tests on eight real-world networks and synthetic graphs show that dynamic scheduling with small chunks yields consistent speedups. The central result is that these changes deliver up to 30 times faster execution than existing sequential methods while preserving exact counts.

Core claim

NI-ORCA computes the orbits of non-induced graphlets up to K4 by first counting triangles and enumerating 4-cliques in parallel, then solving a reformulated system of linear equations that maps those counts to the desired non-induced orbit values; stage-specific thread and vertex-local memory models together with dynamic scheduling produce the reported speedups.

What carries the argument

Reformulated linear system that converts triangle and 4-clique counts into exact non-induced orbit counts, executed after parallel enumeration stages.

If this is right

  • Exact non-induced orbit counts become feasible at larger scales than sequential methods allow.
  • A combination of stage-specific data structures and dynamic scheduling with small chunks balances workload across threads on both real and random graphs.
  • The three-stage pipeline separates enumeration from linear solving so that each part can be tuned independently for parallelism.
  • Performance gains hold across eight real-world datasets and a range of Erdos-Renyi graphs.

Where Pith is reading between the lines

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

  • The same reformulation technique might allow non-induced counting for larger k if the linear dependencies can be derived without loss of exactness.
  • Stage-specific parallel strategies could transfer to other graphlet or motif enumeration problems that already use linear relations among counts.
  • Faster non-induced orbit counting would let downstream tasks such as role detection in networks run on bigger inputs without switching to approximate methods.

Load-bearing premise

The reformulation of the linear system for non-induced orbits preserves exactness without introducing counting errors or requiring additional post-processing corrections.

What would settle it

Execute NI-ORCA and an independent exact sequential non-induced orbit counter on the same small graph with known orbit values; any mismatch in the reported counts would falsify the claim of preserved exactness.

Figures

Figures reproduced from arXiv: 2606.29651 by Arindam Karmakar, Hans Vandierendonck, Syed Ibtisam Tauhidi, Thai Son Mai.

Figure 1
Figure 1. Figure 1: Seventeen graphlets formed using up to four vertices - The nine connected graphlets are considered for further orbit definitions. Definition 2 (Induced Graphlet) Given graph G, an induced graphlet G′ = (V ′ , E′ ) is a connected subgraph of G formed by a subset of nodes V ′ ⊆ V along with all edges in E that exist between nodes in G. Formally — E ′ = {(u, v) ∈ E | {u, v} ∈ V ′ }. (1) Definition 3 (Non-Indu… view at source ↗
Figure 2
Figure 2. Figure 2: Fifteen orbits formed using the nine connected graphlets - The colours in the vertices indicate their orbit roles within the graphlet, i.e., vertices with the same colour belong to the same orbit group. The seventeen graphlets — including both connected and disconnected graphlets — that can be formed using up to four vertices are shown in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Structures around x ∈ V to compute the f∗ internal variables in Stage III then the four vertices—the original two plus the connected pair from their shared neighbours—form a 4-clique. In such a case, the count of K4 is incremented for each of the four involved vertices. Algorithm 1: Stage II - Counting K4 Input: Vertex x ∈ V , array K4 Function CountK4(x, K4 ): neigh = []; for all y ∈ neighbour(x) ∧ (y.id … view at source ↗
Figure 4
Figure 4. Figure 4: Breakdown of the runtime of the three stages of the sequential ni-ORCA algorithm While the study primarily focuses on real-world datasets, for analysis of runtime characteristic changes with the changing density of the graphs, an Erdos–R ˝ enyi random graph generator was used to generate multiple random graphs ´ using NetworkX [30]. The random graphs can be categorised into two classes: (i) SPARSE (with |V… view at source ↗
Figure 5
Figure 5. Figure 5: Speedup using 32 and 64 threads of NI-ORCA compared to various baseline algorithms - JESSE completed execution successfully on only three datasets - CORA did not complete execution on any dataset within the threshold - EVOKE showed the best performance among all the sequential algorithms [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Effect of parallelisation on Stage I - The dashed line corresponds to the runtime of the sequential algorithm. 8.1 Stage-wise Runtime Profile of NI-ORCA The effect of parallelisation on the speedup of Stage I is shown in [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effect of parallelisation on Stage II — The dashed line (at y = 1) corresponds to the runtime of the sequential algorithm. the best performance, achieving the highest speedup across most of the datasets. While ARR (V) occasionally shows comparable performance, it shows the worst performance in datasets like DBLP and PATENTS. The UOM mode, on the other hand, consistently exhibits the worst performance overa… view at source ↗
Figure 8
Figure 8. Figure 8: Effect of parallelisation on Stage III on EPYC platform — The dashed line (at y = 1) corresponds to the runtime of the sequential algorithm. to underperform compared to dynamic scheduling. In dynamic scheduling, this is because the chunk sizes in guided scheduling are large initially and only decrease over time, leading to less efficient use of threads for datasets with varying task complexities. Static sc… view at source ↗
Figure 9
Figure 9. Figure 9: Average per thread Total Cycles and Total Instructions performance monitoring counters profiled using PAPI - Figures in brackets indicate Cycles Per Instruction. Plots on the left are evaluated on the EPYC platform and those on the right on the XEON platform. Plots at the top correspond to the HPRD dataset, and those on the bottom correspond to the YEAST dataset. 8.3 Scalability Across Graph Density and Si… view at source ↗
Figure 10
Figure 10. Figure 10: Speedup using different scheduling algorithms using MIXED mode The evaluation also demonstrated the impact of hardware architecture on performance. NI-ORCA showed significant speedup on multi-socket systems with optimised memory access, such as AMD EPYC and Intel XEON platforms, by effectively balancing workloads across NUMA nodes. However, it was observed that the performance plateaued at high thread cou… view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of speedup for dynamic scheduling and various chunk sizes on the EPYC platform Appendix (NI-ORCA) The equations for the rest of the orbits are as follows — ψ9(x) = f 14 12 + f 12 9 2 (12) ψ8(x) = f 14 13 + f 12 8 2 (13) ψ7(x) =  ψ0(x) 3  (14) ψ6(x) = f 9 6 − f 14 13 2 + f 13 10 + 2×f 14 12 (15) ψ5(x) = 2×f 14 12 + f 8 5 + f 13 10 + f 13 11 (16) 17 [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Boxplots showing variation of runtime across all the threads Stage II and Stage III when running with multiple thread counts on the EPYC platform ψ4(x) = 2×f 14 12 + f 8 4 + f 13 10 + f 12 9 (17) References [1] Jure Leskovec and Andrej Krevl. SNAP Datasets: Stanford large network dataset collection. http://snap. stanford.edu/data, June 2014. [2] Ryan A. Rossi and Nesreen K. Ahmed. The network data reposit… view at source ↗
Figure 13
Figure 13. Figure 13: Effect of parallelisation on random Erdos–R ˝ enyi graphs ´ [7] Nesreen K Ahmed, Jennifer Neville, Ryan A Rossi, and Nick Duffield. Efficient graphlet counting for large networks. In 2015 IEEE International Conference on Data Mining, pages 1–10. IEEE, 2015. [8] Emanuele Martorana, Roberto Grasso, Giovanni Micale, Salvatore Alaimo, Dennis Shasha, Rosalba Giugno, and Alfredo Pulvirenti. Motif finding algori… view at source ↗
read the original abstract

Counting the orbits of graphlets in a network is a vital tool for understanding the structural roles of vertices in various graph analytics tasks. While existing algorithms efficiently compute orbits of induced graphlets, many real-world applications require non-induced orbit counts. However, no current method offers exact, scalable, and parallel support for non-induced orbit counting. This paper presents NI-ORCA, a parallel algorithm to efficiently compute the orbits of non-induced graphlets up to size four (4-clique). NI-ORCA extends the ORCA framework for non-induced orbit counting by reformulating a system of linear equations. The algorithm consists of three stages: triangle counting, 4-clique enumeration, and orbit solving. We design and implement stage-specific parallelisation strategies using thread and vertex-local memory models and data structures, minimising contention and balancing workload. We further analyse the impact of scheduling policies, chunk sizes, and affinity strategies on performance. Experimental analysis on eight real-world datasets and a series of synthetic Erddos-Renyi graphs demonstrates that a mixed mode combining stage-specific data structure, with dynamic scheduling with small chunk sizes, delivers consistent speedup and effective load balancing. Our results show that NI-ORCA significantly outperforms state-of-the-art sequential algorithms, achieving up to 30x speedups.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims to present NI-ORCA, a parallel algorithm extending the ORCA framework for exact counting of non-induced graphlet orbits up to K4 by reformulating a system of linear equations. It consists of triangle counting, 4-clique enumeration, and orbit solving stages with custom parallelization strategies using thread/vertex-local memory models, and reports up to 30x speedups over sequential methods on eight real-world datasets and Erdős-Rényi graphs, along with analysis of scheduling policies and chunk sizes.

Significance. If the reformulation is shown to preserve exact non-induced counts, the work would be significant for filling the gap in scalable parallel non-induced orbit counting up to K4, a task relevant to graph analytics. The stage-specific parallelization and empirical study of scheduling/affinity strategies would provide practical implementation guidance.

major comments (2)
  1. [Abstract (orbit solving stage)] Abstract (orbit solving stage): The reformulation of the linear system for non-induced orbits is stated as a direct algebraic change extending ORCA, but neither the explicit new matrix nor a proof that it matches the non-induced embedding definition is supplied. This is load-bearing for the correctness of all downstream counts and the 30x speedup claim.
  2. [Abstract (experimental analysis)] Abstract (experimental analysis): No validation of non-induced counts against a ground-truth sequential implementation, no error-bar analysis, and no numerical stability discussion for the linear solver are described, leaving the exactness of the reformulation unverified.
minor comments (1)
  1. The abstract is dense; clearer separation between the algorithmic extension, parallelization details, and performance claims would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback highlighting the need for explicit details on the orbit-solving reformulation and additional experimental validation. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract (orbit solving stage)] The reformulation of the linear system for non-induced orbits is stated as a direct algebraic change extending ORCA, but neither the explicit new matrix nor a proof that it matches the non-induced embedding definition is supplied. This is load-bearing for the correctness of all downstream counts and the 30x speedup claim.

    Authors: We agree that the manuscript does not supply the explicit reformulated matrix or a formal proof of equivalence to the non-induced embedding definition. This omission weakens the presentation of correctness. In the revised version we will include the full new matrix (derived from the original ORCA system by adjusting for non-induced embeddings) together with a step-by-step algebraic derivation showing that the solution vector yields the exact non-induced orbit counts. This addition will directly support the correctness of all reported counts. revision: yes

  2. Referee: [Abstract (experimental analysis)] No validation of non-induced counts against a ground-truth sequential implementation, no error-bar analysis, and no numerical stability discussion for the linear solver are described, leaving the exactness of the reformulation unverified.

    Authors: We acknowledge that the current experimental section lacks direct validation of the non-induced counts against a ground-truth sequential implementation, error-bar reporting, and discussion of numerical stability. In the revision we will add (i) side-by-side comparisons on small graphs against a verified sequential non-induced counter, (ii) confirmation that all counts are exact integers (hence error bars are zero), and (iii) a brief note on the linear solver: because the system is solved over integers with exact arithmetic (no floating-point operations), numerical stability is not a concern. These changes will verify the exactness of the reformulation. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents NI-ORCA as an algorithmic extension of the existing ORCA framework via direct algebraic reformulation of a linear system for non-induced orbits, followed by standard parallelization of three computational stages (triangle counting, 4-clique enumeration, orbit solving). No equations or claims reduce a derived quantity to its own inputs by construction, no parameters are fitted to data and then relabeled as predictions, and the reformulation is not justified by self-citation chains or uniqueness theorems from the same authors. The derivation chain consists of independent algorithmic steps whose correctness is asserted via algebraic change rather than empirical fitting or renaming of known results. This is a self-contained algorithmic description with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

No free parameters, invented entities, or ad-hoc axioms are introduced; the work rests on standard graph-theoretic definitions of cliques, triangles, and linear algebra over orbit counts.

axioms (1)
  • standard math Standard definitions of induced vs. non-induced subgraph embeddings and orbit equivalence under automorphism
    Invoked when the paper states it extends ORCA by reformulating the linear system for non-induced counts.

pith-pipeline@v0.9.1-grok · 5782 in / 1193 out tokens · 39589 ms · 2026-06-30T07:27:00.042151+00:00 · methodology

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

34 extracted references · 4 canonical work pages

  1. [1]

    SNAP Datasets: Stanford large network dataset collection

    Jure Leskovec and Andrej Krevl. SNAP Datasets: Stanford large network dataset collection. http://snap. stanford.edu/data, June 2014

    2014

  2. [2]

    Rossi and Nesreen K

    Ryan A. Rossi and Nesreen K. Ahmed. The network data repository with interactive graph analytics and visualization. InAAAI, 2015

    2015

  3. [3]

    Machine learning-based per-instance algorithm selection for high-performance subgraph isomorphism enumeration

    Syed Ibtisam Tauhidi, Arindam Karmakar, Thai Son Mai, and Hans Vandierendonck. Machine learning-based per-instance algorithm selection for high-performance subgraph isomorphism enumeration. InInternational Conference on Metaheuristics and Nature Inspired Computing, pages 214–229. Springer, 2023

    2023

  4. [4]

    Motif-based graph self-supervised learning for molecular property prediction.Advances in Neural Information Processing Systems, 34:15870–15882, 2021

    Zaixi Zhang, Qi Liu, Hao Wang, Chengqiang Lu, and Chee-Kong Lee. Motif-based graph self-supervised learning for molecular property prediction.Advances in Neural Information Processing Systems, 34:15870–15882, 2021

    2021

  5. [5]

    Motif-driven contrastive learning of graph representations.IEEE Transactions on Knowledge and Data Engineering, 36(8):4063–4075, 2024

    Shichang Zhang, Ziniu Hu, Arjun Subramonian, and Yizhou Sun. Motif-driven contrastive learning of graph representations.IEEE Transactions on Knowledge and Data Engineering, 36(8):4063–4075, 2024

    2024

  6. [6]

    On analyzing graphs with motif-paths.Proceedings of the VLDB Endowment, 14(6), 2021

    Xiaodong Li, Reynold Cheng, Kevin Chen-Chuan Chang, Caihua Shan, Chenhao Ma, and Hongtai Cao. On analyzing graphs with motif-paths.Proceedings of the VLDB Endowment, 14(6), 2021. 18 APREPRINT- JUNE30, 2026 E-08 E-07 E-06 E-05 E-04 E-03 E-02 E-02 E-01 E+00 E+01Runtime (sec) SPARSE | V | 10000 20000 30000 Threads 32 64 96 128 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 1...

    2021

  7. [7]

    Efficient graphlet counting for large networks

    Nesreen K Ahmed, Jennifer Neville, Ryan A Rossi, and Nick Duffield. Efficient graphlet counting for large networks. In2015 IEEE International Conference on Data Mining, pages 1–10. IEEE, 2015

    2015

  8. [8]

    Motif finding algorithms: A performance comparison

    Emanuele Martorana, Roberto Grasso, Giovanni Micale, Salvatore Alaimo, Dennis Shasha, Rosalba Giugno, and Alfredo Pulvirenti. Motif finding algorithms: A performance comparison. InFrom Computational Logic to Computational Biology: Essays Dedicated to Alfredo Ferro to Celebrate His Scientific Career, pages 250–267. Springer, 2024

    2024

  9. [9]

    Investigating statistical analysis for network motifs

    Zican Li and Wooyoung Kim. Investigating statistical analysis for network motifs. InProceedings of the 12th ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics, pages 1–6, 2021

    2021

  10. [10]

    Efficiently counting vertex orbits of all 5-vertex subgraphs, by evoke

    Noujan Pashanasangi and C Seshadhri. Efficiently counting vertex orbits of all 5-vertex subgraphs, by evoke. In Proceedings of the 13th International Conference on Web Search and Data Mining, pages 447–455, 2020

    2020

  11. [11]

    Link prediction based on orbit counting and graph auto-encoder.IEEE Access, 8:226773–226783, 2020

    Jian Feng and Shaojian Chen. Link prediction based on orbit counting and graph auto-encoder.IEEE Access, 8:226773–226783, 2020

    2020

  12. [12]

    Graphlet correlation distance to compare small graphs.Plos one, 18(2):e0281646, 2023

    J´erˆome Roux, Nicolas Bez, Paul Rochet, Roc´ıo Joo, and St´ephanie Mah´evas. Graphlet correlation distance to compare small graphs.Plos one, 18(2):e0281646, 2023

    2023

  13. [13]

    A survey on subgraph counting: concepts, algorithms, and applications to network motifs and graphlets.ACM Computing Surveys (CSUR), 54(2):1–36, 2021

    Pedro Ribeiro, Pedro Paredes, Miguel EP Silva, David Aparicio, and Fernando Silva. A survey on subgraph counting: concepts, algorithms, and applications to network motifs and graphlets.ACM Computing Surveys (CSUR), 54(2):1–36, 2021

    2021

  14. [14]

    A combinatorial approach to graphlet counting.Bioinformatics, 30(4):559–565, 2014

    Tomaˇz Hoˇcevar and Janez Demˇsar. A combinatorial approach to graphlet counting.Bioinformatics, 30(4):559–565, 2014

    2014

  15. [15]

    An algorithm to automati- cally generate the combinatorial orbit counting equations.PloS one, 11(1):e0147078, 2016

    Ine Melckenbeeck, Pieter Audenaert, Tom Michoel, Didier Colle, and Mario Pickavet. An algorithm to automati- cally generate the combinatorial orbit counting equations.PloS one, 11(1):e0147078, 2016

    2016

  16. [16]

    Combimotif: A new algorithm for network motifs discovery in protein–protein interaction networks.Physica A: Statistical Mechanics and its Applications, 416:309–320, 2014

    Jiawei Luo, Guanghui Li, Dan Song, and Cheng Liang. Combimotif: A new algorithm for network motifs discovery in protein–protein interaction networks.Physica A: Statistical Mechanics and its Applications, 416:309–320, 2014

    2014

  17. [17]

    Orbitsi: An orbit-based algorithm for the subgraph isomorphism search problem

    Syed Ibtisam Tauhidi, Arindam Karmakar, Thai Son Mai, and Hans Vandierendonck. Orbitsi: An orbit-based algorithm for the subgraph isomorphism search problem. In2024 IEEE International Conference on Knowledge Graph (ICKG), pages 360–369. IEEE, 2024

    2024

  18. [18]

    Efficient orbit-aware triad and quad census in directed and undirected graphs

    Mark Ortmann and Ulrik Brandes. Efficient orbit-aware triad and quad census in directed and undirected graphs. Applied network science, 2:1–17, 2017

    2017

  19. [19]

    Escape: Efficiently counting all 5-vertex subgraphs

    Ali Pinar, Comandur Seshadhri, and Vaidyanathan Vishal. Escape: Efficiently counting all 5-vertex subgraphs. In Proceedings of the 26th international conference on world wide web, pages 1431–1440, 2017

    2017

  20. [20]

    Rage–a rapid graphlet enumerator for large networks.Computer Networks, 56(2):810–819, 2012

    Dror Marcus and Yuval Shavitt. Rage–a rapid graphlet enumerator for large networks.Computer Networks, 56(2):810–819, 2012. 19 APREPRINT- JUNE30, 2026

    2012

  21. [21]

    Biological network comparison using graphlet degree distribution.Bioinformatics, 23(2):e177–e183, 2007

    Nataˇsa Prˇzulj. Biological network comparison using graphlet degree distribution.Bioinformatics, 23(2):e177–e183, 2007

    2007

  22. [22]

    Graphcrunch: a tool for large network analyses.BMC bioinformatics, 9:1–11, 2008

    Tijana Milenkovi´c, Jason Lai, and Nata ˇsa Pr ˇzulj. Graphcrunch: a tool for large network analyses.BMC bioinformatics, 9:1–11, 2008

    2008

  23. [23]

    Graphcrunch 2: software tool for network modeling, alignment and clustering.BMC bioinformatics, 12:1–13, 2011

    Oleksii Kuchaiev, Aleksandar Stevanovi´c, Wayne Hayes, and Nataˇsa Prˇzulj. Graphcrunch 2: software tool for network modeling, alignment and clustering.BMC bioinformatics, 12:1–13, 2011

    2011

  24. [24]

    Beacon: A benchmark for efficient and accurate counting of subgraphs.arXiv preprint arXiv:2504.10948, 2025

    Mohammad Matin Najafi, Xianju Zhu, Chrysanthi Kosyfaki, Laks VS Lakshmanan, and Reynold Cheng. Beacon: A benchmark for efficient and accurate counting of subgraphs.arXiv preprint arXiv:2504.10948, 2025

    work page arXiv 2025

  25. [25]

    Provably powerful graph networks

    Haggai Maron, Heli Ben-Hamu, Hadar Serviansky, and Yaron Lipman. Provably powerful graph networks. Advances in neural information processing systems, 32, 2019

    2019

  26. [26]

    Ordered subgraph aggrega- tion networks.Advances in Neural Information Processing Systems, 35:21030–21045, 2022

    Chendi Qian, Gaurav Rattan, Floris Geerts, Mathias Niepert, and Christopher Morris. Ordered subgraph aggrega- tion networks.Advances in Neural Information Processing Systems, 35:21030–21045, 2022

    2022

  27. [27]

    Cardinality estimation over knowledge graphs with embeddings and graph neural networks.Proceedings of the ACM on Management of Data, 2(1):1–26, 2024

    Tim Schwabe and Maribel Acosta. Cardinality estimation over knowledge graphs with embeddings and graph neural networks.Proceedings of the ACM on Management of Data, 2(1):1–26, 2024

    2024

  28. [28]

    Distributed subgraph counting: a general approach.Proceedings of the VLDB Endowment, 13(12):2493–2507, 2020

    Hao Zhang, Jeffrey Xu Yu, Yikai Zhang, Kangfei Zhao, and Hong Cheng. Distributed subgraph counting: a general approach.Proceedings of the VLDB Endowment, 13(12):2493–2507, 2020

    2020

  29. [29]

    Fast local subgraph counting.Proceedings of the VLDB Endowment, 17(8):1967–1980, 2024

    Qiyan Li and Jeffrey Xu Yu. Fast local subgraph counting.Proceedings of the VLDB Endowment, 17(8):1967–1980, 2024

    1967

  30. [30]

    Exploring network structure, dynamics, and function using networkx

    Aric Hagberg, Pieter J Swart, and Daniel A Schult. Exploring network structure, dynamics, and function using networkx. Technical report, Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2008

    2008

  31. [31]

    Selective parallel loading of large-scale compressed graphs with paragrapher.arXiv preprint arXiv:2404.19735, 2024

    Mohsen Koohi Esfahani, Marco D’Antonio, Syed Ibtisam Tauhidi, Thai Son Mai, and Hans Vandierendonck. Selective parallel loading of large-scale compressed graphs with paragrapher.arXiv preprint arXiv:2404.19735, 2024

    work page arXiv 2024

  32. [32]

    Graphar: An efficient storage scheme for graph data in data lakes.arXiv preprint arXiv:2312.09577, 2023

    Xue Li, Weibin Zeng, Zhibin Wang, Diwen Zhu, Jingbo Xu, Wenyuan Yu, and Jingren Zhou. Graphar: An efficient storage scheme for graph data in data lakes.arXiv preprint arXiv:2312.09577, 2023

    work page arXiv 2023

  33. [33]

    An i/o-efficient disk-based graph system for scalable second-order random walk of large graphs.arXiv preprint arXiv:2203.16123, 2022

    Hongzheng Li, Yingxia Shao, Junping Du, Bin Cui, and Lei Chen. An i/o-efficient disk-based graph system for scalable second-order random walk of large graphs.arXiv preprint arXiv:2203.16123, 2022

    work page arXiv 2022

  34. [34]

    Performance application programming interface.Sun, Baruah and Kaeli, 12:2022, 2022

    Anthony Danalis and Heike Jagode. Performance application programming interface.Sun, Baruah and Kaeli, 12:2022, 2022. 20

    2022