Aligning Multiple Inhomogeneous Random Graphs: Fundamental Limits of Exact Recovery
Published Online:11 Aug 2026https://doi.org/10.1287/opre.2025.1808
References
- (2018) Community detection and stochastic block models: Recent developments. J. Machine Learn. Res. 18(177):1–86.Google Scholar
- (2023) Robust graph matching when nodes are corrupt. Preprint, submitted October 23, https://arxiv.org/abs/2310.18543.Google Scholar
- (2025a) Detecting correlation between multiple unlabeled Gaussian networks. 2025 IEEE Internat. Sympos. Inform. Theory (ISIT) (IEEE, Piscataway, NJ), 1–6.Google Scholar
- (2025b) Exact random graph matching with multiple graphs. 2025 IEEE Internat. Sympos. Inform. Theory (ISIT) (IEEE, Piscataway, NJ), 1–6.Google Scholar
- (2006) Systematic identification of functional orthologs based on protein network comparison. Genome Res. 16(3):428–435.Crossref, Google Scholar
- (2019) (Nearly) efficient algorithms for the graph matching problem on correlated random graphs. Adv. Neural Inform. Processing Systems 32:186–9194.Google Scholar
- (2024) Graph alignment exploiting the spatial organization improves the similarity of brain networks. Human Brain Mapp. 45(1):e26554.Crossref, Google Scholar
- (2024) Efficient graph matching for correlated stochastic block models. Preprint, submitted December 3, https://arxiv.org/abs/2412.02661.Google Scholar
- (2002) The average distances in random graphs with given expected degrees. Proc. Natl. Acad. Sci. USA 99(25):15879–15882.Crossref, Google Scholar
- (2016) Improved achievability and converse bounds for Erdős-Rényi graph matching. ACM SIGMETRICS Performance Evaluation Rev. 44(1):63–72.Crossref, Google Scholar
- (2017) Exact alignment recovery for correlated Erdős-Rényi graphs. Preprint, submitted November 18, https://arxiv.org/abs/1711.06783.Google Scholar
- (2019) Partial recovery of Erdős-Rényi graph alignment via k-core alignment. Proc. ACM Measurement Anal. Comput. Systems 3(3):1–21.Crossref, Google Scholar
- (2019) Analysis of a canonical labeling algorithm for the alignment of correlated Erdős-Rényi graphs. Proc. ACM Measurement Anal. Comput. Systems 3(2):1–25.Crossref, Google Scholar
- (2023) Matching recovery threshold for correlated random graphs. Ann. Statist. 51(4):1718–1743.Crossref, Google Scholar
- (2023) A polynomial-time iterative algorithm for random graph matching with non-vanishing correlation. Preprint, submitted June 1, https://arxiv.org/abs/2306.00266.Google Scholar
- (2023) Efficiently matching random inhomogeneous graphs via degree profiles. Preprint, submitted October 16, https://arxiv.org/abs/2310.10441.Google Scholar
- (2021) Efficient random graph matching via degree profiles. Probab. Theory Related Fields 179:29–115.Crossref, Google Scholar
- (2025) Optimal recovery of correlated Erdos-Renyi graphs. Preprint, submitted February 17, https://arxiv.org/abs/2502.12077.Google Scholar
- (2025) Statistical-computational gap in multiple Gaussian graph alignment. Preprint, submitted November 29, https://arxiv.org/abs/2512.00610.Google Scholar
- (2022) Spectral graph matching and regularized quadratic relaxations II: Erdős-Rényi graphs and universality. Foundations Comput. Math. 23:1567–1617.Crossref, Google Scholar
- (2021) Impossibility of partial recovery in the graph alignment problem. Conf. Learn. Theory (PMLR, New York), 2080–2102.Google Scholar
- (2022) Exact community recovery in correlated stochastic block models. Conf. Learn. Theory (PMLR, New York), 2183–2241.Google Scholar
- (2005) Robust textual inference via graph matching. Proc. Human Language Tech. Conf. Conf. Empirical Methods Natural Language Processing (Association for Computational Linguistics, Stroudsburg, PA), 387–394.Google Scholar
- (2023) Partial recovery in the graph alignment problem. Oper. Res. 71(1):259–272.Link, Google Scholar
- (1983) Stochastic blockmodels: First steps. Soc. Networks 5(2):109–137.Crossref, Google Scholar
- (2024) Information-theoretic thresholds for the alignments of partially correlated graphs. Preprint, submitted June 8, https://arxiv.org/abs/2406.05428.Google Scholar
- (2021) Network recovery from unlabeled noisy samples. 2021 55th Asilomar Conf. Signals Systems Comput. (IEEE, Piscataway, NJ), 1268–1273.Google Scholar
- (2016) Proper: Global protein interaction network alignment through percolation matching. BMC Bioinformatics 17(1):1–16.Crossref, Google Scholar
- (2009) IsoRankN: Spectral methods for global alignment of multiple protein networks. Bioinformatics 25(12):i253–i258.Crossref, Google Scholar
- (2023) Phase transition in noisy high-dimensional random geometric graphs. Electron. J. Statist. 17(2):3512–3574.Crossref, Google Scholar
- (2018) Correcting the output of approximate graph matching algorithms. IEEE INFOCOM 2018-IEEE Conf. Comput. Comm. (IEEE, Piscataway, NJ), 1745–1753.Google Scholar
- (1991) Size and connectivity of the k-core of a random graph. Discrete Math. 91(1):61–68.Crossref, Google Scholar
- (2023a) Exact matching of random graphs with constant correlation. Probab. Theory Related Fields 186(1–2):327–389.Crossref, Google Scholar
- (2023b) Random graph matching at Otter’s threshold via counting chandeliers. Proc. 55th Annual ACM Sympos. Theory Comput., 1345–1356.Google Scholar
- (2017) Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis (Cambridge University Press, Cambridge, UK).Google Scholar
- (2020) Seeded graph matching via large neighborhood statistics. Random Structures Algorithms 57(3):570–611.Crossref, Google Scholar
- (2008) Robust de-anonymization of large sparse datasets. 2008 IEEE Sympos. Security Privacy (SP 2008) (IEEE, Piscataway, NJ), 111–125.Google Scholar
- (2009) De-anonymizing social networks. 2009 30th IEEE Sympos. Security Privacy (IEEE, Piscataway, NJ), 173–187.Google Scholar
- (2011) On the privacy of anonymized networks. Proc. 17th ACM SIGKDD Internat. Conf. Knowledge Discovery Data Mining (Association for Computing Machinery, New York), 1235–1243.Google Scholar
- (2021) Correlated stochastic block models: Exact graph matching with applications to recovering communities. Adv. Neural Inform. Processing Systems 34:22259–22273.Google Scholar
- (2023) Matching correlated inhomogeneous random graphs using the k-core estimator. 2023 IEEE International Sympos. Inform. Theory (ISIT) (IEEE, Piscataway, NJ), 2499–2504.Google Scholar
- (2024) Harnessing multiple correlated networks for exact community recovery. Adv. Neural Inform. Processing Systems 37:53834–53886.Google Scholar
- (2005) Probabilistic subgraph matching based on convex relaxation. Internat. Workshop Energy Minimization Methods Comput. Vision Pattern Recognition (Springer, Berlin, Heidelberg), 171–186.Crossref, Google Scholar
- (2008) Global alignment of multiple protein interaction networks with application to functional orthology detection. Proc. Natl. Acad. Sci. USA 105(35):12763–12768.Crossref, Google Scholar
- (2005) The human connectome: A structural description of the human brain. PLoS Comput. Biol. 1(4):e42.Crossref, Google Scholar
- (2025) The feasibility of multi-graph alignment: A Bayesian approach. Preprint, submitted February 24, https://arxiv.org/abs/2502.17142.Google Scholar
- (2013) Graph matching techniques for computer vision. Image Processing: Concepts, Methodologies, Tools, and Applications (IGI Global, Hershey, PA), 381–421.Crossref, Google Scholar
- (2017) Multiple network alignment via multiMAGNA+. IEEE/ACM Trans. Comput. Biol. Bioinform. 15(5):1669–1682.Crossref, Google Scholar
- (2024) On the feasible region of efficient algorithms for attributed graph alignment. IEEE Trans. Inform. Theory 70(5):3622–3639.Crossref, Google Scholar
- (2022) Settling the sharp reconstruction thresholds of random graph matching. IEEE Trans. Inform. Theory 68(8):5391–5417.Crossref, Google Scholar
- (2016) A short survey of recent advances in graph matching. Proc. 2016 ACM Internat. Conf. Multimedia Retrieval (Association for Computing Machinery, New York), 167–174.Google Scholar
- (2024) Exact graph matching in correlated Gaussian-attributed Erdős-Rényi model. 2024 IEEE Internat. Sympos. Inform. Theory (ISIT) (IEEE, Piscataway, NJ), 3450–3455.Google Scholar
- (2022) Multi-robot active mapping via neural bipartite graph matching. Proc. IEEE/CVF Conf. Comput. Vision Pattern Recognition, 14839–14848.Google Scholar
- (2024) Attributed graph alignment. IEEE Trans. Inform. Theory 70(8):5910–5934.Crossref, Google Scholar
- (2024) k-wise multi-graph matching. IET Image Processing 18(14):4760–4777.Crossref, Google Scholar

