Principal Graph Encoder Embedding and Principal Community Detection
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Abstract (arXiv)
In this paper, we introduce the concept of principal communities and propose a principal graph encoder embedding method that concurrently detects these communities and achieves vertex embedding. Given a graph adjacency matrix with vertex labels, the method computes a sample community score for each community, ranking them to measure community importance and estimate a set of principal communities. The method then produces a vertex embedding by retaining only the dimensions corresponding to these principal communities. Theoretically, we define the population version of the encoder embedding and the community score based on a random Bernoulli graph distribution. We prove that the population principal graph encoder embedding preserves the conditional density of the vertex labels and that the population community score successfully distinguishes the principal communities. We conduct a variety of simulations to demonstrate the finite-sample accuracy in detecting ground-truth principal communities, as well as the advantages in embedding visualization and subsequent vertex classification. The method is further applied to a set of real-world graphs, showcasing its numerical advantages, including robustness to label noise and computational scalability.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 22 of its 50 references that are in the map. First posted on arXiv 24 Jan 2025.
Builds on
22 of 50 references.
References · 22
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
- 2016node2vec: Scalable Feature Learning for Networkscited by 1,913
- 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
- 2016Variational Graph Auto-Encoderscited by 1,373
- 2018FastGCN: Fast Learning with Graph Convolutional Networks via Importance Samplingcited by 583
- 2018From Louvain to Leiden: guaranteeing well-connected communitiescited by 379
- 2020Combining Label Propagation and Simple Models Out-performs Graph Neural Networkscited by 199
- 2019What Can Neural Networks Reason About?cited by 155
- 2017Statistical inference on random dot product graphs: a surveycited by 70
- 2019Inference for multiple heterogeneous networks with a common invariant subspacecited by 39
- 2018On a 'Two Truths' Phenomenon in Spectral Graph Clusteringcited by 24
10 more
- 2021One-Hot Graph Encoder Embeddingcited by 16
- 2019GraSPy: Graph Statistics in Pythoncited by 15
- 2021Spectral embedding for dynamic networks with stability guaranteescited by 13
- 2023Graph Encoder Ensemble for Simultaneous Vertex Embedding and Community Detectioncited by 8
- 2023Synergistic Graph Fusion via Encoder Embeddingcited by 6
- 2023Discovering Communication Pattern Shifts in Large-Scale Labeled Networks using Encoder Embedding and Vertex Dynamicscited by 5
- 2024Refined Graph Encoder Embedding via Self-Training and Latent Community Recoverycited by 5
- 2019Community Correlations and Testing Independence Between Binary Graphscited by 4
- 2020A Simple Spectral Failure Mode for Graph Convolutional Networkscited by 4
- 2024Encoder Embedding for General Graph and Node Classificationcited by 4
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Citing papers per year: 2025: 2.
2 papers.