Identifying influential nodes in hypergraphs is essential for applications in social network analysis and bioinformatics. Conventional centrality metrics, designed for pairwise interactions, fail to capture the higher-order dependencies inherent to hypergraphs. To address this, we have proposed the HDCN (hypergraph dual-branch convolutional network), a dual-branch convolutional network that fuses local and global higher-order signals. The HDCN adopts two existing centrality measures as complementary feature channels, namely, multi-scale hyper-degree centrality (HD) for local topology and hypergraph distance-based fuzzy centrality (HDF) for higher-order neighborhood aggregation, and proposes a dual-branch convolutional architecture with a fully $ \tau $-aligned pairwise ranking objective to fuse them effectively. The two branches are separately encoded by convolutional layers and subsequently fused to yield robust node influence estimates. The task was formulated as a pairwise learning-to-rank problem optimized directly for Kendall's $ \tau $, with ground-truth rankings derived from Monte Carlo susceptible infected recovered (SIR) simulations. Experiments on five real-world hypergraph datasets showed that the HDCN outperforms traditional centrality baselines, ranking first on four of five datasets. On the structurally complex Geometry dataset, the HDCN achieves $ \tau = 0.5253 $, a 56% relative gain over the strongest traditional baseline (EHDF, $ \tau = 0.3368 $). the HDCN also surpasses learning-based methods including the hypergraph neural network (HGNN) on all five datasets, confirming the effectiveness of our dual-branch higher-order fusion strategy.
Citation: Chuan Ran, Xindong Zhang, Juan Liu. Hypergraph node influence ranking via fusing local topology and higher-order fuzzy semantics[J]. Electronic Research Archive, 2026, 34(9): 6513-6541. doi: 10.3934/era.2026285
Identifying influential nodes in hypergraphs is essential for applications in social network analysis and bioinformatics. Conventional centrality metrics, designed for pairwise interactions, fail to capture the higher-order dependencies inherent to hypergraphs. To address this, we have proposed the HDCN (hypergraph dual-branch convolutional network), a dual-branch convolutional network that fuses local and global higher-order signals. The HDCN adopts two existing centrality measures as complementary feature channels, namely, multi-scale hyper-degree centrality (HD) for local topology and hypergraph distance-based fuzzy centrality (HDF) for higher-order neighborhood aggregation, and proposes a dual-branch convolutional architecture with a fully $ \tau $-aligned pairwise ranking objective to fuse them effectively. The two branches are separately encoded by convolutional layers and subsequently fused to yield robust node influence estimates. The task was formulated as a pairwise learning-to-rank problem optimized directly for Kendall's $ \tau $, with ground-truth rankings derived from Monte Carlo susceptible infected recovered (SIR) simulations. Experiments on five real-world hypergraph datasets showed that the HDCN outperforms traditional centrality baselines, ranking first on four of five datasets. On the structurally complex Geometry dataset, the HDCN achieves $ \tau = 0.5253 $, a 56% relative gain over the strongest traditional baseline (EHDF, $ \tau = 0.3368 $). the HDCN also surpasses learning-based methods including the hypergraph neural network (HGNN) on all five datasets, confirming the effectiveness of our dual-branch higher-order fusion strategy.
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Chuan Ran, Xindong Zhang, Juan Liu. Hypergraph node influence ranking via fusing local topology and higher-order fuzzy semantics[J]. Electronic Research Archive, 2026, 34(9): 6513-6541. doi: 10.3934/era.2026285
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