# H3: A Healthcare Three-Hop Index for Physician Referral Network Prediction

arXiv: https://arxiv.org/abs/2605.02150 · HTML: https://mlsanity.com/paper/2605.02150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 55 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [Evaluating Graph Neural Networks for Link Prediction: Current Pitfalls and New Benchmarking](https://mlsanity.com/paper/2306.10453/) (2023)
- [Evaluating Link Prediction Methods](https://mlsanity.com/paper/1505.04094/) (2015)
- [Class-Imbalanced Learning on Graphs: A Survey](https://mlsanity.com/paper/2304.04300/) (2023)
- [A survey of dynamic graph neural networks](https://mlsanity.com/paper/2404.18211/) (2024)
- [Optimizing Long-tailed Link Prediction in Graph Neural Networks through Structure Representation Enhancement](https://mlsanity.com/paper/2407.20499/) (2024)
- [A Survey of Link Prediction in Temporal Networks](https://mlsanity.com/paper/2502.21185/) (2025)
- [Experimental analyses on 2-hop-based and 3-hop-based link prediction algorithms](https://mlsanity.com/paper/1909.00174/) (2019)
- [Analysis of the U.S. Patient Referral Network](https://mlsanity.com/paper/1711.03245/) (2017)
- [The maximum capability of a topological feature in link prediction](https://mlsanity.com/paper/2206.15101/) (2022)

## Abstract (arXiv)

Accurate prediction of physician referral links is essential for optimizing care coordination and reducing fragmentation in healthcare delivery. However, existing computational methods, ranging from triadic closure heuristics to graph neural networks, fail to capture the intrinsic properties of physician referral networks, including sparsity, disassortative degree mixing, and hub-dominated topology. Here, we propose H3, a healthcare three-hop index that addresses these limitations by modeling indirect referral pathways through intermediate physicians, with degree-based normalization and a redundancy penalty to mitigate hub-mediated noise. Using Medicare Physician Shared Patient Patterns data, we evaluate H3 under two complementary prediction regimes: within-period prediction, which assesses recovery of contemporaneous referral links under sparse conditions, and cross-period prediction, which tests robustness to temporal shift as referral windows expand. Across both regimes, H3 consistently outperforms classical heuristics and deep learning-based baselines. Unlike black-box neural network approaches, H3 produces fully decomposable predictions traceable to specific intermediary physicians, offering a transparent and deployable solution for referral network completion.