Graph Representation Learning in Biomedicine

1 Introduction

• Biomedical networks represent biological organization and knowledge, while systems-biology principles connect network structure to phenotypes, disease mechanisms, and health.Examples include regulatory, gene–disease, and electronic-health-record networks; network diversity can improve generalization and interpretability.Source: §1 · pp. 1–2
• Graph representation learning maps nodes or larger graph structures into compact vector spaces whose geometry reflects network neighborhoods, topology, and shared components.These models act as differentiable engines of network-biomedicine principles, including similarity of interacting entities, hub structure, and shared neighbors.Source: §1 · pp. 2–3, Figure 1 · p. 2
• The survey unifies graph representation learning across molecular, genomic, therapeutic, and precision-medicine applications rather than focusing only on particular graph or biomedical domains.It complements reviews of structured data, graph neural networks, heterogeneous and dynamic graphs, data fusion, network propagation, topology, network construction, and specialized biomedical applications.Source: §1 · p. 3

2 Graph representation learning

• Graph representation learning automatically learns network features despite complex topology, absent node ordering, heterogeneous entities, and diverse interactions that fixed-grid or sequence models cannot directly capture.Learned embeddings encode graph structure and semantics for node, link, and graph property prediction, latent graph learning, and graph generation.Source: §2 · pp. 3–4

2.1 Shallow graph embedding approaches

• Shallow embedding methods optimize node lookup vectors so predefined graph similarities, including random-walk co-occurrence and relation types, are preserved in embedding space.They are transductive and typically require separate downstream models for classification or regression.Source: §2.1 · p. 6

2.2 Graph neural networks

• Graph neural networks iteratively pass, aggregate, and transform neighborhood messages to learn higher-order, nonlinear representations while jointly optimizing graph structure and supervised signals.Architectures address attention, structural priors, pooling, molecular domain knowledge, large-scale sampling, heterogeneous relations, dynamic graphs, and limited labels.Source: §2.2 · pp. 6–7

2.3 Generative graph models

• Generative graph models learn distributions over graph structures and decode new graphs with desired properties, addressing discrete, unordered, and variable-sized graph generation.Deep approaches use variational autoencoders or generative adversarial networks and may generate graphs through subgraph decomposition, graph matching, or sequential node-edge sampling.Source: §2.3 · p. 7

3 Application areas in biology and medicine

• Biomedical graph learning leverages multimodal network structure from molecules through healthcare systems to support biological insight and personalized patient representations.Networks connect proteins, drugs, diseases, patient images, and EHR-derived concepts across domains.Source: §3 · p. 7, Figure 3 · p. 8

4 Graph representation learning for molecules

• Across molecular biology, graph learning improves protein-function prediction, discovers new molecules and interactions, and supports representations of proteins, compounds, and their physical relationships.Molecular graphs encode atoms and bonds, while protein-interaction networks encode physical or functional relationships informed by network-medicine principles.Source: §3 · p. 7, §4 · p. 9

4.1 Modeling protein molecular graphs

• Protein molecular graphs encode residues or atoms with spatial, sequential, and geometric relationships, enabling embeddings that predict sequences from structures and generate new three-dimensional structures.Hierarchical embeddings capture motif-, connectivity-, and atomic-level organization despite the computational difficulty of flexible molecular generation.Source: §4.1 · p. 9

4.2 Quantifying protein interactions

• Graph convolutions combined with sequence modeling quantify protein interactions, enrich incomplete PPI networks, and remove less credible edges to improve network reliability.These models integrate structural information from interaction graphs with amino-acid sequence dependencies, sometimes treating concatenated outputs as CNN image inputs.Source: §4.2 · p. 10

4.3 Interpreting protein functions and cellular phenotypes

• Protein-function and cellular-phenotype models integrate gene ontologies, transcriptomics, protein interactions, and cell-specific expression to produce interpretable predictions at single-cell resolution.Cell-type-aware embeddings support cellular-function prediction, disease-feature identification, and experimentally validated ligand-receptor analyses in spatially heterogeneous tumors.Source: §4.3 · pp. 10–11

5 Graph representation learning for genomics

• In genomics, graph learning integrates gene expression, regulatory and co-expression networks, and clinical information to connect genome-wide molecular alterations with disease diagnosis and biomarkers.Disease-associated gene expression can be injected into PPI networks, while heterogeneous graphs support predictions across genomic and clinically relevant data.Source: §3 · p. 9, §5.1 · p. 11, §5 · p. 11

5.1 Leveraging gene expression measurements

• Gene-expression graph methods transform noisy measurements into topological representations or fuse them with GO and PPI knowledge, improving interpretability while addressing incomplete regulatory interactomes.GNNs can learn robust molecular representations and inductively infer missing edges when PPI networks fail to capture all gene-regulatory activity.Source: §5.1 · pp. 11–12

5.2 Injecting single cell and spatial information into molecular networks

• Single-cell and spatial graph learning models cell states, imputes expression, predicts clusters, infers ligand-receptor interactions, and represents diseases as phenotype subgraphs for improved disorder differentiation.Spatial edges may reflect cellular proximity, while phenotype-subgraph embeddings capture complex relationships beyond individual disease nodes or edges.Source: §5.2 · pp. 12–13

6 Graph representation learning for therapeutics

• Integrating chemical structures, protein interactions, and clinical data enables graph models to predict drug interactions, targets, side effects, diseases, and repurposing opportunities.These models can characterize drugs at the systems level without patient data, addressing costly and time-consuming discovery processes.Source: §6 · p. 13

6.1 Modeling compound molecular graphs

• Molecular graphs encode atoms, bonds, distances, angles, and rotations, while message passing, attention, junction trees, and fragment editing learn chemistry for property prediction and molecule generation [98].These representations capture local chemical neighborhoods, atom interactions, reaction outcomes, and desirable molecular substructures.Source: §6.1 · pp. 13–14

6.2 Quantifying drug-drug and drug-target interactions

• Fusing compound sequence, structure, and clinical features with protein and molecule graph representations improves interpretable drug-drug interaction and drug-target affinity predictions [117] [124].Drug and target embeddings can be learned from similarity graphs, topological data analysis, shallow network embeddings, or graph neural networks before downstream prediction.Source: §6.2 · p. 14

6.3 Identifying drug-disease associations and biomarkers for complex disease

• Heterogeneous graphs integrating drugs, targets, diseases, genomic features, and protein interactions better represent drug action, while cell-line-specific transfer learning prioritizes candidate drug combinations and captures tissue-dependent effects.Multimodal drug-protein networks predict interacting drug pairs across cell lines and can reduce experimental costs by prioritizing promising combinations.Source: §6.3 · p. 15

7 Graph representation learning for healthcare

• Graph learning fuses multimodal biomedical knowledge with histopathology images and EHRs, enabling precision-medicine predictions tailored to individual patients.This integration supports patient-specific predictions by connecting biological mechanisms with clinical information.Source: §7 · p. 15, §7.2 · p. 17

7.1 Leveraging networks for diagnostic imaging

• Cell, tissue, lymph-node, MRI, chest-X-ray, and whole-slide image graphs capture spatial and relational structure for disease progression, diagnosis, localization, cancer staging, treatment response, and survival [147].Hierarchical and attention-based models can aggregate morphology, tissue architecture, genomic data, and spatial context, while graph pruning supports interpretability.Source: §7.1 · p. 16

7.2 Personalizing medical knowledge networks with patient records

• Embedding hierarchical medical knowledge, temporal EHR dependencies, and patient-specific biomedical networks supports predictions of diagnoses, future disease, prescriptions, adverse events, and effective treatments [107] [114] [157] [163].Patient meta-nodes connect individuals to biomedical entities, enabling edge-regression predictions of disease development or treatment effectiveness.Source: §7.2 · pp. 16–17

8 Outlook

• Graph representation learning could improve fine-scale variant mapping by representing GWAS, eQTL, chromatin, and Hi-C data as networks.These approaches may reveal disease-relevant gene modules, propagate QTL candidate information, model long-range genomic interactions, and reconstruct 3D chromosome structure.Source: §8 · p. 19
• Dynamic graph neural networks may capture expression changes in single-cell RNA sequencing across time or perturbations, extending graph analysis of spatial molecular profiles.Source: §8 · p. 19
• Integrating healthcare data with molecular, genomic, disease, and drug knowledge could produce more accurate and interpretable predictions of biological systems.Knowledge graphs are being developed to synthesize multi-scaled, multi-modal data across genotype–phenotype associations and population-level epidemiology.Source: §8 · p. 19
• Spatial and temporal public-health networks can model disease states and infection susceptibility to identify trends, detect anomalies, and interpret temporal dynamics.Source: §8 · p. 19
• Clinical graph representation learning should prioritize explainable, fair, and robust representations while addressing algorithmic bias and health disparities.Source: §8 · p. 19

Supplementary Information for

• The supplementary information includes Supplementary Notes 1 to 4.Source: Supplementary Information for · p. 34

3 Further Details on Representation Learning Approaches S6

• Graph theoretic techniques are identified as subsection 3.1 of the further representation-learning approaches.Source: §3 · p. 35
• Network diffusion is identified as subsection 3.2 of the further representation-learning approaches.Source: §3 · p. 35
• Topological data analysis is identified as subsection 3.3 of the further representation-learning approaches.Source: §3 · p. 35
• Manifold learning is identified as subsection 3.4 of the further representation-learning approaches.Source: §3 · p. 35

1 Further Information on Graph Notation and Definitions

• A biomedical graph G = (V, E) contains nodes and edges, with adjacency matrix A encoding connectivity or edge weights and |V| = n, |E| = m.Nodes may represent entities from atoms to patients, while edges represent relations such as molecular bonds, disease associations, or referrals.Source: §1 · p. 36
• Subgraphs select subsets of nodes and edges, while node features describe attributes and labels define targets for nodes, edges, subgraphs, or entire graphs.A subgraph can represent a disease module or patient-doctor community, and node features are vectors xv ∈ R^d.Source: §1 · p. 36
• Walks are node sequences, simple paths have distinct nodes, and d(u, v) is the shortest-path distance; heterogeneous graphs additionally support meta-paths across node and edge types.The k-hop neighborhood is Nk(v) = {u|d(u, v) = k}, while N(v) contains connected nodes and determines degree.Source: §1 · pp. 36–37
• Simple, weighted, and attributed graphs differ in whether nodes and edges carry weights or multidimensional properties, such as gene-expression vectors in cell-cell interaction networks.Binary protein-protein interactions form an unweighted network, whereas attributes encode node or edge properties.Source: §1 · p. 37
• Heterogeneous graphs connect diverse node and edge types, while biomedical knowledge graphs represent typed relations as triplets (u, r, v) retrieved from literature and biorepositories.A drug-target-disease network can include drugs, proteins, and diseases linked by binding, mutation, and treatment relations.Source: §1 · p. 37
• Multi-layer graphs organize networks into contextual layers such as tissues or diseases and can add inter-layer edges linking corresponding proteins across tissues.Each layer may contain a tissue-specific protein-interaction network arranged within a tissue taxonomy.Source: §1 · p. 37
• Temporal graphs sequence networks over time, spatial graphs assign nodes or edges coordinates, and these graph types can be combined into multimodal temporal or multi-layer spatial graphs.Temporal examples include time-varying brain activity and connectivity, while spatial examples include 3D tissues and protein atomic coordinates.Source: §1 · pp. 37–38

• Biomedical graph machine learning comprises three broad categories: graph prediction, latent graph learning, and graph generation.Each category contains several individual graph machine learning tasks.Source: §2 · p. 38
• Canonical graph prediction covers node, link, edge, and graph classification or regression, respectively predicting labels for nodes, node pairs, edges, or entire graphs.Link prediction determines whether a link exists between a given pair of nodes.Source: §2 · p. 38
• Additional biomedical graph prediction tasks include module detection, clustering or community detection, subgraph classification or regression, and dynamic graph prediction.These tasks detect modules, partition graphs into similar-node subgraphs, classify subgraphs or modules, or perform predictions across graph sequences.Source: §2 · p. 38
• Latent graph learning infers underlying graph structure from nodes and their feature attributes, supporting graph prediction, topology discovery, and low-dimensional representations.Its function learns the graph structure, such as edges, given only nodes and feature attributes.Source: §2 · pp. 38–39
• Graph generation learns a distribution from training graphs and uses it to create new graphs sharing their characteristics or having optimized properties.The generated graph is never-before-seen and is intended to exhibit properties of interest.Source: §2 · p. 39

3 Further Details on Representation Learning Approaches

• Four approaches extend graph representation learning: graph theoretic techniques, network diffusion, topological data analysis, and manifold learning.The approaches respectively use structural statistics, diffusion profiles, topological representations, and low-dimensional mappings.Source: §3 · p. 39

3.1 Graph theoretic techniques

• Graph-theoretic techniques use node-, link-, and subgraph-level statistics; centrality measures node roles, link-level statistics support link prediction, and length-3-path methods show strong PPI-network performance.The PPI network does not follow homophily because interacting proteins are not necessarily similar 8.Source: §3.1 · p. 40

3.2 Network diffusion

• Network diffusion represents influence along graph paths through scalar source–destination measures or diffusion profiles capturing local connectivity patterns.GraphWave learns unsupervised embeddings from heat-wavelet diffusion, allowing nodes in different graph regions to share structural roles.Source: §3.2 · pp. 40–41

3.3 Topological data analysis

• Topological data analysis converts data topology into representations through persistent homology vectors or Mapper graphs built from filtered clusters.Persistent homology tracks shapes across resolutions, while Mapper supports subtype and developmental-trajectory analysis but depends strongly on its filter function.Source: §3.3 · p. 41

3.4 Manifold learning

• Manifold learning constructs connectivity graphs from distances and maps high-dimensional data into low-dimensional embeddings using graph operators or distance-preserving objectives.Traditional methods are multistage and distance-dependent, whereas newer approaches learn the manifold end-to-end from downstream prediction signals 28,29.Source: §3.4 · pp. 41–42

Formulation 1 Graph theoretic techniques

• Graph-theoretic techniques map network components to real values capturing structural properties such as node proximity and centrality.Betweenness quantifies a node’s influence through the shortest paths passing through it.Source: §4 · p. 42

Formulation 2 Network diffusion

• Network diffusion computes influence signatures from propagation, with Diffusion State Distance [17] comparing nodes’ diffusion vectors using an L1 norm.Each diffusion vector records expected random-walk visits to every node, and smaller differences indicate similar local connectivity.Source: §4 · p. 42

Formulation 3 Geometric representations

• Geometric representations use preassigned guiding functions, with a mapper generating the data topology T from data D [4,34].The standard mapper procedure is introduced as a sequence of steps.Source: §4 · p. 43

1. Reference Map. Given a set of data D, we first define a continuous filter function

• A topology graph is built by filtering data, covering the filter range, clustering pre-images, and connecting clusters that share data points.The resulting graph is the nerve of the cover by path-connected components.Source: §1 · p. 43
• Shallow network embeddings map nodes to vectors, define network and embedding similarities, and minimize a loss measuring preserved network distances.The embedding is optimized so f_n(u, v) and f_z(h_u, h_v) agree.Source: §1 · p. 43
• Persistent homology constructs Rips-complex filtrations across distance thresholds and records homology classes by their birth and death in persistence diagrams.These diagrams capture connected components, holes, and cavities, with longer-lived structures represented farther from the diagonal.Source: §1 · p. 44
• Manifold learning seeks low-dimensional embeddings of high-dimensional data by constructing a nearest-neighbor graph, computing shortest-path distances, and optimizing low-dimensional vectors.The Isomap example uses a k-nearest neighbor graph and its shortest-path distance matrix.Source: §1 · pp. 44–45
• Graph neural networks learn compact representations from graph structure and node features through repeated message passing, neighborhood aggregation, and nonlinear embedding updates.Each propagation layer computes messages for linked nodes, aggregates neighbors’ messages, and updates node embeddings.Source: §1 · p. 45
• Generative graph models learn graph distributions to generate graphs with desirable properties; VGAE encodes adjacency and node features into latent distributions and decodes latent samples into networks.Its probabilistic decoder generates edges using the sigmoid of latent-node dot products.Source: §1 · pp. 45–46