Graph Foundation Models: A Comprehensive Survey

• Large-scale pretraining and adaptation enable GFMs to generalize across graph domains and tasks, including node classification, link prediction, graph classification, and graph-to-text generation.OFA [22] aligns textual node features across eight text-attributed graphs using a shared encoder and prompt graph, while GFT [23] learns transferable structural patterns through computation-tree reconstruction.Source: Figure 1 · p. 5, §1 · p. 6
• GFMs target transferable intelligence for graph data, whose relational dependencies, permutation invariance, and non-Euclidean geometry support applications from molecular prediction to recommendation systems [19] [21].Figure 1 contrasts multi-domain pretraining and adaptation with traditional single-domain, task-specific GNN training.Source: Figure 1 · p. 5, §1 · p. 6
• Existing surveys remain fragmented across architectures, pretraining objectives, transferability, cross-domain learning, applications, and GNN–LLM integration, without a unified account of GFM design and theory [35] [37] [38] [39] [40] [41] [43].They often omit cross-task generalization and structural alignment across diverse graph types.Source: §1 · p. 6
• This survey decomposes GFMs into backbone architectures, pretraining strategies, and adaptation mechanisms, then classifies them as universal, domain-specific, or task-specific according to scope and generalization capacity.It also reviews representative methods, theoretical foundations, benchmark resources, limitations, and future directions.Source: §1 · pp. 6–7
• Designing GFMs requires addressing feature, structural, and task heterogeneity, which create distinctive difficulties for learning from graph-structured data at scale.These challenges are presented as three core dimensions of GFM construction.Source: §1 · pp. 6–7
• The survey identifies open problems in scalable architectures, graph data scarcity, realistic evaluation, effective adaptation, multimodal utilization, transferability, distribution shifts, and theoretical guarantees.Proposed directions include automated data collection, synthetic generation, quality-centric curation, robust benchmarks, zero-shot and prompt-based learning, and deeper generalization theory.Source: §1 · p. 7

2.1 A Brief History of Graph Learning

• Graph learning evolved from classical, handcrafted methods through embeddings and message-passing GNNs to pretrained GFMs targeting scalable, general-purpose intelligence across tasks and domains.Traditional methods lacked scalability and transferable representations; embeddings were largely transductive and omitted attributes, while GNNs faced oversmoothing, limited receptive fields, and task-specific tuning [19] [21]. GFMs use self-supervised pretraining on large-scale graphs to support transfer, including zero-shot and few-shot generalization [23] [30].Source: Figure 2 · p. 8, §2.1 · pp. 8–9

2.2 Background of Foundation Models

• Foundation models learn general-purpose representations through large-scale, diverse pretraining, enabling adaptation by fine-tuning, prompting, or instruction tuning and supporting few-shot and zero-shot learning.GFMs extend this paradigm to graphs by modeling nodes, edges, topology, and relational structure for tasks including node classification, link prediction, and graph generation, with transfer across domains and limited labeled data.Source: §2.2 · pp. 9–10

2.3 Definitions & Notations

• The paper formalizes graphs as G = (V, E), attributed graphs as G = (X, A), and text-attributed graphs as G = (X, A, D), alongside definitions of GNNs, LLMs, and GFMs.GFMs are defined as large-scale models pretrained on cross-domain and cross-task graph datasets to acquire transferable knowledge and emergent capabilities for applications such as molecular prediction, recommendation, social analysis, and anomaly detection.Source: §2.3 · pp. 10–11

3 Challenges in Designing Graph Foundation Models

• GFMs must learn transferable, adaptable representations across diverse graph datasets and learning scenarios despite feature, structure, and task heterogeneity.These three forms of heterogeneity collectively make universal graph modeling difficult.Source: §3 · p. 12

3.1 Feature Heterogeneity

• Feature heterogeneity arises from domain-specific semantics and inconsistent preprocessing, producing incompatible node, edge, and graph-level feature spaces.Citation networks may encode textual attributes, whereas molecular graphs encode atom types, bond orders, and spatial configurations; even Cora and Pubmed use different input dimensions.Source: §3.1 · pp. 12–13, Figure 3 · p. 12

3.2 Structure Heterogeneity

• Structural heterogeneity spans domain-specific topologies, while deeper or larger GNNs remain limited by over-smoothing, over-squashing, and locality bias.Proposed remedies include structure-aware augmentation, graph prompt tuning, and discrete structural codebooks, but full-spectrum adaptation remains unresolved.Source: §3.2 · p. 13

3.3 Task Heterogeneity

• Task heterogeneity covers node, link, graph, and specialized tasks with distinct objectives and inductive biases, making seamless universal adaptation largely unsolved.Explicit alignment reformulates tasks into shared objectives, whereas implicit alignment learns generalizable representations without task-specific reformulation.Source: §3.3 · p. 13

4.1 Unified Framework

• GFMs are pretrained on diverse graph datasets and then adapted to a broad spectrum of downstream scenarios, unlike traditional task-specific GNNs.The paradigm uses a large-scale graph database Dpt and a model backbone θ to learn generalized graph representations.Source: §4.1 · p. 14
• After pretraining, parameters θ∗ encode transferable knowledge about graph structure, semantics, and dynamics that can be directly applied or further adapted.Adaptation uses downstream data Dadapt and minimizes an adaptation loss to improve task-specific generalization.Source: §4.1 · p. 14
• The unified GFM framework comprises three components: backbone architecture, pretraining strategy, and adaptation mechanism.These components form the core methodology surveyed in subsequent sections.Source: §4.1 · p. 14
• Backbones process graph structure, attributes, and global context through architectures including GNNs, LLMs, and hybrid models.Backbone design enables scalability, multimodal integration, and cross-domain generalization.Source: §4.1 · p. 14
• Pretraining learns general-purpose graph representations from large-scale, often unlabeled corpora using objectives such as contrastive learning, graph masking, and predictive modeling.The goal is to capture universal graph patterns that support transferability, robustness, data efficiency, and zero-shot or few-shot generalization.Source: §4.1 · p. 14
• Adaptation aligns pretrained models with downstream tasks or domains through full or partial fine-tuning, lightweight tuning, or task-specific prediction heads.Proper adaptation leverages generalized knowledge to enhance performance, reduce data requirements, and accelerate deployment across graph scenarios.Source: §4.1 · p. 14

4.2 Backbone Architectures

• GFMs organize backbone architectures into graph models as predictors, language models as predictors, and graph-language co-training frameworks.Figure 4 depicts these as graph model prediction, language model prediction, and joint graph-language optimization through alignment.Source: §4.2 · p. 15, Figure 4 · p. 15

4.2.2 Language Model as Predictor

• Language-model predictors serialize nodes, features, and neighborhoods into text so LLMs can perform graph inference, but they may miss structural inductive biases.LangGFM, BeyondText, and GLM demonstrate textual graph reasoning, while structured tokenization, retrieval, and tuning address topology-related limitations.Source: §4.2.2 · p. 17

4.2.3 Graph-Language Co-Training

• Graph-language co-training treats graph and language models as co-equal components through shared-space alignment or iterative mutual refinement.GraphCLIP and ConGraT use cross-modal alignment, whereas GLEM alternates textual pseudo-labeling with graph propagation through a shared latent variable.Source: §4.2.3 · pp. 17–18

4.2.4 Discussion

• Graph backbones preserve connectivity and are parameter-efficient, language backbones generalize across textual and multimodal settings, and hybrid backbones jointly model structure and semantics at greater computational and design cost.Hybrid systems require careful alignment or pretraining to avoid modality collapse and overfitting, while graph and language systems respectively struggle with long-range dependencies and precise topology.Source: §4.2.4 · p. 18

4.2.1 Graph Model as Predictor

• Graph-model predictors use message passing or global attention to encode relational structure, supporting efficient graph reasoning but limiting long-range and multimodal modeling.GNNs aggregate neighborhood information, while Graph Transformers extend this to attention across all node pairs; auxiliary language modules can add textual knowledge.Source: §4.2.1 · pp. 15–16, §4.2.4 · p. 18

4.3 Pretraining Strategies

• GFMs organize pretraining around supervised, generative, and contrastive paradigms that learn transferable representations from graph data.Figure 5 depicts label-guided subgraph prediction, reconstruction of masked or corrupted graph components, and discrimination between similar and dissimilar graph views.Source: §4.3 · p. 18, Figure 5 · p. 19

4.3.1 Supervised Pretraining

• Supervised pretraining directly optimizes labeled node-, edge-, or graph-level objectives, aligning representations with downstream tasks but requiring costly high-quality annotations.OFA [22] unifies graph prediction tasks through nodes-of-interest, while Prodigy generates subgraph tasks through structural and semantic decomposition; supervised pretraining is often complemented by self-supervision.Source: §4.3.1 · p. 19

4.3.2 Generative Pretraining

• Generative pretraining learns transferable graph representations without task-specific labels by modeling raw data through autoregressive generation or auto-encoding reconstruction.Graph autoregressive models map graphs into ordered sequences to generate nodes and edges history-dependently, while graph auto-encoders reconstruct masked node features, edge features, or structure.Source: §4.3.2 · pp. 19–21

4.3.3 Contrastive Pretraining

• Contrastive pretraining learns discriminative representations by bringing positive pairs together and separating negative pairs, using instance-instance or instance-context objectives.Instance-instance methods compare augmented views, whereas instance-context methods align local representations with global graph summaries; DGI established the latter, with later extensions adding structural priors and few-shot adaptation.Source: §4.3.3 · pp. 21–22

4.3.4 Discussion

• No pretraining paradigm is universally superior: supervised methods maximize task alignment, generative methods provide scalable label-free reconstruction, and contrastive methods produce strong representations but depend on augmentation quality and intensive computation.Generative objectives may correlate weakly with downstream performance, while contrastive learning is sensitive to sampling and informative negatives and can be costly on large or densely connected graphs.Source: §4.3.4 · pp. 22–23

4.4 Adaptation

• The survey organizes GFM adaptation into transfer learning, distillation, test-time adaptation, graph prompting, in-context learning, and prototype learning, each targeting different supervision levels and deployment constraints.Figure 6 summarizes these paradigms and their differing supervision, generalization, and computational-efficiency profiles.Source: §4.4 · p. 23, Figure 6 · p. 24

4.4.1 Transfer Learning

• Transfer learning reuses pretrained structural and semantic knowledge, ranging from zero-shot direct application to full, adaptive, or parameter-efficient fine-tuning for limited-data downstream tasks.Full fine-tuning maximizes flexibility but risks overfitting, whereas adaptive and parameter-efficient methods reduce computation and trainable parameters through selective updates or lightweight modules.Source: §4.4.1 · pp. 23–24

4.4.2 Distillation

• Distillation transfers predictive, representational, and structural knowledge from large teacher GFMs to smaller students, reducing inference and resource costs while preserving relational information.Objectives combine ground-truth supervision with teacher-output matching; graph-specific methods can align embeddings, topology, attention, or multi-view knowledge.Source: §4.4.2 · pp. 24–25

4.4.3 Test-Time Adaptation

• Test-time adaptation updates models or inputs during inference using unlabeled test data and self-supervised signals, addressing distribution shifts without source data or retraining.GTrans refines graph features and topology, while LLM-TTT generates pseudo-labels for test nodes before adapting the GNN, avoiding manual annotations.Source: §4.4.3 · p. 25

4.4.4 Graph Prompting

• Graph prompting freezes the GFM and learns task-specific signals at the data or representation level, including feature prompts, inserted prompt nodes, and latent gating vectors.This data-centric strategy guides model behavior without parameter updates, but prompt construction can operate on graph inputs or hidden node representations.Source: §4.4.4 · p. 26

4.4.5 In-Context Learning

• In-context learning adapts language-capable GFMs without parameter updates by conditioning on demonstrations, but graph dependencies make representative example retrieval crucial for reliable predictions.AskGNN uses structural and semantic similarity to retrieve demonstrations, while retrieval-augmented generation supports graph tasks including knowledge graph completion.Source: §4.4.5 · pp. 26–27

4.4.6 Prototype Learning

• Prototype learning classifies nodes or graphs by proximity to class prototypes, offering interpretable, parameter-efficient, and few-shot-friendly adaptation through averaged representations or learnable class nodes.Prototype quality depends on well-formed embedding clusters; distance-based classification may miss complex boundaries in noisy or heterophilic graphs.Source: §4.4.6 · p. 27

4.4.7 Discussion

• The six paradigms occupy distinct operating regimes: transfer learning and distillation suit labeled static settings, while TTA, prompting, ICL, and prototypes target dynamic, low-resource, zero-shot, or few-shot use.Their limitations include overfitting, incomplete knowledge transfer, unstable unsupervised updates, prompt misalignment, poor demonstrations, and assumptions about embedding geometry.Source: §4.4.7 · pp. 27–28

5.1 Design Principle

• Universal GFMs must generalize across heterogeneous graph distributions, reconcile conflicting task objectives, and promote positive transfer through shared representations and task-aware adaptation [22] [25].The design targets cross-domain and cross-task generalization while preserving task-specific nuances.Source: §5.1 · p. 29
• Existing universal GFMs are organized into model-level unification, pretrain-level domain alignment, and adaptation-level mechanisms for efficient transfer.This framework examines how methods address the three core challenges of universal graph learning.Source: §5.1 · p. 29

5.2 Graph Model-Based Universal GFM

• Graph model-based universal GFMs generally follow a pretrain-then-adapt paradigm, using diverse multi-domain graph databases to learn transferable structural and semantic patterns before adapting to unseen graphs.Their backbones, pretraining methods, adaptation strategies, and handling of feature, structural, and task heterogeneity are summarized in Table 2.Source: §5.2 · p. 29

5.2.1 Model Unification

• Model unification follows explicit task reformulation or implicit architectural generalization, with explicit methods operating at link, subgraph, or tree levels.Explicit approaches include link prediction with class nodes, ego-graph encoding, and virtual-node representations, while implicit approaches modify architectures without changing task definitions.Source: §5.2.1 · pp. 29–31
• Implicit unification improves cross-task and cross-domain flexibility through permutation-aware architectures, semantic interaction graphs, mixture-of-experts, and topology-aware tokenization.HoloGNN, SCORE, AnyGraph, and OpenGraph respectively target symmetry, semantic relations, high-order interactions, and variable-sized graph representations.Source: §5.2.1 · p. 31

5.2.2 Domain Alignment in Pretraining

• Domain alignment addresses heterogeneous features through textual or multimodal encoders, model-based projections, reprogramming, SVD transformations, learnable tokens, expert routing, and graph patches.However, model-based alignment can fail on unseen domains because its mechanisms may be tightly coupled to pretraining feature distributions and structural patterns.Source: §5.2.2 · pp. 31–32
• Structural alignment uses domain-invariant objectives, shared motif vocabularies, graph prompts, and mixture-of-experts routing to accommodate diverse graph topologies.These methods respectively disentangle domain-specific structure, encode reusable motifs, calibrate spectral or contextual representations, and select specialized experts to reduce negative transfer.Source: §5.2.2 · pp. 32–33

5.2.3 Downstream Task Adaptation

• Downstream adaptation combines fine-tuning and transfer learning with prompt learning, prototype learning, and structural augmentation to improve efficiency and generalization.Prompting updates learnable tokens instead of the backbone; prototypes support few-shot and zero-shot prediction; UniAug uses diffusion-based structural generation pretrained on graphs from over 1,000 datasets.Source: §5.2.3 · p. 34

5.3 Language Model-Based Universal GFM

• LLM-based universal GFMs comprise graph tokenization, graph-specific post-training, and downstream adaptation through prompting, in-context learning, or instruction tuning.Tokenization maps nodes, edges, and attributes to sequences; post-training uses objectives such as masked token prediction or topology autoencoding; adaptation decodes task-specific predictions.Source: §5.3 · pp. 34–35

5.3.1 Model Unification

• Graph-to-text unification uses natural-language narratives or structured formats such as JSON and nested lists to align graph structure with LLM processing.Natural-language methods emphasize interpretability, templates, hierarchical neighborhoods, and guided reasoning, whereas structured methods preserve topology through serialized data, APIs, and recursive context trees.Source: §5.3.1 · pp. 35–36

5.3.2 Domain Alignment in Model Training

• Post-training improves graph-task alignment through supervised instruction tuning, preference optimization, and self-supervised objectives tailored to topology and node features.InstructGraph and InstructGLM use instruction-based training for graph reasoning and cross-task transfer, while LangGFM reports strong downstream performance, label efficiency, and robustness to domain shifts using topology and feature masked autoencoding.Source: §5.3.2 · pp. 36–37

5.3.3 Downstream Task Adaptation

• Downstream adaptation ranges from zero-shot prediction and basic in-context learning to structured prompting and agentic planning with memory.GraphICL combines task descriptions, anchor nodes, structural information, and demonstrations; GraphAgent uses hierarchical memory; QueryRAG integrates query nodes, neighbors, and labels.Source: §5.3.3 · p. 37

5.4 Graph-Language Co-Training Universal GFM

• Graph-language GFMs address information loss from graph linearization by combining GNN structural representations with LLM semantic reasoning through projection into token space.The framework comprises graph encoding, cross-modality projection, and language-based inference over prompts containing graph representations and task instructions.Source: §5.4 · pp. 37–38

5.4.1 Model Unification

• Model-unification methods align graph structures with LLM inputs using neighborhood and hop-field templates, graph-token grounding, translation, node tokenization, and task-structured prompts.These approaches target alignment, interpretability, topological integrity, and cross-task reasoning by converting graph entities or embeddings into token-compatible representations.Source: §5.4.1 · pp. 38–39

5.4.2 Domain Alignment in Model Training

• Domain alignment uses supervised fine-tuning, self-supervised objectives, and CLIP-like contrastive learning to couple graph structure with textual reasoning and improve transfer across tasks and domains.Self-supervised methods include text matching, sentence completion, topology autoencoding, and feature masked autoencoding, while GraphCLIP trains on LLM-generated graph-summary pairs for zero- and few-shot transfer.Source: §5.4.2 · p. 39

5.4.3 Downstream Task Adaptation

• Downstream adaptation supports zero-shot inference, in-context demonstrations and retrieval, and human-readable multi-turn explanations across graph applications.AskGNN purifies support examples for more representative and balanced prompts, while GraphTranslator demonstrates interpretability in behavioral analytics, social networks, and recommendation scenarios.Source: §5.4.3 · pp. 39–40

Discussion

• Across universal GFMs, GNNs prioritize efficiency and structure, LLMs prioritize language-driven flexibility, and hybrids pursue unified capabilities at the cost of greater system complexity.These differences reflect broader trade-offs among model expressiveness, scalability, generalization, and interpretability.Source: §5.5 · p. 40

Language Model-Based GFMs

• LLM-based GFMs enable flexible zero-shot and in-context reasoning across heterogeneous tasks, but linearization can reduce structural fidelity and large models impose high computational costs.They also support multimodal inputs and produce interpretable natural-language reasoning, while requiring template engineering because they lack graph inductive biases.Source: §5.5 · p. 40

Graph-Language Co-Training GFMs

• Hybrid GFMs such as LLaGA, GraphTranslator, and GraphCLIP combine structural and semantic reasoning for multimodal, cross-domain transfer, but require complex architectures and careful representation alignment.These models support structured and unstructured inputs and can adapt through prompting, fine-tuning, or contrastive alignment, while multimodal supervision integration remains challenging.Source: §5.5 · p. 40

6.1 Design Principle

• Task-specific GFMs must preserve task-aware inductive biases while aligning disparate graph distributions and balancing domain generalization against task-specific adaptation.Design principles include domain-adaptive architectures, feature modulation, regularization, normalization, and adversarial training to reduce domain overfitting and catastrophic forgetting.Source: §6.1 · p. 41

6.2.1 Handling Graph Heterogeneity

• Node-level GFMs address heterogeneous feature and structure spaces through imputation, bipartite transformations, fully inductive features, generative pretraining, prompting, and structure-aware self-supervision.GCNmf and PCPI recover missing features; GRAFENNE, GraphAny, and FUG target dynamic or diverse feature spaces, while GPT-GNN, GPPT, and simMLP model structural information.Source: §6.2.1 · pp. 42–43

6.2.2 Cross-domain Alignment

• Cross-domain node classification methods include unified GNNs, structural alignment, graph prompting, graph class-incremental learning, Transformer encoders, and hybrid GNN–LLM pipelines.GCOPE [25], TPP [239], GraphControl, GraphLoRA, MDGFM, GraphAny, GSPT, GraphFM, GDL4LLM, and hybrid methods such as G2P2 and ENGINE target transfer across domains and feature or structure distributions.Source: §6.2.2 · pp. 43–44

6.2.3 Domain Generalization v.s. Task-specific Adapation

• For node-level tasks, future research should explore graph pattern modeling beyond message-passing frameworks, alongside robustness and explainability of GNNs, which remain under-explored.Source: §6.2.4 · p. 44

6.3 Link-Level Task

• Link-level GFMs must transfer across arbitrary entity and relation vocabularies while handling heterogeneous relation semantics and temporal dynamics.A major setting involves novel nodes and relation types at test time, requiring representations that generalize across domains and datasets.Source: §6.3 · p. 45, §6.3.1 · p. 45

6.3.1 Inductive Reasoning Approaches

• Inductive link reasoning uses relation-graph transformations, double equivariance, motif-based relational encoders, prompting, and in-context learning to support unseen nodes, relations, and graphs.Ultra [28] and UltraQuery [29] parameterize unseen relations; MTDEA, DEq-InGram, and ISDEA+ establish double-equivariant approaches; KG-ICL and UniLP use prompts or in-context learning for transfer.Source: §6.3.1 · p. 45, §6.3.2 · p. 45

6.3.3 Transformer-based Approaches

• Transformer and hybrid link-level methods combine graph aggregation with language modeling or adversarial transfer, while future work targets dynamic heterogeneous graphs and lower preprocessing and training costs.GraphFormers and Edgeformers integrate textual and structural information; DGASN and GITL address cross-network transfer through domain adaptation or graph intersection.Source: §6.3.3 · p. 46, §6.3.4 · p. 46, §6.3.5 · p. 46

6.4.4 Graph Generation

• LGGM pretrains on over 5,000 graphs across 13 domains for zero-shot and fine-tuned generation, while text prompts control graph structure and domain.InstructG2I combines graph, image, and text attributes to guide controllable diffusion-based image generation with smooth interpolation across styles or domains.Source: §6.4.4 · p. 48

6.4.5 Hybrid Approaches

• CDFSGC and CDTC enable few-shot cross-domain graph classification by learning transferable graph views or coordinating source meta-tasks with labeled target prompts.CDFSGC uses contextual and topological views with metric-based meta-learning, whereas CDTC combines task coordination, optimization-based meta-learning, and reinforcement learning.Source: §6.4.5 · pp. 48–49

6.4.6 Future Directions

• Future task-specific GFMs should unify structural encodings, hierarchical pooling, scalable training, prompt-based adaptation, multimodal integration, cross-domain benchmarks, explainability, and fairness.Proposed techniques include subgraph sampling, linearized attention, distributed training, denoising autoencoders, data augmentation, interpretable pooling, and adversarial debiasing.Source: §6.4.6 · p. 49

6.5 Question Answering

• For question answering, GFM-RAG retrieves from knowledge-graph indexes without target fine-tuning, while G-Retriever, GITA, and related multimodal methods support graph-text-image reasoning.G-Retriever provides the GraphQA benchmark; VGCURE evaluates visual-language understanding across 22 tasks, and GT2VEC aligns graph and text embeddings contrastively.Source: §6.5 · pp. 49–50

6.6 Graph Anomaly Detection

• Graph anomaly GFMs support cross-domain, few-shot, and zero-shot detection through domain alignment, prompt tuning, in-context learning, and graph-agnostic representations.Future work emphasizes dynamic and heterogeneous graphs, adversarial and noise robustness, and interpretability for high-stakes applications such as cybersecurity and fraud detection.Source: §6.6 · pp. 50–51

6.7 Recommendation

• Recommendation GFMs combine pretrained or LLM-enhanced GNNs with semantic alignment and scalable architectures to model cross-domain preferences, sparse feedback, and massive user-item graphs.PCRec uses contrastive pretraining, LLMRec augments interactions and attributes, RLMRec aligns collaborative and semantic representations, and introduces a two-tower heterogeneous GFM.Source: §6.7 · p. 51

7.1 Design Principle

• Domain-specific GFMs require customized architectures, pretraining, and adaptation because molecular motifs and knowledge-graph relations demand different inductive biases.Shared representations can benefit multiple tasks within a domain, but task interference may cause negative transfer; task-aware heads and alignment strategies address this challenge [30].Source: §7.1 · p. 52

7.2 Biology & Molecule Graph

• Molecular GFMs must model chemical symmetries, multiscale interactions, quantum effects, flexible 3D conformations, huge chemical space, and limited labels.Graph backbones span equivariant 3D models such as the Equivariant Foundation Model and JMP [30], 2D multitask models including Mole-BERT and Graphium, and compact designs such as MiniMol.Source: §7.2 · p. 52, §7.2.1 · p. 53

7.2.2 Language Model-based Approaches

• Molecular language-based GFMs tokenize molecular structures or sequences, ranging from hybrid graph–Transformer models to LLMs for property prediction, protein folding, genomics, and cross-modal retrieval.Auxiliary GNN embeddings can be converted into molecule tokens and combined with text, images, or instruction-based frameworks for generation, retrieval, captioning, and editing.Source: §7.2.2 · p. 54

7.2.3 Hybrid Approaches

• Hybrid molecular GFMs combine graph inductive biases with language reasoning for reaction prediction, zero-shot discovery, scalable property prediction, simulation, retrieval, and text-guided molecular manipulation.Future directions emphasize equivariant architectures, large-scale self-supervised pretraining, physics-informed modeling, and multimodal retrieval augmentation for robust and interpretable molecular applications.Source: §7.2.3 · p. 54, §7.2.4 · p. 55

7.3 Algorithmic Graphs

• Algorithmic graph GFMs target procedural tasks such as shortest paths, satisfiability, sorting, and symbolic mathematics, requiring structural invariants, multistep reasoning, and size generalization.Task-oriented systems include multitask message passing, program synthesis with compiler feedback, pattern recognition, instruction tuning, reasoning traces, graph-to-text serialization, and native topological embeddings.Source: §7.3 · p. 55, §7.3.1 · pp. 55–56

7.3.2 Benchmarking and Multi-Agent Collaboration

• Benchmarks evaluate correctness, hallucination, natural-language graph queries, semantic and structural reasoning, while multi-agent and tool-augmented systems decompose graph problems into parsing, retrieval, coding, reasoning, and node-level subtasks [33].Encoding strategies preserve neighborhoods through JSON, centrality-ordered linearization, staged reasoning, logarithmic-depth transformers, hypergraph prompts, structural-shift tests, path comparison, and conversation-tree reasoning [375].Source: §7.3.2 · p. 56, §7.3.3 · p. 56

7.4 Document Network

• Semantic document GFMs jointly model textual semantics and graph structure but face content–structure alignment difficulties and cross-domain scalability challenges.Prompting, dual objectives, contrastive alignment, topology refinement, variational EM, and explanation-enriched GNN inputs combine relation-aware semantics with structural reasoning.Source: §7.4 · p. 57

7.5 Heterogeneous Graph

• Heterogeneous graph GFMs evolve from self-supervised and prompting methods to language and hybrid models that jointly represent node types, relations, structural context, and textual semantics.Representative approaches address auxiliary-task balancing, few-shot scarcity, contrastive learning, graph prompting, structural-textual tokens, metapath prompts, and GNN–LLM dual encoders; hybrid models such as Heterformer and THLM harmonize these signals.Source: §7.5 · pp. 58–59
• Heterogeneous graph GFMs should improve multimodal structural-semantic alignment, interpretability, adaptation to evolving graphs, scalability, and evaluation standardization.These directions target more robust and contextually comprehensive models.Source: §7.5 · p. 59

7.6 Knowledge Graph

• Knowledge graph GFMs primarily target logical query answering and inductive link prediction under compositional, logical, and unseen-entity or relation generalization.KGs require inferring implicit correlations among entity-relation-entity triplets while maintaining logical consistency.Source: §7.6 · p. 59
• Logical query methods use vocabulary-independent operators, query-specific prompt graphs, or LLM textual understanding to support multi-hop reasoning and zero-shot generalization across knowledge graphs [29].UltraQuery [29] handles projection and logical operations inductively, KG-ICL uses distinct message-passing networks, and KICGPT enhances knowledge graph completion with LLMs.Source: §7.6 · p. 59
• Inductive link prediction transfers relation representations to unseen entities and graphs through relation-based meta-graphs and higher-order multi-relation motifs [28].ULTRA [28] propagates across relations rather than entities, while Higher-order KGFM captures complex relational dependencies.Source: §7.6 · p. 59

7.7 Temporal Graph

• Temporal graph GFMs must jointly model within-snapshot spatial structure and across-snapshot temporal dependencies, since handcrafted temporal diffusion often fails on unseen patterns and rich evolving text.LLM4DyG finds performance declines as graph size N and temporal density T increase, while DST2 separates spatial from temporal reasoning; FlowGPT evaluates diffusion tracing and influential-node identification.Source: §7.7 · p. 60
• Cross-network pretraining enables temporal transfer: MiNT [392] uses one temporally aware encoder across diverse networks and outperforms temporal GNNs trained on individual datasets.Future temporal GFMs should explore hierarchical temporal abstraction, adaptive serialization, and hybrid GNN-LLM architectures for short- and long-term reasoning.Source: §7.7 · p. 60

7.8 Academic Network

• LitFM integrates citation-graph retrieval and instruction tuning to support citation prediction, related-work generation, and literature-review summarization while mitigating citation hallucination and knowledge incompleteness.Its graph retriever uses adjacency proximity and citation-aware embeddings, with future extensions including temporal citations, multimodal paper signals, and composed scholarly tasks.Source: §7.8 · pp. 60–61

7.9 Causal Graph

• Causal GFMs combine textual evidence with sparse, directional graph structure, but current LLM methods struggle with indirect causal chains and degrade on high-degree nodes or long paths.Causal-LLM performs unsupervised pairwise causal discovery, while CLEAR shows sensitivity to graph structure, phrasing, and context order; future work emphasizes causal priors, uncertainty-aware embeddings, and multimodal integration.Source: §7.9 · p. 61

8.1 Emergence and Scaling Law

• Scaling laws link larger models, datasets, and compute to improved performance, but whether graph models reproduce these effects remains unresolved [12] [13].Graph scaling laws remain less established than in language models.Source: §8.1 · p. 62

8.1.1 Well-Structured Graphs

• Molecular and atomic graphs support scaling and transfer: JMP [30] pretrained on approximately 120 million systems, while DPA-2 used over 10 million atomic structures for unseen-task transfer.These results attribute stronger performance and transferability to large-scale pretraining on naturally structured graphs [30].Source: §8.1.1 · p. 62
• Molecular scaling exponents reached 0.17 for the largest dataset and 0.26 for equivariant GNN potentials, while modality, pretraining, partitioning, and capacity strongly affected scaling.Pretraining helps most in low-data regimes, random splits are most efficient, and larger models are not uniformly optimal.Source: §8.1.1 · p. 62
• MiNT pretrained on 64 temporal transaction networks and transferred to 20 unseen networks, achieving superior zero-shot performance that improved with more training networks.This extends scaling evidence beyond molecular and atomic graphs.Source: §8.1.1 · p. 62

8.1.2 General Graphs

• For general graphs, model depth matters, node or edge counts better define data scale than graph-instance counts, and graph SSL lacks consistent downstream scaling.Existing analyses are also limited by small datasets or by examining model scaling without data-scaling effects.Source: §8.1.2 · p. 63

8.2.1 Single-Task Transferability

• Single-task transferability requires unified handling of homophily and heterophily, expressive link proximity modeling, and motif representations beyond standard message-passing limits.Textual context, prediction aggregation, labeling tricks, positional embeddings, disentanglement, invariance learning, and expressive GNNs address these challenges.Source: §8.2.1 · pp. 63–64

8.2.2 Cross-Task Transferability

• Graphon-based transferability assumes shared latent graph structure, but strong assumptions and difficulty identifying a common graphon limit practical cross-domain use [409, 410, 288, 411].Graphon methods provide embedding bounds and pretraining or fine-tuning strategies when target graphs lie in the shared graphon space.Source: §8.2.2 · p. 64
• Cross-task transfer can use motifs, spectral stability, shared underlying spaces, or subtree patterns; subtrees are GNN-learnable but may discard structural dependencies [22] [23].Higher ego-graph similarity correlates with better transferability, whereas tree representations trade expressiveness for potential information loss.Source: §8.2.2 · p. 64

9.1 Tasks and Domains Overview

• Benchmark datasets cover e-commerce, academia, knowledge bases, molecular science, temporal graphs, social networks, brain graphs, and images across varied graph-learning scenarios.Together, these resources encompass different scales, features, structures, and application domains.Source: §9 · p. 65, §9.1 · p. 65, §9.1.2 · p. 65

9.1.1 Tasks

• Node, link, and graph classification require modeling node features, neighborhood structure, higher-order connectivity, and graph-level local and global topology.Graph classification commonly uses hierarchical pooling to identify discriminative subgraphs while progressively coarsening representations.Source: §9.1.1 · p. 65

9.1.2 Domains

• Domain characteristics materially shape benchmark design, from heterogeneous interaction types and temporal citation evolution to ontological constraints and chemically regular molecular structures.E-commerce graphs contain product interactions; academic graphs evolve over time; knowledge bases encode hierarchical relations; molecular graphs reflect bonding constraints.Source: §9.1.2 · p. 65
• Temporal, social, brain, and image graphs add evolving dependencies, small-world structure, multi-scale organization, and irregular spatial relationships to benchmark coverage.These properties support temporal prediction and anomaly detection, social-network analysis, neurological studies, and visual recognition tasks.Source: §9.1.2 · pp. 66–67

9.2 Benchmark Descriptions

• Recent benchmarks include text-attributed, temporal, molecular, structural-only, and specialized datasets for node, link, temporal, property-prediction, topology, and domain-specific tasks.Examples include Text-space Graph Foundation Models, Knowledge Base Benchmarks [28], Temporal Graph Benchmarks, TAGLAS, Graph Pattern Recognition, and specialized resources,, [418].Source: §9.2 · p. 67

10.1 How to Enhance Scalability?

• GFMs need scalable backbones, high-level semantic pretraining objectives, and unified learning instances to establish graph scaling laws across tasks.Graph transformers and substructure tokens may improve scalability, while reconstructing high-level structures and scaling subgraphs or trees remain open directions.Source: §10.1 · p. 68

10.2 How to Mitigating Data Scarcity?

• Mitigating graph data scarcity requires automated collection, synthetic generation that preserves structure and semantics, and high-quality data valuation.Potential sources include academic repositories, biomedical databases, and online knowledge graphs; diffusion models and LLMs can augment graph structures and attributes, but graph-quality metrics remain open.Source: §10.2 · pp. 68–69

10.3 How to Better Evaluate GFMs?

• Effective GFM evaluation requires large-scale benchmarks aligned with real-world scenarios and metrics for generalization, robustness, interpretability, reliability, and ethics.Benchmarks should cover diverse graph structures, multiple tasks, and varying supervision levels, while testing domain adaptation and behavior under distribution shifts and adversarial or noisy data.Source: §10.3 · p. 69

10.4 How to Better Utilize GFMs?

• GFMs should support zero-shot and in-context adaptation, target applications beyond conventional graph models, integrate multimodal knowledge, and retain human oversight.Open directions include autoregressive graph learning without explicit task-specific adaptation, chip design, combinatorial optimization, relational databases, unified or modality-specific multimodal models, and human feedback for interpretability and reliability.Source: §10.4 · pp. 69–70

10.5 Advanced Theoretical Understandings

• Theory must explain cross-domain transfer, resolve pattern conflicts, guarantee robustness and trustworthiness, and characterize generalization beyond subtree-based learning tokens.The same triangle pattern can have different meanings in social and molecular graphs, while real-world challenges include structural shifts, adversarial perturbations, missing or noisy data, fairness, and the fitting–generalization trade-off.Source: §10.5 · pp. 70–71

• The survey proposes a modular framework comprising backbone architectures, pretraining strategies, and adaptation mechanisms for unifying diverse GFM approaches.This framework addresses challenges arising from graph heterogeneity, non-Euclidean structure, and cross-domain transferability.Source: §11 · p. 72
• GFMs are organized into universal, task-specific, and domain-specific classes according to their intended generalization scope.The survey reviews representative methods, design principles, and relative strengths and limitations across these categories.Source: §11 · p. 72
• The survey examines theoretical foundations including expressiveness, transferability, and generalization guarantees alongside empirical trends.Source: §11 · p. 72
• Key open challenges include scaling GFMs to massive graphs, integrating multimodal signals, establishing principled evaluation protocols, and explaining transferability and generalization theoretically.Source: §11 · p. 72
• Future research should develop more scalable, interpretable, and adaptable architectures, expand real-world graph pretraining corpora, and advance theoretical frameworks for GFM behavior.The survey envisions GFMs as foundational infrastructure for general-purpose graph intelligence in scientific discovery, industrial systems, and structured-data decision-making.Source: §11 · p. 72