Graph Generation

Generating large attributed graphs requires reproducing the topology, generating attributes jointly with the structure, and remaining scalable. Many real-world graphs exist as a single large graph, so a generative model has to generalize from the one graph it is fit on, without independent samples. We present Schema, which recursively decomposes a reference graph into a hierarchy of soft communities, assigning each node a membership distribution. Generation is then split into three stages, each trained independently: (1) synthesizing node attributes conditioned on soft memberships, (2) generating intra-community edges from local structural context, and (3) modeling inter-community connections over bridge nodes whose membership mass is distributed across several communities. No stage forms the full adjacency matrix, and each stage operates on a subgraph bounded by the community size. We also introduce an evaluation protocol that covers structural fidelity, memorization, downstream utility, and scalability. On four real-world attributed graphs, Schema recovers the balance between local and long-range structure more closely than any other model that generates attributes, while reproducing only a small fraction of the reference edges. It retains the downstream accuracy of the reference graph without raising it artificially above that level. Baselines that match its structural fidelity memorize the reference, while those with higher downstream accuracy either exceed the reference accuracy or fail to complete on the larger graphs. We measure scalability on six additional graphs with up to 10 million nodes.

Several discrete design tasks, such as molecular discovery, require diverse collections of useful candidates at low computational cost. High validity alone does not guarantee a useful candidate library: repeatedly generating the same valid structures leaves few distinct alternatives. Training for both feasibility and diversity is challenging because many relevant criteria can only be evaluated after hard decoding. To address this challenge, we propose EGO (Evolutionary Generators with One-step inference), a framework for training compact generators directly on discrete outputs. The method combines distribution matching with structural constraints and optional diversity or history-dependent rewards, using antithetic low-rank evolution strategies without requiring criterion-specific differentiable surrogates. Once trained, the generator produces the entire graph in a single neural-network evaluation. On molecular generation benchmarks, our compact generator achieves over $50\times$ the valid-and-unique yield per estimated dense operation compared to recent one-step flow-map baselines while retaining high chemical validity. In scaffold completion, EGO achieves an observed $44.3\times$ speedup over MoLeR in generation to SMILES and produces approximately $10\times$ as many filter-passing proposals within matched time budgets for generation and screening. Beyond chemistry, EGO produces $1.54\times$ as many distinct held-out elite architectures as relaxed gradient training on NAS-Bench-101. The low generation cost may enable real-time candidate generation across discrete design tasks, supporting interactive exploration of constrained design spaces and rapid construction of candidate sets for downstream evaluation.

Planar graphs are central to applications across science and engineering, yet existing generators provide limited support for goal-directed generation under hard structural and geometric feasibility constraints. We propose a dataset-free method for generating planar graph embeddings by combining parametric graph grammars with safe reinforcement learning to optimize generic task-specific objectives while satisfying constraints during construction. We formulate the generation process as a constrained Markov decision process, where the graph grammar defines the state and action spaces. We further introduce an action projection that maps sampled actions toward state-dependent safe sets, improving constraint satisfaction during training. In contrast to classical graph generators and deep generative models, which typically offer limited goal-directed control or rely on weak constraint satisfaction, our method constructs feasible planar graph embeddings directly during generation. We also introduce a benchmark suite for constrained and goal-directed planar graph generation, together with classical and deep generative baselines. Across all benchmark tasks, our method consistently outperforms baselines while satisfying the formulated constraints.

Graphs provide a natural representation of many complex systems, ranging from social platforms to ecosystems. However, the development of graph-based machine learning methods is often constrained by the limited availability of large and diverse graph datasets. In this paper, we introduce $\texttt{DCBA}$, a model-based approach to graph data augmentation that infers the configuration of a synthetic graph generator from an observed network. We instantiate the proposed framework using the $\texttt{ABCD}$ generator, which produces scale-free networks with community structure. Our model learns a joint representation of graphs and generator parametrisations using a multi-positive contrastive objective with soft negative weighting. The learned representation enables the prediction of an $\texttt{ABCD}$ configuration whose stochastic realisations preserve the macrostructural properties encoded by the generator. Experiments show that $\texttt{DCBA}$ recovers generator parameters more accurately and robustly than an algorithmic inverse-modelling baseline. Its downstream utility is further demonstrated in community detection, where inferred configurations used to fine-tune $\texttt{PRoCD}$ improve AMI on average by $161\%$ on synthetic and $273\%$ on real-world networks.

Generative modeling of graph-structured data is crucial for tasks ranging from drug discovery to social network simulation. Among these models, denoising diffusion models have achieved great success in graph generation by learning to progressively reverse a process that adds noise to the original graph. However, the standard noise-prediction approach of diffusion models is suboptimal for graph data. The goal for a graph generative model is to learn the clean graphs' topological properties, such as connectivity and degree distribution. Because a diffusion model that predicts noise does not explicitly learn these topological properties, it is challenging for the model to output graphs with the desired structural statistics. To address this challenge, we introduce Direct Graph Flow Matching (DiGFM), a novel graph transformer model guided by two goals: predict clean graphs and improve sampling efficiency. Distinct from the prevailing diffusion approach, DiGFM employs a continuous flow-matching paradigm and integrates direct graph prediction. Specifically, DiGFM maps the prior noise distribution to the clean graph distribution via a multi-step process: the model repeatedly predicts the underlying clean graph, and a transformation is employed to convert the model output to the velocity vector that points in the direction toward the clean graph distribution. This design enables DiGFM to generate high-quality samples using only 2.5% to 15.6% of the steps required by diffusion-based models, which leads to a 5.3x to 257x speedup in wall-clock inference time. Experiments demonstrate that DiGFM outperforms or matches prior state-of-the-art models across general graph benchmarks and molecular datasets, generating graphs with strong adherence to ground-truth structural statistics at significantly faster inference speeds.

Graph generative models increasingly rely on Graph Transformers (GT) to capture complex dependencies among nodes and edges. While deeper architectures should provide greater expressive capacity and a broader receptive field, their effectiveness can decline with depth: repeated self-attention progressively contracts node representations, impeding information flow and gradient propagation. We analyse this phenomenon from a dynamical systems perspective, focusing on how the denoiser's spectral dynamics affect graph generation. We show that standard GT denoisers become increasingly dissipative as depth grows, leading to vanishing gradients and representation collapse. To isolate the effect of these dynamics, we construct a permutation-equivariant GT with inherently stable, non-dissipative transport. We also introduce a damping mechanism that continuously interpolates between non-dissipative and increasingly contractive regimes, enabling a direct assessment of how dissipation influences generation. Experiments on synthetic and molecular graph generation benchmarks show that the gap between these regimes widens with depth: non-dissipative dynamics preserve representation diversity and gradient flow, sustaining strong generative performance, whereas greater contraction progressively impairs it. These findings identify the denoiser's dynamical regime as a key design factor for deep graph generative models.

Tree-like branching structures are common in nature, from botanical trees to neurons, blood vessels and respiratory trees. Their branching shape often reflects function, making structural modelling central to understanding how these systems work. Because acquiring real-world 3D data is often expensive or infeasible, realistic generative models are valuable for simulation and data augmentation. Existing morphology-specific models either constrain how topology is generated or rely on hand-tuned, mechanistic procedures. Generic 3D graph generators, by contrast, do not exploit or enforce the structure of trees. We propose Autoregressive Frontier Expansion, a generative framework that constructs trees through an iterative expansion process, simulating the biological growth of real trees. At each step, a flow-matching model parameterised by an SO(2)-equivariant GNN expands the frontier by predicting whether each active branch bifurcates or terminates. We evaluate our method on cortical neurons and botanical trees in unconditional, class-conditioned, and morphology-guided generation. Across both domains, the generated morphologies agree closely with the reference distributions and, in conditional experiments, with the specified targets.

Natural load-bearing and transport networks are not assembled in a single step; they emerge through a temporally ordered process of growth, branching, reinforcement, and loop formation. Inspired by this developmental logic, this work introduces a morphogenetic graph-generation framework for mechanical lattices in which a discrete dot matrix provides potential nodes and the final architecture is created by sequential cross-layer and intra-layer growth. The same rule is visualized in two dimensions as a leaf-vein-like developmental sequence and implemented in three dimensions on a 3x3x3 nodal matrix containing 27 candidate nodes. A dataset of distinct three-dimensional lattices was evaluated by beam-based finite element analysis and represented directly as graphs. A graph convolutional neural network (GCNN) with three graph-convolution layers and dual global pooling learns the topology-property mapping and predicts effective compressive stiffness. Coupling the GCNN surrogate with rapid structural sampling enables inverse design: for a target stiffness of 1000 MPa, the selected design was predicted at 1042.43 MPa and validated by finite element analysis at 1027.49 MPa. Beyond straight members, the framework has also been extended to parameterized horseshoe-shaped curved beams made of nonlinear materials, enabling topology-geometry design toward prescribed deformation shapes. Our work provides a paradigm for augmenting the database of mechanical metamaterials, and the resulting perspective links biological morphogenesis, graph learning, and nonlinear shape programming in a unified generative design framework for architected materials.

Discrete diffusion models are a prominent family for graph generation, but standard class-conditional mechanisms embed the class signal in the denoiser during training, tying the conditioning mechanism to the trained model. Classifier guidance avoids this coupling in continuous domains by steering a frozen model with a classifier's gradient, but discrete graph diffusion samples discrete edge states, so gradients cannot propagate through the sampled graph. We introduce ProtoGuide, a post-hoc, backbone-agnostic framework that recovers an analogous mechanism. At each reverse step the denoiser's per-edge output is relaxed into a differentiable soft adjacency, embedded by a frozen Siamese graph neural network, and scored against a target-class prototype and its nearest competitor; the resulting per-edge gradient, damped by a cosine schedule, is injected back into the denoiser output. All components stay frozen, so guidance is retargeted by supplying a different prototype. On five classes of real-world networks and two architecturally different backbones, EDGE and DiGress, ProtoGuide raises macro classification accuracy from 50.7% to 73.5% and from 73.6% to 83.8%, and outperforms DiGress's built-in conditional training under our configuration. Gains are largest where the unguided models are weakest, and are not uniform across classes. Per-graph coverage remains high in most settings, while distributional effects are class-dependent. A Best-of-N selection baseline matches this accuracy given enough oversampling, but at a substantial cost in graph diversity. An independently initialized classifier, a directionality test, and a few-shot analysis support target-directed steering and robustness to very small support sets.

Graph Neural Networks (GNNs) are powerful models for handling attributed graphs in tasks such as classification, link prediction, and community detection, as they enable the aggregation of information from both structural and semantic sources. However, progress in community detection is hindered by the lack of high-quality datasets, since ground-truth community labels are often unavailable and most algorithms proposed in recent literature rely on the same benchmark datasets for model training and evaluation. To address this issue, attributed random graph generators are commonly employed to create synthetic graphs for assessing the strengths and limitations of GNN-based models. Nevertheless, most existing generators rely heavily on power-law degree distributions, despite recent evidence indicating that scale-free networks are rare, particularly in social network contexts. Moreover, state-of-the-art attributed graph generators provide limited flexibility, as they do not allow users to construct communities with varying densities, degree distributions, and sub-community structures. To overcome these limitations, we introduce the Synthetic Community-Aware Attributed Graph Generator (SynCo), a graph generation algorithm that allows users to control the node degree distribution and sub-community structure. We evaluate SynCo across three different tasks: graph mimicking, hyperparameter evaluation, and node clustering tuning. The results show that our model outperforms state-of-the-art approaches in synthetic graph generation and data augmentation, while preserving the original distributions of duplicated and augmented datasets, as confirmed by statistical tests well know in literature. We also demonstrate the ability of SynCo to generate nodes in large scale, up to 2.1 million nodes.

Learning graph structures from data is a fundamental problem that spans a wide range of signal processing and machine learning tasks. While significant effort has been made to tackle the problem, existing research has largely evolved along two parallel directions. The first seeks to infer the topology of an individual graph from observations supported on it, whereas the second seeks to learn a generative distribution from observed graph instances, enabling the sampling of new graphs. This review presents a unified framework that connects these formulations by viewing them as inverse problems of a common generation process for graph data. We review the major methodologies within this framework, highlight their relationships, strengths, and limitations, and identify opportunities for integrating ideas across paradigms. By bridging graph topology learning and graph generation, this review provides a broader cross-disciplinary perspective on the field and outlines promising directions for future research.

Multi-Agent Systems (MAS) have recently moved from static workflows toward dynamically generated collaboration topologies. However, existing topology generation methods rely primarily on the parametric knowledge of large language models, with external search or retrieval used only as a reactive tool rather than an explicit determinant of collaboration structure. This leads to structure-knowledge misalignment, where systems exhibit redundant interactions or insufficient verification in knowledge-intensive tasks. We propose K-GAT (Knowledge-Guided Agent Topology Generator), a neuro-symbolic framework that formulates collaboration topology design as a knowledge-conditioned structure learning problem, integrating external evidence directly into autoregressive graph generation. Extensive experiments on knowledge-intensive benchmarks demonstrate K-GAT's efficiency and effectiveness: notably on the expert-level GPQA dataset, K-GAT outperforms the LLM-Debate baseline by a substantial margin of +15.7% in accuracy, while consuming less than half the computational tokens.

Recent Large Multimodal Models (LMMs) have achieved impressive performance in recipe generation from food images.However, cooking is a structured transformation process in which ingredients undergo state changes through ordered actions,while free-form recipe language leaves the corresponding entities, intermediate states, and dependencies largely implicit and entangled.A graph representation makes this procedural knowledge explicit and compositional, providing a structured basis for assessing whether model outputs encode process-level knowledge rather than merely presenting plausible textual descriptions. To address this limitation, we present ReGraph, a large-scale recipe graph dataset that represents ingredients, cooking actions, and tools as entities, uses entity attributes to describe ingredient state changes, and employs typed relations to encode manipulation targets, destinations, and procedural ordering. ReGraph further incorporates explicit Recipe Reasoning Chain-of-Thought (RR-CoT) traces, providing auxiliary supervision for procedural decomposition and structured graph generation. Building on ReGraph, we propose Recipe Graph Learning (RGL), a two-stage framework that enables LMMs to generate a plausible fine-grained cooking workflow from a food image in the form of a structured recipe graph. Under a deterministic, schema-aware matching protocol, our experiments reveal a substantial gap between text-generation quality and recoverable procedural structure: recipes produced by existing approaches achieve competitive text-generation scores yet yield limited reference-aligned entity and relation structure under the ReGraph schema. In contrast, across two representative LMM backbones, RGL consistently improves the generation of cooking entities and procedural relations, while our analysis further shows that fine-grained ingredient-state capture remains the most challenging dimension.

Generative models of temporal graphs are trained on one stretch of an evolving network and deployed on the next, and they degrade badly in the gap. We show this degradation is derivable, general, and not fixable from observations. The masked flow-matching loss decomposes exactly, with no independence assumption, into an irreducible entropy plus a divergence whose derivative along the training path is positive precisely for structures rare during training and common at deployment, diverging as their training probability goes to zero. Empirically the trade-off is a power law with exponent $-0.605$ ($R^2=0.9977$), and drift raises the sampler's error floor without changing how many steps reach it: across seven well-powered conditions the drift-period marginal error varies by at most $6\%$ over a $50\times$ range of sampling budgets, while the floor sits $2.2\times$ to $34.3\times$ above the in-period floor. Because the deployment period is observed, correction looks like a matter of measurement. It is not. We prove that any corrector measurable with respect to past observations leaves at least the conditional variance of the statistic it tracks, and that trend extrapolation beats trusting the last observation only when $μ^2>v(1-2ρ)$. Both premises are measurable and both go the wrong way: the drift is trendless and mean-reverting, with a one-step innovation as large as the drift itself. An oracle removes $60\%$ of the error, the best observation-based corrector recovers $5.7\%$ of that, and extrapolation is strictly worse than doing nothing clever.

Data-driven generative models can extend partially observed simulation trajectories into ensembles of alternative future scenarios. However, consistency with a learned trajectory distribution does not ensure that generated continuations satisfy the structural conditions of the simulated system. This paper presents a method for learned scenario continuation and post-generation structural validation in dynamic graph simulations. A conditional diffusion model generates future graph-state trajectories from partial histories, while an external symbolic layer evaluates each continuation using a Boolean admissibility indicator and a continuous violation score. This information supports hard filtering and soft weighting, with optional projection considered as a deterministic repair baseline. The method is evaluated on two controlled dynamic-graph regimes sharing the same continuation architecture and training protocol but differing in dimensionality and dependency complexity. Evaluation considers invalid probability mass, scenario retention, effective sample size, diversity, robustness, and calibration. In the compact positive-control regime, unconstrained invalid mass is 0.002996, indicating near-complete overlap between the learned and admissible scenario spaces. In the medium-complexity regime, invalid mass rises to 0.155929. Hard filtering removes all invalid scenarios while retaining 84.4% of generated continuations. Soft weighting preserves an effective sample size ratio of 0.998764 but reduces invalid mass only to 0.148807. These results show that learned-distribution support, structural admissibility, and probability calibration can diverge and should therefore be assessed separately in learned simulation-scenario generation and management.

Neural Markov Logic Networks (NMLNs) are a flexible neurosymbolic relational model. Previous work has shown that, although NMLNs achieve strong performance as generative models for small relational structures, they underperform diffusion-based generative graph models on larger structures. In this paper, we strengthen NMLNs along two main dimensions: (i) we increase the expressive capacity of their potential functions using graph neural networks, and (ii) we develop a new training and inference algorithm inspired by parallel-tempering Markov chain Monte Carlo methods, which we name parallel noising. Together, these enhancements enable NMLNs to attain strong performance in graph generation relative to general diffusion-based generative graph models. Furthermore, they allow NMLNs to match the performance of specialized text-based recurrent models when generating small molecular structures.

We present the GEST-Engine, a complete system that goes from natural-language text to fully-annotated multi-actor video. At its core is an explicit world model: rather than encoding state as a learned latent, the engine maintains a complete, inspectable representation of the world (which actors exist, where they are, what they are doing, which objects they hold, and how events relate in time and space), expressed as a formal Graph of Events in Space and Time (GEST) and realized deterministically inside the open world of a commercial game engine driven through an open-source multiplayer scripting framework. GESTs are produced either procedurally or by an agentic text-to-GEST system in which an LLM Director plans a story through tool calls validated by a programmatic state backend, so every generated specification is executable by construction. A GEST then enters a four-stage execution pipeline: graph parsing and validation, entity and action grounding, temporal orchestration (Allen-style constraints resolved by Floyd-Warshall transitive closure), and execution and capture. In a single simulation pass the engine emits frame-aligned RGB video, dense per-pixel depth, instance segmentation, per-actor skeletal pose, per-frame pairwise spatial-relation graphs, 2D bounding boxes, event-to-frame temporal mappings, and natural-language descriptions, all at zero marginal annotation cost. We further describe an in-game world editor, runtime capability extraction, a text-generation pipeline, and a production system that renders corpora at scale across parallel virtual machines. Because every frame traces back to a semantic specification, the engine guarantees object permanence, multi-actor coordination, and temporal consistency by construction, making its output valuable as training data, evaluation benchmarks, and diagnostic tools for video understanding.

Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem. We approach this question in the dense-graph setting through the lens of graphons, the size-agnostic limit objects of dense graph sequences, to study how structural graph statistics behave across node-size scales. This perspective leads to DiPhon, a diffusion framework for size-scalable graph generation. Specifically, we formulate a continuous diffusion process on the graphon space via a Jacobi stochastic differential equation (SDE), and propose DiPhon, a discretized graph-level process that mimics these dynamics on finite graphs. We further derive the corresponding reverse-time process, which requires access to the marginal score. For the Jacobi process, this score interestingly admits a tractable form, which we estimate from data via graph denoising and plug into the reverse process to generate graph samples. We prove that DiPhon matches exactly the first moment of the marginal distributions induced by the continuous graphon process, and approximates the second moment up to a closed-form discrepancy. Thus, DiPhon inherits key size-agnostic statistical properties of the graphon dynamics, providing a principled route toward scalable graph generation. Empirically, we demonstrate this scalability by training on small graphs and generating progressively larger graphs at inference time, without retraining, while preserving their core topological properties.

Designing deployable and resilient network topologies from natural language requirements remains a challenging problem in network automation. This work investigates the ability of Large Language Models (LLMs) to generate structurally valid and constraint-compliant network topologies through a constraint-driven pipeline combining hierarchical modeling and systematic validation. The framework is evaluated via a multimodel comparison of proprietary and open-weight LLMs across four realistic network scenarios released as a public dataset. We assess structural correctness using node and edge F1-scores against reference topologies, and evaluate resilience through server and content connectivity metrics. In addition, we analyze common failure modes, including interface mismatches and directional inconsistencies in generated topologies. Overall, this work provides a systematic benchmark for understanding how LLMs handle structural and resilience constraints in topology synthesis, and supports informed model selection for AI-driven network design.

Lane topology reasoning aims to construct a lane graph from onboard sensor observations. Existing methods follow a detection and association paradigm that treats each lane instance independently, leading to geometric inconsistency at connected endpoints and incomplete graphs due to visual occlusions. To address these issues, we propose TopoGPT, a generative framework that learns the geometry prior from typical lane graph structures through autoregressive sequence modeling. Specifically, we construct a large-scale map dataset comprising 3.3M scenes. For each lane graph, a lane tokenizer serializes it into discrete tokens, while a scene context encoder converts it into a rasterized image and extracts global features as scene tokens. We pre-train an autoregressive lane sequence transformer via scene-conditioned next-token prediction, endowing the model with the geometry prior over lane graph structures. Building upon this prior, a perception adapter aligns BEV features from multi-view images with the pre-trained scene condition, transferring the learned geometry prior to sensor-based lane graph prediction. On the OpenLane-V2 benchmark, TopoGPT outperforms existing methods by an average of +6.4 on lane-level and +11.6 on point-level metrics, and produces geometrically consistent and structurally complete lane graphs.

We propose an information-theoretic framework for graph novelty generation, which aims to generate data that are distinct from existing patterns while preserving global structural consistency. Our approach embeds data into a latent space, models the latent distribution using finite mixture models, and generates novel samples by imposing explicit novelty and reliability conditions formulated in terms of description length. Specifically, novelty is enforced by requiring generated samples to be poorly explained by all existing mixture components, while reliability constrains their impact on the overall mixture structure under the Minimum Description Length (MDL) principle. We provide a theoretical analysis showing that, with appropriate threshold choices, the probabilities of misclassifying non-novel or unreliable samples converge to zero with explicit rates. Experiments on synthetic and benchmark graph datasets demonstrate that the proposed method enables principled novelty generation with quantifiable risk.

The Deep Graph Generation's panorama spans two extremes: one-shot and sequential models. The former generates nodes and edges jointly, while the latter samples them autoregressively. Each method performs better in different graph domains depending on size and topology, but neither is applicable to all graph categories. For instance, one-shot methods struggle with generating large graphs, while sequential methods underperform on smaller graphs. A possible way to overcome these limitations is to flexibly combine the two methods in a unique system. In this work, we propose the FLAGG (Flexible Autoregressive Graph Generation) framework, which sequentially generates portions of graphs with one-shot models. FLAGG can apply any one-shot model to make it autoregressive, allowing flexibility in choosing the sequential policy. This policy is specified through a stochastic node removal process, which an Insertion Model learns to reverse. We evaluate FLAGG with the DiGress one-shot model on several data sets of different graph sizes and domains. We show that the approach outperforms both one-shot and autoregressive baselines in terms of sampling quality.

Generating realistic and diverse graphs is a key problem in machine learning, with applications in molecular discovery, circuit design, cybersecurity, and beyond. However, current graph generative models remain limited by scalability and novelty. Diffusion-based methods often require costly full-adjacency operations and long denoising chains, while many autoregressive and hybrid models have at least quadratic complexity. In addition, these models often imitate training graphs rather than generalize beyond them. We propose a lightweight autoregressive framework to address these issues. It uses a structure-guided topological ordering to serialize graphs into regular edge sequences, enabling near log-linear generation, and a two-phase training strategy that combines exploration-oriented augmentation with iterative refinement to reduce overfitting and promote controlled novelty. Experiments on molecular and non-molecular benchmarks show that our approach improves novelty while preserving high validity and uniqueness. The framework also supports both LSTM and Mamba-style causal sequence backbones, with large-memory accelerators enabling longer graph-sequence experiments beyond typical GPU limits.

Network data are ubiquitous across the social sciences, biology, and information systems. Generating realistic synthetic network data has broad applications from network simulation to scientific discovery. However, many existing black-box approaches for network generation tend to overfit observed data while overlooking characteristic network structure, and incur substantial computational overhead at scale. These practical challenges call for synthetic network generation methods that are both efficient and capable of capturing structural properties of networks. In this paper, we introduce Synthetic Network Generation via Latent Embedding Reconstruction (SyNGLER), a general and efficient framework for synthetic network generation that builds on latent space network models. Given an observed network, SyNGLER first learns low-dimensional latent node embeddings via a latent space network model and then reconstructs the latent space by building a distribution-free generator over these embeddings. For generation, SyNGLER first samples (or resamples) node embeddings from the generator in the latent space and then produces synthetic networks using the latent space network model. Through the latent space framework, SyNGLER preserves unique characteristics in networks such as sparsity and node degree heterogeneity, while allowing for efficient training with lower computational cost than many existing deep architectures. We provide theoretical guarantees by developing consistency results on the distance between the true and synthetic edge distributions. Empirical studies further demonstrate the effectiveness of SyNGLER, which efficiently produces networks that better preserve key network characteristics such as network moments and degree distributions compared with existing approaches. Code is available at https://github.com/FeifanJiang/syngler.

Generating realistic graph-structured data is challenging due to discrete connectivity, varying graph sizes, and class-specific structural patterns. Recent Generative Adversarial Networks (GAN)-based graph generation methods improve edge modelling by learning connectivity and matching class-specific density distributions. However these models still exhibit noticeable deviations such as in degree and spectral distribution when compared to real graphs, indicating that important structural properties are not fully preserved. This work aims to reduce these deviations by refining the graphs produced by an existing GAN-based graph generator framework with a Genetic Algorithm (GA). In the GAN framework, the generator produces both node features and connectivity patterns, while a GNN-based critic evaluates graph realism and class consistency to ensure global structural and class alignment. Building on this foundation, we apply a GA to refine the edges of generated graphs. The refinement process guides synthetic graphs toward closer agreement with real data, while preserving diversity and novelty. Experimental results show that the GA refinement consistently lowers combined Maximum Mean Discrepancy (MMD) compared to the base model, leading to graphs that more closely match real structural patterns. This demonstrates that evolutionary refinement is an effective and flexible way to correct residual structural deviations in GAN-based graph generators, improving their suitability for realistic graph synthesis and data augmentation.

Generating graph ensembles with precisely controlled structural properties is central to investigating how network structure shapes function. Canonical ensembles impose constraints only in expectation (soft constraints), letting individual realizations fluctuate around the target, whereas enforcing hard constraints with prescribed precision in every realization remains challenging beyond fixing the degree sequence. Here we show that a reinforcement learning framework can drive a graph through degree-preserving rewirings to satisfy a prescribed assortativity, which characterizes the degree--degree correlation of adjacent nodes. By replacing the entropically dominated Metropolis--Hastings random walk with directed transport, the learned policy reduces generation cost by at least an order of magnitude while retaining over 98% of configurational diversity. Trained on small graphs, the framework generalizes across sizes and topologies without retraining, enabling quantitative isolation of secondary observables such as the clustering coefficient. These results establish reinforcement learning as a practical paradigm for hard-constrained graph generation.

It remains unclear whether graph language models learn structural regularities or merely memorize training graphs; this cannot be resolved by current aggregate fidelity metrics alone. We develop a calibrated diagnostic protocol that combines frequent subgraph mining, a graph-level bootstrap baseline, and three-level frequency stratification to disentangle memorization from structural alignment. Using this framework, we show that graph language models can acquire structural regularities beyond memorization at scale, primarily in the high-frequency regime. This is supported by the following empirical evidence: On five TU benchmarks, LLaMA-style graph language models reach high subgraph-rank correlation, yet their alignment is matched or exceeded by the memorization bootstrap in most cases. At small scale, under our bootstrap diagnostic, fidelity is largely indistinguishable from verbatim recall. In contrast, at large scale with 3.75M graphs, verbatim memorization drops sharply while rank correlation remains near ceiling. Crucially, in a separate fixed-subsample analysis, frequent subgraph mining restricted to the novel-only subset closely tracks the corresponding all-generation Spearman correlation, providing evidence that the alignment is not driven solely by verbatim recall. Across all scales, high-frequency patterns are well reproduced, while rare patterns remain poorly covered, and this deficit narrows only marginally as capacity increases. We observe the same scale-dependent crossover under two distinct graph serializations (canonical DFS code and action sequences), providing evidence of robustness in our analysis.

Structure aware graph generation aims to generate graphs that satisfy given topological properties. It has applications in domains such as drug discovery, social network modeling, and knowledge graph construction. Unlike existing methods that only provide coarse control over graph properties, we introduce a novel conditional variational autoencoder for fine-grained structural control in graph generation. The approach refines the decoder's latent space by dynamically aligning graph- and property-driven representations to improve both graph fidelity and control satisfaction. Specifically, the approach implements a mixture scheduler that progressively integrates graph and control priors. Experiments on five real-world datasets show the efficacy of the proposed model compared to recent baselines, achieving high generation quality while maintaining high controllability.

Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an information-geometric framework that reinterprets the diffusion sampling trajectory as a parametric curve on a Riemannian manifold. Our key observation is that the Fisher-Rao metric provides a principled measure of the intrinsic distance. By analyzing this metric, we derive the Drift Variation Score (DVS), a geometry-aware indicator that quantifies the instantaneous rate of distributional change. Unlike prior heuristic-based adaptive samplers, our DVS solver enforces a constant informational speed on the statistical manifold, automatically maintaining a uniform rate of distributional change along the sampling trajectory. This equal arc-length strategy ensures that each discretization step contributes equally to the information speed. Theoretical analysis verifies that DVS characterizes the local stiffness of the sampling dynamics in the Fisher-Rao sense. Experimental results on molecule and social network generation show that DVS significantly improves structural fidelity and sampling efficiency. Code is at https://github.com/kunzhan/DVS

Spatial graphs provide a lightweight and elegant representation of curvilinear anatomical structures such as blood vessels, lung airways, and neuronal networks. Accurately modeling these graphs is crucial in clinical and (bio-)medical research. However, the high spatial resolution of large networks drastically increases their complexity, resulting in significant computational challenges. In this work, we aim to tackle these challenges by proposing VesselTok, a framework that approaches spatially dense graphs from a parametric shape perspective to learn latent representations (tokens). VesselTok leverages centerline points with a pseudo radius to effectively encode tubular geometry. Specifically, we learn a novel latent representation conditioned on centerline points to encode neural implicit representations of vessel-like, tubular structures. We demonstrate VesselTok's performance across diverse anatomies, including lung airways, lung vessels, and brain vessels, highlighting its ability to robustly encode complex topologies. To prove the effectiveness of VesselTok's learnt latent representations, we show that they (i) generalize to unseen anatomies, (ii) support generative modeling of plausible anatomical graphs, and (iii) transfer effectively to downstream inverse problems, such as link prediction.