Graph generation is an important area in network science. Traditional approaches focus on replicating specific properties of real-world graphs, such as small diameters or power-law degree distributions. Recent advancements in deep learning, particularly with Graph Neural Networks, have enabled data-driven methods to learn and generate graphs without relying on predefined structural properties. Despite these advances, current models are limited by their reliance on node IDs, which restricts their ability to generate graphs larger than the input graph and ignores node attributes. To address these challenges, we propose Latent Graph Sampling Generation (LGSG), a novel framework that leverages diffusion models and node embeddings to generate graphs of varying sizes without retraining. The framework eliminates the dependency on node IDs and captures the distribution of node embeddings and subgraph structures, enabling scalable and flexible graph generation. Experimental results show that LGSG performs on par with baseline models for standard metrics while outperforming them in overlooked ones, such as the tendency of nodes to form clusters. Additionally, it maintains consistent structural characteristics across graphs of different sizes, demonstrating robustness and scalability.

Causal discovery aims to infer causal graphs from observational or experimental data. Methods such as the popular PC algorithm are based on conditional independence testing and utilize enabling assumptions, such as the faithfulness assumption, for their inferences. In practice, these assumptions, as well as the functional assumptions inherited from the chosen conditional independence test, are typically taken as a given and not further tested for their validity on the data. In this work, we propose internal coherency scores that allow testing for assumption violations and finite sample errors, whenever detectable without requiring ground truth or further statistical tests. We provide a complete classification of erroneous results, including a distinction between detectable and undetectable errors, and prove that the detectable erroneous results can be measured by our scores. We illustrate our coherency scores on the PC algorithm with simulated and real-world datasets, and envision that testing for internal coherency can become a standard tool in applying constraint-based methods, much like a suite of tests is used to validate the assumptions of classical regression analysis.

Graph neural networks (GNNs) have emerged as a promising solution to deal with unstructured data, outperforming traditional deep learning architectures. However, most of the current GNN models are designed to work with a single graph, which limits their applicability in many real-world scenarios where multiple graphs may be involved. To address this limitation, we propose a novel graph-based deep learning architecture to handle tasks where two sets of signals exist, each defined on a different graph. First we consider the setting where the input is represented as a signal on top of one graph (input graph) and the output is a graph signal defined over a different graph (output graph). For this setup, we propose a three-block architecture where we first process the input data using a GNN that operates over the input graph, then apply a transformation function that operates in a latent space and maps the signals from the input to the output graph, and finally implement a second GNN that operates over the output graph. Our goal is not to propose a single specific definition for each of the three blocks, but rather to provide a flexible approach to solve tasks involving data defined on two graphs. The second part of the paper addresses a self-supervised setup, where the focus is not on the output space but on the underlying latent space and, inspired by Canonical Correlation Analysis, we seek informative representations of the data that can be leveraged to solve a downstream task. By leveraging information from multiple graphs, the proposed architecture can capture more intricate relationships between different entities in the data. We test this in several experimental setups using synthetic and real world datasets, and observe that the proposed architecture works better than traditional deep learning architectures, showcasing the importance of leveraging the information of the two graphs.

In many causal learning problems, variables of interest are often not all measured over the same observations, but are instead distributed across multiple datasets with overlapping variables. Tillman et al. (2008) presented the first algorithm for enumerating the minimal equivalence class of ground-truth DAGs consistent with all input graphs by exploiting local independence relations, called ION. In this paper, this problem is formulated as a more computationally efficient answer set programming (ASP) problem, which we call ION-C, and solved with the ASP system clingo. The ION-C algorithm was run on random synthetic graphs with varying sizes, densities, and degrees of overlap between subgraphs, with overlap having the largest impact on runtime, number of solution graphs, and agreement within the output set. To validate ION-C on real-world data, we ran the algorithm on overlapping graphs learned from data from two successive iterations of the European Social Survey (ESS), using a procedure for conducting joint independence tests to prevent inconsistencies in the input.

It is known that LLMs do hallucinate, that is, they return incorrect information as facts. In this paper, we introduce the possibility to study these hallucinations under a structured form: graphs. Hallucinations in this context are incorrect outputs when prompted for well known graphs from the literature (e.g. Karate club, Les Mis\'erables, graph atlas). These hallucinated graphs have the advantage of being much richer than the factual accuracy -- or not -- of a fact; this paper thus argues that such rich hallucinations can be used to characterize the outputs of LLMs. Our first contribution observes the diversity of topological hallucinations from major modern LLMs. Our second contribution is the proposal of a metric for the amplitude of such hallucinations: the Graph Atlas Distance, that is the average graph edit distance from several graphs in the graph atlas set. We compare this metric to the Hallucination Leaderboard, a hallucination rank that leverages 10,000 times more prompts to obtain its ranking.

This paper approaches the problem of separating the notes from a quantized symbolic music piece (e.g., a MIDI file) into multiple voices and staves. This is a fundamental part of the larger task of music score engraving (or score typesetting), which aims to produce readable musical scores for human performers. We focus on piano music and support homophonic voices, i.e., voices that can contain chords, and cross-staff voices, which are notably difficult tasks that have often been overlooked in previous research. We propose an end-to-end system based on graph neural networks that clusters notes that belong to the same chord and connects them with edges if they are part of a voice. Our results show clear and consistent improvements over a previous approach on two datasets of different styles. To aid the qualitative analysis of our results, we support the export in symbolic music formats and provide a direct visualization of our outputs graph over the musical score. All code and pre-trained models are available at https://github.com/CPJKU/piano_svsep

Many state-of-the-art causal discovery methods aim to generate an output graph that encodes the graphical separation and connection statements of the causal graph that underlies the data-generating process. In this work, we argue that an evaluation of a causal discovery method against synthetic data should include an analysis of how well this explicit goal is achieved by measuring how closely the separations/connections of the method's output align with those of the ground truth. We show that established evaluation measures do not accurately capture the difference in separations/connections of two causal graphs, and we introduce three new measures of distance called s/c-distance, Markov distance and Faithfulness distance that address this shortcoming. We complement our theoretical analysis with toy examples, empirical experiments and pseudocode.

We propose a novel and trainable graph unpooling layer for effective graph generation. Given a graph with features, the unpooling layer enlarges this graph and learns its desired new structure and features. Since this unpooling layer is trainable, it can be applied to graph generation either in the decoder of a variational autoencoder or in the generator of a generative adversarial network (GAN). We prove that the unpooled graph remains connected and any connected graph can be sequentially unpooled from a 3-nodes graph. We apply the unpooling layer within the GAN generator. Since the most studied instance of graph generation is molecular generation, we test our ideas in this context. Using the QM9 and ZINC datasets, we demonstrate the improvement obtained by using the unpooling layer instead of an adjacency-matrix-based approach.

In this work we propose a novel end-to-end multi-stage Knowledge Graph (KG) generation system from textual inputs, separating the overall process into two stages. The graph nodes are generated first using pretrained language model, followed by a simple edge construction head, enabling efficient KG extraction from the text. For each stage we consider several architectural choices that can be used depending on the available training resources. We evaluated the model on a recent WebNLG 2020 Challenge dataset, matching the state-of-the-art performance on text-to-RDF generation task, as well as on New York Times (NYT) and a large-scale TekGen datasets, showing strong overall performance, outperforming the existing baselines. We believe that the proposed system can serve as a viable KG construction alternative to the existing linearization or sampling-based graph generation approaches. Our code can be found at https://github.com/IBM/Grapher

This paper presents a method to simulate the thermal behavior of 3D systems using a graph neural network. The method discussed achieves a significant speed-up with respect to a traditional finite-element simulation. The graph neural network is trained on a diverse dataset of 3D CAD designs and the corresponding finite-element simulations, representative of the different geometries, material properties and losses that appear in the design of electronic systems. We present for the transient thermal behavior of a test system. The accuracy of the network result for one-step predictions is remarkable (\SI{0.003}{\%} error). After 400 time steps, the accumulated error reaches \SI{0.78}{\%}. The computing time of each time step is \SI{50}{ms}. Reducing the accumulated error is the current focus of our work. In the future, a tool such as the one we are presenting could provide nearly instantaneous approximations of the thermal behavior of a system that can be used for design optimization.