Generating Large Semi-Synthetic Graphs of Any Size

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.

Kernel Corrector LSTM

Forecasting methods are affected by data quality issues in two ways: 1. they are hard to predict, and 2. they may affect the model negatively when it is updated with new data. The latter issue is usually addressed by pre-processing the data to remove those issues. An alternative approach has recently been proposed, Corrector LSTM (cLSTM), which is a Read \& Write Machine Learning (RW-ML) algorithm that changes the data while learning to improve its predictions. Despite promising results being reported, cLSTM is computationally expensive, as it uses a meta-learner to monitor the hidden states of the LSTM. We propose a new RW-ML algorithm, Kernel Corrector LSTM (KcLSTM), that replaces the meta-learner of cLSTM with a simpler method: Kernel Smoothing. We empirically evaluate the forecasting accuracy and the training time of the new algorithm and compare it with cLSTM and LSTM. Results indicate that it is able to decrease the training time while maintaining a competitive forecasting accuracy.