This paper introduces LSTMGraph, a unified time-series model designed for demand prediction across multiple products. This method integrates Long Short-Term Memory (LSTM) networks to capture temporal dynamics, such as price fluctuations, and Graph Convolutional Networks (GCN) to model global dependencies between products. We represent demand data as a network where each product is a node, constructing three distinct graphs with different types of edges: (i) a weekly sales similarity graph, (ii) a customer-based relationship graph, and (iii) an invoice-based similarity graph. These graphs are merged to enhance predictive accuracy by incorporating diverse temporal and relational patterns. Extensive experiments show that LSTMGraph significantly outperforms existing baseline models. Additionally, an ablation study is conducted to quantify the impact of each graph type on overall performance.

Edge prediction is a fundamental challenge in network science, with broad applications, notably in social networks. It plays a crucial role in unveiling complex system dynamics by forecasting connections between entities. Our paper introduces UniMHe (Unified Multi Hyperedge Prediction), a novel framework for predicting multiple hyperedges associated with each node using hypergraph representations. We present a case study focused on crime network analysis, where UniMHe reveals intricate patterns in criminal activities, including crime types, locations, and seasonal variations. Our research leverages extensive historical crime data encompassing geographical information, timestamps, points of interest, and crime categories. In an extensive evaluation, we benchmark UniMHe against state-of-the-art hypergraph deep learning techniques, highlighting its superior performance. These findings underscore the significance of UniMHe across various domains and problem-solving scenarios.