MARA: A deep learning based framework for multilayer graph simplification

In many scientific fields, complex systems are characterized by a multitude of heterogeneous interactions/relationships that are challenging to model. Multilayer graphs constitute valuable tools that can represent such complex systems, thus making possible their analysis for downstream decision-making processes. Nevertheless, modeling such complex information still remains challenging in real-world scenarios. On the one hand, holistically including all relationships may lead to noisy or computationally intensive graphs. On the other hand, limiting the amount of information to model through the selection of a portion of the available relationships can introduce boundary specification biases. However, the current research studies are demonstrating that it is more beneficial to retain as much information as possible and at a later stage perform graph simplification i.e., removing uninformative or redundant parts of the graph to facilitate the final analysis. While simplification strategies, based on deep learning methods, have been already extensively explored in the context of single-layer graphs, only a limited amount of efforts have been devoted to simplification strategies for multilayer graphs. In this work, we propose the MultilAyer gRaph simplificAtion (MARA) framework, a GNN-based approach designed to simplify multilayer graphs based on the downstream task. MARA generates node embeddings for a specific task by training jointly two main components: (i) an edge simplification module and (ii) a (multilayer) graph neural network. We tested MARA on different real-world multilayer graphs for node classification tasks. Experimental results show the effectiveness of the proposed approach: MARA reduces the dimension of the input graph while keeping and even improving the performance of node classification tasks in different domains and across graphs characterized by different structures. Moreover, deep learning-based simplification allows MARA to preserve and enhance important graph properties for the downstream task. To our knowledge, MARA represents the first simplification framework especially tailored for multilayer graphs analysis.