By stacking all node feature vectors, a matrix V ∈ {0, 1} Nv×23 was obtained that contains the node information of the graph, where N v stands for the number of nodes in the graph. Similarly, for all edges, a matrix E ∈ {0, 1} Ne×6 can be constructed, where N e denotes the number of edges in the graph. The connectivity of the graph can be specified by an adjacency matrix A ∈ {0, 1} Nv×Nv . The Figure : DES pairs available in the dataset collected by . connectivity of the graph is defined by constructing a matrix C ∈ N 2×2Ne that contains the indices of the source nodes in one row, and the indices of the receiver nodes in the second row. Notice that, given that molecular graphs are often constructed as undirected (due to the undirected nature of covalent bonds), the number of columns in C is twice the number of edges, denoting that all nodes in the graph can act as both source and receivers. Hence, a graph is completely specified by defining the node feature matrix V, the edge feature matrix E, and the connectivity matrix C. All graphs in this work were constructed using PyTorch Graphs can be globally attributed with information pertinent to the entire graph structure, as suggested by . This methodology has been applied in predicting the properties of organic mixtures and polymer solutions . In our work, global features (outlined in Table ) are integrated into graphs processed by a designated GNN architecture, herein referred to as GNN-MG. Detailed explanations of this architecture are provided in subsequent sections. Consequently, when global features are incorporated, a graph is completely characterized by its node feature matrix V, edge feature matrix E, connectivity matrix C, and a global-feature vector u ∈ R 3 . The global features deployed in our study are in alignment with those utilized in existing literature for predicting infinite-dilution activity coefficients. For the computation of global-level molecular descriptors, the Python package Mordred was employed.