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The graph neural network (GNN) has been a powerful deep-learning tool in chemistry domain, due to its close connection with molecular graphs. Most GNN models collect and update atom and molecule features from the fed atom (and, in some cases, bond) features, which are basically based on the two-dimensional (2D) graph representation of 3D molecules. Correspondingly, the adjacency matrix, containing the information on covalent bonds, or equivalent data structures (e.g., lists) have been the main core in the feature-updating processes, such as graph convolution. However, the 2D-based models do not faithfully represent 3D molecules and their physicochemical properties, exemplified by the overlooked field effect that is a "through-space" effect, not a "through-bond" effect. The GNN model proposed herein, denoted as MolNet, is chemically intuitive, accommodating the 3D non-bond information in a molecule, with a noncovalent adjacency matrix $\bf{\bar A}$, and also bond-strength information from a weighted bond matrix $\bf{B}$. The noncovalent atoms, not directly bonded to a given atom in a molecule, are identified within 5 $\unicode{x212B}$ of cut-off range for the construction of $\bf{\bar A}$, and $\bf{B}$ has edge weights of 1, 1.5, 2, and 3 for single, aromatic, double, and triple bonds, respectively. Comparative studies show that MolNet outperforms various baseline GNN models and gives a state-of-the-art performance in the classification task of BACE dataset and regression task of ESOL dataset. This work suggests a future direction of deep-learning chemistry in the construction of deep-learning models that are chemically intuitive and comparable with the existing chemistry concepts and tools.