Hi-C experiments allow researchers to study and understand the three-dimensional (3D) organization of the genome at various structural scales. Unfortunately, sequencing costs and technical constraints severely restrict analyses that can be reliably performed at high resolutions. Existing deep learning methods to improve the resolution of Hi-C matrices utilize conventional convolutional neural network (CNN) based frameworks. These methods treat Hi-C data as an image, which imposes a strict 2D euclidean structure that, in reality, represents a 3D structure. Moreover, CNNs rely on smaller structural features to construct a global representation that might be missing altogether when the input Hi-C data is very sparse. We propose GrapHiC, a Hi-C imputation framework that utilizes a conditional Graph Autoencoder network to impute Hi-C contact matrices. We reformulate Hi-C data as a graph, where each node represents binned genomic regions, and we assign edge weights using the observed Hi-C contacts between those regions. Our formulation captures the 3D structure accurately and integrates the sparse input Hi-C signals with easy-to-obtain 1D genomic signals incorporating cell-type-specific information when the Hi-C signal is noisy or outright missing. Our experiments on five GM12878 datasets with varying sparsity levels suggest that GrapHiC provides ~ 3.4% improvement in the Hi-C similarity scores over state-of-the-art deep learning models. We observe the highest performance boost of 26% on the sparsest dataset. More importantly, our framework allows us to predict the Hi-C reads reliably in a cell line with missing Hi-C data by using a surrogate Hi-C map and auxiliary genomic signals. Thus, our generalizable framework can accelerate and make the research on 3D genomics more accessible.Availabilityhttps://github.com/rsinghlab/GrapHiC