COVID-19, a viral infection originated from Wuhan, China has spread across the world and it has currently affected over 115 million people. Although vaccination process has already started, reaching sufficient availability will take time. Considering the impact of this widespread disease, many research attempts have been made by the computer scientists to screen the COVID-19 from Chest X-Rays (CXRs) or Computed Tomography (CT) scans. To this end, we have proposed GraphCovidNet, a Graph Isomorphic Network (GIN) based model which is used to detect COVID-19 from CT-scans and CXRs of the affected patients. Our proposed model only accepts input data in the form of graph as we follow a GIN based architecture. Initially, pre-processing is performed to convert an image data into an undirected graph to consider only the edges instead of the whole image. Our proposed GraphCovidNet model is evaluated on four standard datasets: SARS-COV-2 Ct-Scan dataset, COVID-CT dataset, combination of covid-chestxray-dataset, Chest X-Ray Images (Pneumonia) dataset and CMSC-678-ML-Project dataset. The model shows an impressive accuracy of 99% for all the datasets and its prediction capability becomes 100% accurate for the binary classification problem of detecting COVID-19 scans. Source code of this work can be found at GitHub-link.