The Brain Tumor presents a highly critical situation concerning the brain, characterized by the uncontrolled growth of an abnormal cell cluster. Early brain tumor detection is essential for accurate diagnosis and effective treatment planning. In this paper, a novel Convolutional Neural Network (CNN) based Graph Neural Network (GNN) model is proposed using the publicly available Brain Tumor dataset from Kaggle to predict whether a person has brain tumor or not and if yes then which type (Meningioma, Pituitary or Glioma). The objective of this research and the proposed models is to provide a solution to the non-consideration of non-Euclidean distances in image data and the inability of conventional models to learn on pixel similarity based upon the pixel proximity. To solve this problem, we have proposed a Graph based Convolutional Neural Network (GCNN) model and it is found that the proposed model solves the problem of considering non-Euclidean distances in images. We aimed at improving brain tumor detection and classification using a novel technique which combines GNN and a 26 layered CNN that takes in a Graph input pre-convolved using Graph Convolution operation. The objective of Graph Convolution is to modify the node features (data linked to each node) by combining information from nearby nodes. A standard pre-computed Adjacency matrix is used, and the input graphs were updated as the averaged sum of local neighbor nodes, which carry the regional information about the tumor. These modified graphs are given as the input matrices to a standard 26 layered CNN with Batch Normalization and Dropout layers intact. Five different networks namely Net-0, Net-1, Net-2, Net-3 and Net-4 are proposed, and it is found that Net-2 outperformed the other networks namely Net-0, Net-1, Net-3 and Net-4. The highest accuracy achieved was 95.01% by Net-2. With its current effectiveness, the model we propose represents a critical alternative for the statistical detection of brain tumors in patients who are suspected of having one.