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Three dimensional (3D) object recognition is becoming a key desired capability for many computer vision systems such as autonomous vehicles, service robots and surveillance drones to operate more effectively in unstructured environments. These real-time systems require effective classification methods that are robust to various sampling resolutions, noisy measurements, and unconstrained pose configurations. Previous research has shown that points' sparsity, rotation and positional inherent variance can lead to a significant drop in the performance of point cloud based classification techniques. However, neither of them is sufficiently robust to multifactorial variance and significant sparsity. In this regard, we propose a novel approach for 3D classification that can simultaneously achieve invariance towards rotation, positional shift, scaling, and is robust to point sparsity. To this end, we introduce a new feature that utilizes graph structure of point clouds, which can be learned end-to-end with our proposed neural network to acquire a robust latent representation of the 3D object. We show that such latent representations can significantly improve the performance of object classification and retrieval tasks when points are sparse. Further, we show that our approach outperforms PointNet and 3DmFV by 35.0% and 28.1% respectively in ModelNet 40 classification tasks using sparse point clouds of only 16 points under arbitrary SO(3) rotation.