Graph neural networks (GNNs) gain significant interest in the domain of network representation learning. To obtain a graph level vector representation from individual node embeddings, hierarchical pooling algorithms are proposed in the recent literature which adhere the hierarchical structure of an input graph. A major limitation for most of the existing supervised GNNs is their dependency on large number of graph labels (often 80%-90%) to train the parameters of the neural architecture. But obtaining labels of a large number of graphs is expensive for real world applications. So in this work, we propose an unsupervised hierarchical neural network, referred as GraPHmax, for obtaining graph level representation. We propose the concept of periphery representation and show its effectiveness to obtain discriminative features of an input graph. Further, inspired by the concepts from self-supervised learning, we propose to maximize periphery and hierarchical information in the context of hierarchical GNN. Thorough experimentation on both synthetic and real-world graph datasets shows that GraPHmax is not only able to outperform unsupervised graph embedding techniques, it often achieves state-of-the-art performance even with respect to a set of popular supervised GNN algorithms.