Many real-world complex systems can be described as graphs. For a large-scale graph with low sparsity, a node's adjacency vector is a long and sparse representation, limiting the practical utilization of existing machine learning methods on nodal features. In practice, graph embedding (graph representation learning) attempts to learn a lower-dimensional representation vector for each node or the whole graph while maintaining the most basic information of graph. Since various machine learning methods can efficiently process lowerdimensional vectors, graph embedding has recently attracted a lot of attention. However, most node embedding or whole graph embedding methods suffer from the problem of having more sophisticated methodology, hyperparameter optimization, and low explainability. This paper proposes a hyperparameterfree, extensible, and explainable whole graph embedding method, combining the DHC (Degree, H-index and Coreness) theorem and Shannon Entropy (E), abbreviated as DHC-E. The new whole graph embedding scheme can obtain a trade-off between simplicity and quality under supervised classification learning tasks, using molecular, social, and brain networks. In addition, the proposed approach has a good performance in lowerdimensional graph visualization. Overall, the new methodology is simple, hyperparameter-free, extensible, and explainable for whole graph embedding with promising potential for exploring graph classification, prediction, and lower-dimensional graph visualization.