  Graphs can be used to describe complex systems. Recently, whole graph
embedding (graph representation learning) can compress a graph into a compact
lower-dimension vector while preserving intrinsic properties, earning much
attention. However, most graph embedding methods have problems such as tedious
parameter tuning or poor explanation. This paper presents a simple and
hyperparameter-free whole graph embedding method based on the DHC (Degree,
H-index, and Coreness) theorem and Shannon Entropy (E), abbreviated as DHC-E.
The DHC-E can provide a trade-off between simplicity and quality for supervised
classification learning tasks involving molecular, social, and brain networks.
Moreover, it performs well in lower-dimensional graph visualization. Overall,
the DHC-E is simple, hyperparameter-free, and explainable for whole graph
embedding with promising potential for exploring graph classification and
lower-dimensional graph visualization.
