On Graph Representation with Smallest Numerical Encoding

The study of succinct representation of graphs has received relevant attention to allow efficiency in modeling interconnected systems. Related work on graph representation has achieved compact encodings by benefiting from structural regularities, such as triangularity, separability, planarity, symmetry and sparsity; whereas the case of arbitrary unstructured graphs has remained elusive. In this paper, we propose an scheme to represent arbitrary graphs by using the smallest integer number. We believe our approach is useful to represent graphs efficiently.