On succinct representation of directed graphs

Directed graphs encode meaningful dependencies among objects ubiquitously. This paper introduces new and simple representations for labeled directed graphs with the properties of being succinct (space is information-theoretically optimal); in which we avoid exploiting a-priori knowledge on digraph regularity such as triangularity, separability, planarity, symmetry and sparsity. Our results have direct implications to model directed graphs by using single integer numbers effectively, which is significant to enable canonical (generation of graph instances is unique) and efficient (coding and decoding take polynomial time) encodings for learning and optimization algorithms. To the best of our knowledge, the proposed representations are the first known in the literature.