Horizontal visibility graphs are uniquely determined by their directed degree sequence

• Published in: Physica A Vol. 536; p. 120923
• Main Author: O’Pella, Justin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15-12-2019
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2019.04.159

Horizontal visibility graphs (HVGs) are graphs generated from time (or otherwise ordered) series data. Components of the graph reveal key underlying properties of the series data that generated the graph and there are several applications that use HVGs to uncover information about series data. Recently, a bijection between the degree sequence and adjacency matrix of canonical form HVGs was established. This paper extends the relation between the degree sequence and adjacency matrix of HVGs and then presents an algorithm to uniquely construct an HVG from its directed degree sequence.
•The relation between the degree sequence and adjacency matrix of an HVG is extended.•An algorithm to construct the full HVG from its directed degree sequence is shown.•The n2 bits needed to store an HVG are compressed to 2n with no loss of information.