The networks of the solar eclipses from the column of Saros series

This article demonstrates that the structure of Saros series – particularly the column of Saros series, enables the identification of networks composed of solar eclipses with identical durations, establishing links between different Saros series. We present examples of eclipse networks corresponding to cycles of 17, 20, 28, and 37 years from January-February 1972 to 2149. We show that any three distinct eclipses form the vertices of a temporal triangle, where the longest edge equals the sum of the two shorter edges. A graphical analysis of cycle durations from George van den Bergh’s catalog reveals three distinct regions, which also appear in plots of synodic, draconic, and anomalistic periods. This pattern suggests the potential existence of undiscovered cycles that could contribute to a smoother curve. The use of eclipse cycle networks provides a novel method for identifying previously unknown eclipse cycles. In the studied period, known cycles include those of 9, 18, 19, 20, 29, 36, 50, 54, and 56 years. However, additional cycles – such as those spanning 8, 10, 16, 17, 27, 28, 30, 35, 37, 47, 48, 49, 50, 66, and 73 years, may also exist but remain unrecognized.