Millisecond pulsars phenomenology under the light of graph theory

We compute and apply the minimum spanning tree (MST) of the binary millisecond pulsar population, and discuss aspects of the known phenomenology of these systems in this context. We find that the MST effectively separates different classes of spider pulsars, eclipsing radio pulsars in tight binary systems either with a companion with a mass in the range of approximately 0.1-0.8 solar masses (redbacks) or with a companion of less than or approximately 0.06 solar masses (black widows), into distinct branches. The MST also separates black widows located in globular clusters from those found in the field and groups other pulsar classes of interest, including transitional millisecond pulsars. Using the MST and a defined ranking for similarity, we identify possible candidates likely to belong to these pulsar classes. In particular, based on this approach, we propose the black widows' classification of J1300+1240, J1630+3550, J1317-0157, J1221-0633, J1627+3219, J1737-0314A, and J1701-3006F, discuss that of J1908+2105, and analyze J1723-2837, J1431-4715, and J1902-5105 as possible transitional systems. We introduce an algorithm that quickly locates where new pulsars fall within the MST and use this to examine the positions of the transitional millisecond pulsar IGR J18245-2452 (PSR J1824-2452I), the transitional millisecond pulsar candidate 3FGL J1544.6-1125, and the accreting millisecond X-ray pulsar SAX J1808.4-3658. Assessing the positions of these sources in the MST assuming a range for their unknown variables (e.g., the spin period derivative of PSR J1824-2452I) we can effectively narrow down the parameter space necessary for searching and determining key pulsar parameters through targeted observations.