Description
Millisecond pulsars (MSPs) in binary systems display a rich phenomenology, including spider pulsars,
commonly classified as black widows or redbacks, as well as transitional millisecond pulsars.
Understanding how these systems relate to one another within the broader MSP population remains
an open question.
In this talk, I present a set of algorithms in the context of graph theory, specifically those based
on the Minimum Spanning Tree (MST), to analyze and classify the binary MSP population in a
multidimensional parameter space.
The MST provides a graph-based representation in which distinct pulsar classes naturally emerge
as separate branches. In particular, we show that black widows, redbacks, and transitional systems
occupy well-defined regions of the tree, enabling their separation without relying on predefined
boundaries. We also define a similarity-based ranking to identify candidate systems associated
with specific classes. This approach enables the promotion of new candidates.
Building on this structure, we apply an algorithm to partition the MST into statistically meaningful
subgroups and systematically explore their phenomenological classification.
Finally, we introduce a method for locating pulsars with uncertain measurements within the MST.
By analyzing their positions relative to well-characterized sources, we constrain the plausible
ranges of unknown parameters and guide targeted observational searches.
These results demonstrate that MST-based methods offer an interpretable and flexible framework
for classifying and exploring MSP populations, with direct applicability to current and future pulsar
surveys.