  Haros graphs is a graph-theoretical representation of real numbers in the
unit interval. The degree distribution of the Haros graphs provides information
regarding the topological structure and the associated real number. This
article provides a comprehensive demonstration of a conjecture concerning the
analytical formulation of the degree distribution. Specifically, a theorem
outlines the relationship between Haros graphs, the corresponding continued
fraction of its associated real number, and the subsequent symbolic paths in
the Farey binary Tree. Moreover, an expression continuous and piece-wise linear
in subintervals defined by Farey fractions can be derived from an additional
conclusion for the degree distribution of Haros graphs.
