  In this paper, we observe graph fractaloids, which are the graph groupoids
with fractal property. In particular, we classify them in terms of the spectral
data of certain Hilbert space operators, called the radial operators. Based on
these information, we can define the pair of two numbers $(N_{0},$ $N^{0})$,
for a given graph fractaloid G, called the fractal pair of G. The graph
fractaloids are classified by such pairs.
