  The minimal spanning tree (MST) algorithm is a graph-theoretical
cluster-finding method. We previously applied it to gamma-ray bidimensional
images, showing that it is quite sensitive in finding faint sources. Possible
sources are associated with the regions where the photon arrival directions
clusterize. MST selects clusters starting from a particular "tree" connecting
all the point of the image and performing a cut based on the angular distance
between photons, with a number of events higher than a given threshold. In this
paper, we show how a further filtering, based on some parameters linked to the
cluster properties, can be applied to reduce spurious detections. We find that
the most efficient parameter for this secondary selection is the magnitude M of
a cluster, defined as the product of its number of events by its clustering
degree. We test the sensitivity of the method by means of simulated and real
Fermi-Large Area Telescope (LAT) fields. Our results show that sqrt(M) is
strongly correlated with other statistical significance parameters, derived
from a wavelet based algorithm and maximum likelihood (ML) analysis, and that
it can be used as a good estimator of statistical significance of MST
detections. We apply the method to a 2-year LAT image at energies higher than 3
GeV, and we show the presence of new clusters, likely associated with BL Lac
objects.
