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The minimal spanning tree (MST) algorithm is a graph-theoreticalcluster-finding method. We previously applied it to gamma-ray bidimensionalimages, showing that it is quite sensitive in finding faint sources. Possiblesources are associated with the regions where the photon arrival directionsclusterize. MST selects clusters starting from a particular "tree" connectingall the point of the image and performing a cut based on the angular distancebetween photons, with a number of events higher than a given threshold. In thispaper, we show how a further filtering, based on some parameters linked to thecluster properties, can be applied to reduce spurious detections. We find thatthe most efficient parameter for this secondary selection is the magnitude M ofa cluster, defined as the product of its number of events by its clusteringdegree. We test the sensitivity of the method by means of simulated and realFermi-Large Area Telescope (LAT) fields. Our results show that sqrt(M) isstrongly correlated with other statistical significance parameters, derivedfrom a wavelet based algorithm and maximum likelihood (ML) analysis, and thatit can be used as a good estimator of statistical significance of MSTdetections. We apply the method to a 2-year LAT image at energies higher than 3GeV, and we show the presence of new clusters, likely associated with BL Lacobjects.

Minimal spanning tree algorithm for gamma-ray source detection in sparse photon images: cluster parameters and selection strategies