We propose a formal algorithm for identification of aftershocks following a main event. Our approach is based on the analysis of the local statistics: the number of events following the 'initial' earthquake displayed as a function of distance and time. By comparing this distribution with the random catalog, we establish, for several magnitude ranges, spatiotemporal thresholds for detection of aftershocks. High-confidence thresholds correspond to the limit at which the number of events derived from the actual catalog (corrected for the background seismicity) exceeds by a factor of 10 the expected level of background seismicity; marginal confidence threshold correspond to the spatiotemporal boundary along which these two values are approximately equal. After several iterations, the final thresholds are derived. The swarming parameter is defined as the number of aftershocks, with a cut-off lower magnitude range, following an initial earthquake of certain magnitude. If a correction for the recurrence law is applied, we find that the swarming parameter is magnitude independent. This allows us to apply this technique to the analysis of global seismicity. Using a catalog derived from the ISC Bulletin for the years from 1964 to 1975, we determine for shallow earthquakes the average values of the swarming parameter in 9¿¿9¿ cells. A global map produced in this manner shows a very wide range of variations in the swarming property, undoubtedly reflecting variations in the local geological conditions. Triple junctions are among the areas with the highest swarming values. At the present time there is an insufficient amount of data to study regional variations in the swarming property of deep earthquakes. Considering the clustering as a function of depth alone, we find detectable swarming for two depth ranges: from 100 to 250 km and from 450 to 650 km. Not a single aftershock has been detected among nearly 200 earthquakes with mb?5 in a depth range from 250 to 450 km. The average swarming parameter for earthquakes deeper than 100 km is 10 times smaller than that for the shallow earthquakes.