Risk of mid-air collision estimation using minimum spanning tree of air traffic graph

The safety of air transportation is based on different risk estimations and control. A mid-air collision is one of the dangerous events in aviation due to both air-planes involved in the catastrophe. Risk of a mid-air collision is considered as a probability of airplane deviation to the safety area of another airspace user in horizontal and vertical planes. A double exponential function is used as a probability density function to estimate probability of airplane deviation from a preplanned position. A theory of Graph has been used to detect the closest pairs of airplanes. Thus, air traffic has been represented as an undirected, connected graph. The probability density function is fixed at nodes of the air traffic graph along of optimal minimum spanning tree path. A minimum of separation is used to build a safety area around each airspace user. In numerical application, live air traffic data within Ukrainian airspace has been used under Automatic-Dependent Surveillance-Broadcast technology.