A graph-theoretical algorithm for detecting configuration defects in triangular geodetic networks

Summary

The problem to detect configurational defects in geodetic networks is solved by a graph-theoretical algorithm, here applied to triangular geodetic networks and being presented as a computer program in the Appendix. Based on an analysis of the incidence matrix the algorithm detects, for instance, missing vertical directions which cause two types of deficiencies. In case of only vertical direction measurements from one point to another, but no counter vertical direction measurements backwards, the rank deficiency of the first type is identified. Furtheron if there are “bare” points with no vertical direction measurements at all, the rank deficiency of the second type is found. The algorithm has proved a rank deficiency of 4+13=17 in theSW Finland triangular network which before has been found as the surprizing rank defect ofTAGNET 3d-operational adjustment.