  We present the complete analytical classification of the atoms arising at the
critical points of rank 1 of the Kowalevski-Yehia gyrostat. To classify the
Smale-Fomenko diagrams, all separating values of the gyrostatic momentum are
found. We present a kind of constructor of the Fomenko graphs; its application
gives the complete description of the rough topology of this integrable case.
It is proved that there exists exactly nine groups of identical molecules (not
considering the marks). These groups contain 22 stable types of graphs and 6
unstable ones with respect to the number of critical circles on the critical
levels.
