The Conditions Oatabase (CondOB) of the LHCb experiment provides versioned, time dependent geometry and conditions data for all LHCb data processing applications (simulation, high level trigger, reconstruction, analysis). The evolution of CondOB and of the LHCb applications is a weakly-homomorphic process. It means that compatibility between a CondOB state and LHCb application state may not be preserved across different database and application generations. More over, a CondOB state by itself belongs to a complex three-dimensional phase space which evolves according to certain CondOB self-compatibility criteria, so it is sometimes difficult even to determine a self-consistent CondOB state. These compatibility issues may lead to various kinds of problems in the LHCb production, varying from unexpected application crashes to incorrect data processing results. Thus, there is a need for defining a well-established set of compatibility criteria between mentioned above entities, together with developing a compatibility tracking system which will help to discover incompatibilities avoiding their negative consequences. This paper describes an attempt to approach this goal in the frame of the graph theory which allows to formalize elegantly the task of compatibility tracking.
