© 2018 The Combustion Institute. The topology of flame-flame interaction is analysed for single turbulent premixed flames with increasing turbulence intensity. Morse theory for critical points is used for identifying the flame-flame interaction and characterising the local topology. The interactions have been categorised into four different groups, namely reactant pocket, tunnel formation, tunnel closure and product pocket. A histogram showing the frequency of occurrence of each of these groups is presented for single flames representative of hydrocarbon-air combustion and is compared with the results of colliding hydrogen-air flames. It is observed that most interactions for a single flame occur toward the leading edge. Also, more interactions are observed for higher intensity turbulence. The cylindrical topology types are found to dominate over spherical topology types. The relative frequency of occurrence of each type of topology is observed to change with changes in turbulence intensity. With increasing turbulence intensity, the fraction of product pockets and tunnel formation events increases whereas the fraction of reactant pockets and tunnel closure events decreases. The rise in product pockets is mirrored by the drop in reactant pockets, and likewise, the rise in tunnel formation events is mirrored by the drop in tunnel closure events.