We present an analysis of the formation of atmospheric ﬂux ropes in a magnetohydrodynamic solar ﬂux emergence simulation. The simulation domain ranges from the top of the solar interior to the low corona. A twisted magnetic ﬂux tube emerges from the solar interior and into the atmosphere where it interacts with the ambient magnetic ﬁeld. By studying the connectivity of the evolving magnetic ﬁeld, we are able to better understand the process of ﬂux rope formation in the solar atmosphere. In the simulation, two ﬂux ropes are produced as a result of ﬂux emergence. Each has a different evolution resulting in different topological structures. These are determined by plasma ﬂows and magnetic reconnection. As the ﬂux rope is the basic structure of the coronal mass ejection, we discuss the implications of our ﬁndings for solar eruptions.