To study the controllability of a class of directed signed multi-agent systems based on directed paths, the Laplacian matrix and graph theory are used to analyze. Firstly, it is proved that adding or removing a specific class of edges in the network does not change the system's controllability. Secondly, the controllability of the directed paths is studied, and then we check the system's controllability after adding reverse or forward edges in the directed paths. The results show that increasing the reverse edges in directed paths has no influences on its original controllability, However, the system's controllability needs to be analyzed according to the specific situations while increasing the forward ones by taking advantage of the almost equitable partitons. Finally, combined with the results above, a method of constructing directed complex network topologies is given.
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