The Role of Directed Edges

Directed edges make community detection more difficult because a path of directed edges can cut across communities in unexpected ways. So far, we have symmetrised followership edges but here we explore community detection when we leave these edges directed. Our spectral embedding approach generalises elegantly: the followership layer is replicated, with two versions of each profile, one to which the ‘out’ edges are attached, and the other to which the ‘in’ edges are attached. The resulting graph has 5 layers (instead of the previous 4) and can be embedded in the same way. Results show that the community structure is much more difficult to detect. This is not surprising since have previously observed that Instagram is a mixture of an information dissemination network (highly directed) and a more conventional social network.