Clustering for an undirected graph often assumes a symmetric adjacency matrix. You can always convert your directed graph to an undirected one if you accept the corresponding loss of information. This is a common approach and works well enough in many cases. Otherwise, there are specific algorithms for directed graphs. For example, spectral clustering can be applied to directed graphs by adapting the graph Laplacian (for details, see this master thesis on spectral clustering algorithms for directed graphs). Modularity-based algorithms have also been extended to directed graphs (e.g. paper on the directed Louvain algorithm).