We consider the web community detection problem by providing a cost function that, not only penalizes external connections, but also rewards the internal ones. Our formulation addresses limitations of cut-clustering and extends web communities to digraphs. The formulation is parametric, resulting in a hierarchy of communities that is representable in linear storage and computable in a linear number of maxflow computations. Experimental results on synthetic and real-world datasets show that the proposed method can find better web communities and more densest subgraphs than previous formulations. Simple examples also show it can return different and more meaningful communities than other formulations based on graph conductance, map equation and modularity score.