  Some temporal networks, most notably citation networks, are naturally
represented as directed acyclic graphs (DAGs). To detect communities in DAGs,
we propose a modularity for DAGs by defining an appropriate null model (i.e.,
randomized network) respecting the order of nodes. We implement a spectral
method to approximately maximize the proposed modularity measure and test the
method on citation networks and other DAGs. We find that the attained values of
the modularity for DAGs are similar for partitions that we obtain by maximizing
the proposed modularity (designed for DAGs), the modularity for undirected
networks and that for general directed networks. In other words, if we neglect
the order imposed on nodes (and the direction of links) in a given DAG and
maximize the conventional modularity measure, the obtained partition is close
to the optimal one in the sense of the modularity for DAGs.
