  Analyzing and characterizing the differences between networks is a
fundamental and challenging problem in network science. Previously, most
network comparison methods that rely on topological properties have been
restricted to measuring differences between two undirected networks. However,
many networks, such as biological networks, social networks, and transportation
networks, exhibit inherent directionality and higher-order attributes that
should not be ignored when comparing networks. Therefore, we propose a
motif-based directed network comparison method that captures local, global, and
higher-order differences between two directed networks. Specifically, we first
construct a motif distribution vector for each node, which captures the
information of a node's involvement in different directed motifs. Then, the
dissimilarity between two directed networks is defined on the basis of a matrix
which is composed of the motif distribution vector of every node and
Jensen-Shannon divergence. The performance of our method is evaluated via the
comparison of six real directed networks with their null models as well as
their perturbed networks based on edge perturbation. Our method is superior to
the state-of-the-art baselines and is robust with different parameter settings.
