# Directed Network Comparison Using Motifs

## TL;DR

This paper introduces a new method to compare directed networks by analyzing their motif structures, which captures local and global differences more effectively than existing methods.

## Contribution

The novel contribution is a motif-based approach for comparing directed networks using node-specific motif distributions and Jensen–Shannon divergence.

## Key findings

- The proposed method outperforms existing baselines in comparing real directed networks and their perturbed versions.
- The method is robust to different parameter settings and captures higher-order network differences effectively.

## Abstract

Analyzing and characterizing the differences between networks is a fundamental and challenging problem in network science. Most previous 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 the 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.