Explainability in Graph Data Science: Interpretability, replicability, and reproducibility of community detection

In many modern data science problems, data are represented by a graph (network), e.g., social, biological, and communication networks. Over the past decade, numerous signal processing and machine learning (ML) algorithms have been introduced for analyzing graph structured data. With the growth of interest in graphs and graph-based learning tasks in a variety of applications, there is a need to explore explainability in graph data science. In this article, we aim to approach the issue of explainable graph data science, focusing on one of the most fundamental learning tasks, community detection, as it is usually the first step in extracting information from graphs. A community is a dense subnetwork within a larger network that corresponds to a specific function. Despite the success of different community detection methods on synthetic networks with strong modular structure, much remains unknown about the quality and significance of the outputs of these algorithms when applied to real-world networks with unknown modular structure. Inspired by recent advances in explainable artificial intelligence (AI) and ML, in this article, we present methods and metrics from network science to quantify three different aspects of explainability, i.e., interpretability, replicability, and reproducibility, in the context of community detection.