An Automorphic Distance Metric and Its Application to Node Embedding for Role Mining

Role is a fundamental concept in the analysis of behavior and function interacting entities complex networks. discovery task uncovering hidden roles nodes within network. Node are commonly defined terms equivalence classes. Two have same role if they fall class. Automorphic equivalence, where two equivalent when can swap their labels to form an isomorphic graph, captures this notion role. The binary too restrictive, real-world networks rarely belong Instead, relaxed definition similarity or distance used compute degree which equivalent. In paper, we propose novel metric called automorphic distance, measures how far from being automorphically We also study its application node embedding, showing our be generate role-preserving vector representations nodes. Our experiments confirm that proposed outperforms state-of-the-art equivalence-based different techniques for generation embeddings role-related tasks.