Distinguishing Arc Types to Understand Complex Network Strength Structures and Hierarchical Connectivity Patterns

Many real-world networks consisting of nodes representing (in)tangible asymmetric information or energy flows must be modeled as directed graphs (digraphs). Several methods for classifying non-directional edges in terms of strong or weak ties have been developed for well-known non-directional networks, but none specifically for directed networks. In almost all cases, definitions and identification methods are simple, incomplete, reliant on intuition, and based on the assumption that anything that is not weak must be strong. Researchers have generally failed to consider overlapping and hierarchical community properties that accurately reflect organizational structures or the functional components commonly found in real-world complex networks, resulting in multiple challenges to analyzing many types of directed networks. In this paper we describe a method that considers asymmetric definitions of arc strength, especially when arcs hold important directional significance. To more fully capture overlapping and hierarchical network community structures, we used hierarchy-based definitions to identify bond arcs, $k$ th-layer local bridges, global bridges, and silk arcs and to create a hierarchical arc type analysis (HATA) algorithm. The algorithm employs a mix of common middle node measures and statistical parameters generated by randomized directed networks corresponding to the network being investigated. To test the HATA algorithm, we conducted four experiments involving a mix of arc rewiring and additions, multiple datasets associated with the Travian game, 56 empirical networks from previous studies, and 3 bird song transition networks. Our results indicate that HATA offers a novel perspective to understanding arc strengths and structures in directed complex networks.