Beyond bond links in complex networks:Local bridges, global bridges and silk links

Many network researchers use intuitive or basic definitions when discussing the importance of strong and weak links and their roles. Others use an approach best described as “if not strong, then weak” to determine the strengths and weaknesses of individual links, thus deemphasizing hierarchical network structures that allow links to express different strength levels. Here we describe our proposal for a hierarchical edge type analysis (HETA) algorithm for determining link types at multiple network hierarchy levels based on the common neighbor concept plus statistical factors such as bond links, kth-layer local bridges, global bridges, and silk links—all generated during long-term network development and evolution processes. Two sets of networks were used to validate our proposed algorithm, one consisting of 16 networks employed in multiple past studies, and one consisting of two types of one-dimensional small-world networks expressing different random rewiring or shortcut addition probabilities. Two applications with potential for developmental contributions are demonstrated: a network fingerprint analysis framework, and a hierarchical network community partition method.