The distance backbone of complex networks

Abstract Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks multivariate interactions. We investigate complexity such interactions by inferring connection transitivity that includes all possible measures path length for weighted graphs. The result, without breaking graph into smaller components, distance backbone subgraph sufficient to compute shortest paths. This important understanding dynamics spread communication phenomena real-world networks. general methodology we formally derive yields principled reduction technique provides finer triangular geometry edges—those contribute paths those do not but are involved other network phenomena. demonstrate very small large across domains ranging from air traffic human brain connectome, revealing attacks failures seems stem surprisingly vast amounts redundancy.