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