Felipe Xavier Costa1,2,3,†, Rion B. Correia1,3,†, Luis M. Rocha1,3,*
1Systems Science and Industrial Engineering Department, Binghamton University (State University of New York), Binghamton NY 13902, USA
2Department of Physics, State University of New York at Albany, Albany NY 12222, USA
3Instituto Gulbenkian de Ciencia, Portugal
† Equal contribution. * To whom correspondence she be addressed.
Citation: F.X. Costa, R.B. Correia, L.M. Rocha [2022]. The distance backbone of directed networks. In: The 11th International Conference on Complex Networks and their Applications. Palermo, Italy, 8-10 November 2022.
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In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We have previously developed a parameter-free, algebraically-principled methodology to uncover such redundancy and reveal the distance backbone of weighted graphs, which has been shown to be important in transmission dynamics, inference of important paths, and quantifying the robustness of networks. However, the method was developed for undirected graphs. Here we expand this methodology to weighted directed graphs and study the redundancy and robustness found in nine networks ranging from social, biomedical, and technical systems. We found that similarly to undirected graphs, directed graphs in general also contain a large amount of redundancy, as measured by the size of their (directed) distance backbone. Our methodology adds an additional tool to the principled sparsification of complex networks and the measure of their robustness.
Keywords: Directed networks, Weighted graphs, Network backbones, Sparsification. Shortest path, Redundancy