Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distance backbone of complex networks   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.

29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math