2020/11/30 by Yi-Jiao Zhang, Kai-Cheng Yang, Kai‐Cheng Yang +1 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · Social Sciences · #Artificial intelligence #Centrality #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Discrete mathematics #Embedding #Geometric networks #Geometry #Geometry and topology #Human Mobility and Location-Based Analysis #Mathematics #Metric (unit) #Metric space #Node (physics) #Opportunistic and Delay-Tolerant Networks #Pairwise comparison #Physics #Simple (philosophy) #Space (punctuation) #Theoretical computer science #Topology (electrical circuits) #physics.soc-ph
paper · pdf · doi:10.1103/physreve.103.012305
published in Physical review. E 103(1), 012305 (American Physical Society) · 15 pages, 12 figures, 1 table
arxiv created 2021/01/14 · openalex publication_date 2021/01/14 · arxiv updated 2021/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular methods employed in network embedding either rely on implicit approximations of the principle of proximity preservation or implement it by enforcing the geometry of the embedding space, thus hindering geometric properties that networks may spontaneously exhibit. Here we take advantage of a model-free embedding method explicitly devised for preserving pairwise proximity and characterize the geometry emerging from the mapping of several networks, both real and synthetic. We show that the learned embedding has simple and intuitive interpretations: the distance of a node from the geometric center is representative for its closeness centrality, and the relative positions of nodes reflect the community structure of the network. Proximity can be preserved in relatively low-dimensional embedding spaces, and the hidden geometry displays optimal performance in guiding greedy navigation regardless of the specific network topology. We finally show that the mapping provides a natural description of contagion processes on networks, with complex spatiotemporal patterns represented by waves propagating from the geometric center to the periphery. The findings deepen our understanding of the model-free hidden geometry of complex networks.