ArticlePNAS nexus2025
Economical representation of spatial networks.
Article in PNAS nexus, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
What it found
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
0 citing papers in PubMed.
No citing paper in PubMed yet.
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Authors and funding
2 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Network representation is crucial across various scientific, societal, technological, and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication, and support decision-making. This is typically achieved by rearranging the nodes to minimize the edge crossings responsible of unintelligible and often unesthetic trends. But when the nodes cannot be moved, as in spatial and physical networks, this procedure is not viable. Here, we overcome this impasse by turning the edge crossing problem into a graph filtering optimization. By introducing the concept of progressive cost, we demonstrate that longer connections prompt the optimal solution to yield sparser networks, thereby limiting the number of intersections and getting more readable layouts. This theoretical result matches human behavior and provides an ecologically inspired criterion to visualize and model real-world interconnected systems.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.