HierX: Fast multi-scale distance-decay interaction on million-node networks

Clicks: 24
ID: 328598
2026
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Steady

Ranked #48 of 151 articles by views in PNAS nexus

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 151 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
Abstract Many models across the sciences require global distance-decay interactions on large sparse networks. Gravity models, accessibility measures, spatial economic models, and network influence processes all evaluate distance-weighted potential fields: each location accumulates contributions from every other location, weighted by a decaying function of the shortest-path travel cost between them. Computed directly, such aggregate fields require the dense matrix of all pairwise network costs, which scales quadratically in time and memory. Common approximations either discard long-range contributions or fail when interaction is governed by network distances rather than geometric proximity. We introduce HierX, a hierarchical sparse-plus-correction operator for distance-decay potential fields on networks. HierX constructs multi-scale representative layers with explicit correction terms ensuring each location pair contributes exactly once at the finest available resolution. Under bounded-growth assumptions common in spatially embedded networks, applying HierX scales as O(n log n). Systematic benchmarks confirm quasi-linear scaling to 100,000 nodes. In head-to-head comparison with distance cutoff truncation and Nyström low-rank approximation on 25,000-zone networks, HierX achieves 5–9% RMSE at a fraction of the computational work; Nyström degrades severely on steep decay kernels. Case studies compute population-weighted accessibility on the 2.58-million-node Great Britain driving network and the 1.77-million-node London pedestrian network: a one-time hierarchy construction (∼1 hour) yields a compact reusable operator that then evaluates each national-scale accessibility field in under one second (∼700 ms for Great Britain, ∼150 ms for London). Open-source code and worked examples are provided.
Reference Key
openalex_W7210627954 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Alexander Hellervik, J. Bohlin, Claes Andersson
Are you one of these authors? Claim your profile
Journal PNAS nexus
Year 2026
DOI
10.1093/pnasnexus/pgag317
URL
https://doi.org/10.1093/pnasnexus/pgag317
Keywords Keywords not found

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.