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Shortest-Path Percolation on Random Networks.

Minsuk Kim1, Filippo Radicchi1

  • 1Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, <a href="https://ror.org/01kg8sb98">Indiana University</a>, Bloomington, Indiana 47408, USA.

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This summary is machine-generated.

We introduce a bond-percolation model for transport network resource exhaustion. Removing shortest paths causes a percolation transition, revealing distinct behaviors for finite versus infinite budgets.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Transportation Systems

Background:

  • Transport networks face resource consumption and exhaustion challenges.
  • Understanding network resilience under demand is crucial for infrastructure management.

Purpose of the Study:

  • To propose and analyze a bond-percolation model for resource exhaustion in transport networks.
  • To investigate the shortest-path-percolation transition and its characteristics.

Main Methods:

  • Development of a bond-percolation model where edges on shortest paths are removed based on a budget.
  • Study of the percolation transition in homogeneous random graphs.
  • Application of finite-size scaling analysis to characterize the transition.

Main Results:

  • For a finite budget, the transition mirrors ordinary percolation, with a single giant cluster shrinking.
  • For an infinite budget, the transition is abrupt, causing sudden fragmentation of the giant component.
  • The model fully characterizes the shortest-path-percolation transition in random graphs.

Conclusions:

  • The proposed model effectively describes resource exhaustion and network fragmentation.
  • Network behavior under resource constraints differs significantly based on budget limitations.
  • Findings offer insights into transport network resilience and critical transition points.