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Fragmentation properties of two-dimensional proximity graphs considering random failures and targeted attacks
C Norrenbrock1, O Melchert1, A K Hartmann1
1Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany.
Physical Review. E
|January 14, 2017
Summary
Proximity graphs remain connected until a critical fraction of nodes are removed, causing fragmentation. This study quanties this fragmentation threshold for various graph types and removal strategies.
Area of Science:
- Network science
- Graph theory
- Complex systems
Background:
- Proximity graphs are characterized by connectivity, enabling robust network function against failures.
- Understanding graph fragmentation is crucial for network resilience.
Purpose of the Study:
- To investigate the structural impact of successive node removal on proximity graphs.
- To identify the fragmentation threshold and characterize the process.
Main Methods:
- Analyzing different proximity graph types under various node-deletion strategies.
- Employing observables like component size, hop diameter, and backup capacity.
- Utilizing finite-size scaling analysis to determine critical thresholds.
Main Results:
- Graph fragmentation upon node removal exhibits characteristics of a second-order phase transition.
- The study numerically assesses the threshold fraction of removed nodes triggering fragmentation.
- Fragmentation thresholds are dependent on graph type and node deletion strategy.
Conclusions:
- Node removal in proximity graphs leads to fragmentation, predictable via phase transition dynamics.
- The identified thresholds are critical for understanding network decomposition.
- This research provides insights into network robustness and failure mechanisms.
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