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Bootstrap percolation on spatial networks.

Jian Gao1, Tao Zhou1,2, Yanqing Hu3,4

  • 1CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China.

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|October 2, 2015
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Summary
This summary is machine-generated.

This study explores bootstrap percolation on spatial networks. A critical exponent of -1 reveals a universal double phase transition, crucial for understanding information spread in social networks.

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Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • Bootstrap percolation models networked activation processes, explaining social phenomena like information propagation.
  • Online social networks exhibit complex spatial structures influencing these processes.

Purpose of the Study:

  • Investigate bootstrap percolation on spatial networks with power-law distributed long-range links.
  • Analyze the impact of the power-law exponent on phase transitions and network behavior.

Main Methods:

  • Utilized bootstrap percolation theory on undirected spatial networks.
  • Modeled long-range link lengths using a power-law probability density function with a tunable exponent.
  • Employed the size of the giant active component as the order parameter to identify phase transitions.

Main Results:

  • A parameter-dependent critical value for the power-law exponent was identified.
  • Above this critical value, a double phase transition (second-order and hybrid) occurs.
  • Below this value, only a second-order phase transition is observed.
  • A parameter-independent critical value around -1 was discovered, where double phase transition critical points remain stable.
  • This critical value of -1 closely matches exponents found in real online social networks (e.g., LiveJournal).

Conclusions:

  • The study clarifies the self-organization of spatial structures in online social networks.
  • Findings offer insights into the mechanisms of information spreading within these networks.
  • The critical exponent of -1 appears to be a significant universal feature for information diffusion in real-world networks.