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Related Experiment Videos

Degree-dependent intervertex separation in complex networks.

S N Dorogovtsev1, J F F Mendes, J G Oliveira

  • 1Departamento de Física da Universidade de Aveiro, Portugal. sdorogov@fis.ua.pt

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 29, 2006
PubMed
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We analyzed shortest path lengths in growing networks. Deterministic scale-free networks show a power-law correction to logarithmic dependence, while growing trees exhibit linear dependence on degree.

Area of Science:

  • Network Science
  • Statistical Physics

Background:

  • Understanding network structure is crucial for various fields.
  • Growing networks, where nodes and edges are added over time, present unique structural properties.
  • Correlations within networks significantly influence path lengths.

Purpose of the Study:

  • To investigate the mean shortest path length between vertices of a specific degree (k) in growing networks.
  • To analyze the impact of network correlations on shortest path lengths.
  • To compare path length dependencies in deterministic and random growing networks.

Main Methods:

  • Analysis of deterministic scale-free networks.
  • Study of random scale-free networks with preferential attachment.
  • Examination of stochastic and deterministic growing trees with exponential degree distributions.

Related Experiment Videos

  • Comparison with uncorrelated graphs.

    • Main Results:

    • Deterministic scale-free networks exhibit a power-law correction to logarithmic dependence for mean shortest path length: (l)(k) = A ln[N/k((gamma-1)/2)]-Ck(gamma-1)/N.
    • Growing trees show a linear dependence on degree: (l)(k) approximately A ln N-Ck.
    • Observed differences in path length dependencies between deterministic and random growing networks.

    Conclusions:

    • Network correlations play a vital role in shaping shortest path lengths in growing networks.
    • The studied growing network models display distinct shortest path length behaviors.
    • Findings provide insights into the topological properties of complex growing systems.