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Related Experiment Video

Updated: Feb 8, 2026

The Power of Simplicity: Sea Urchin Embryos as in Vivo Developmental Models for Studying Complex Cell-to-cell Signaling Network Interactions
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Dense power-law networks and simplicial complexes.

Owen T Courtney1, Ginestra Bianconi1

  • 1School of Mathematical Sciences, Queen Mary University of London, E1 4NS, London, United Kingdom.

Physical Review. E
|June 17, 2018
PubMed
Summary

This study introduces a new model for generating dense, scale-free networks using the Pitman-Yor process. This framework can create complex structures like directed simplicial complexes, applicable to social networks and brain data.

Area of Science:

  • Network Science
  • Complex Systems Theory
  • Computational Neuroscience

Background:

  • Dense and scale-free networks are prevalent in online social systems, recommendation engines, and biological systems like the brain.
  • Existing network growth models, such as preferential attachment, can generate scale-free networks but typically produce sparse structures.
  • The constant addition of links and nodes in traditional models limits their ability to create dense, scale-free networks.

Purpose of the Study:

  • To present a novel modeling framework capable of generating networks that are both dense and scale-free.
  • To explore variations of the model for producing undirected and directed scale-free networks with specific degree distribution exponents.
  • To extend the modeling framework to directed two-dimensional simplicial complexes, which generalize networks to capture many-body interactions.

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Main Methods:

  • The proposed model utilizes the Pitman-Yor process as the underlying mechanism for network growth.
  • The framework is adapted to generate undirected scale-free networks with a degree exponent (γ) of 2.
  • The model is extended to create directed networks with tunable power-law out-degree distributions (γ∈(1,2)) and directed simplicial complexes.

Main Results:

  • The developed modeling framework successfully generates networks that exhibit both density and scale-free properties.
  • The model produces undirected scale-free networks with γ=2 and directed networks with tunable power-law out-degree distributions.
  • The extended model generates dense directed simplicial complexes with a power-law distribution of generalized out-degrees.

Conclusions:

  • The Pitman-Yor process provides a viable mechanism for constructing dense, scale-free networks.
  • The model offers flexibility in generating various network types, including directed simplicial complexes, with controlled degree distributions.
  • This framework has potential applications in analyzing complex systems, from social interactions to neural connectivity.