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Updated: Aug 1, 2026
10:32
Design, Surface Treatment, Cellular Plating, and Culturing of Modular Neuronal Networks Composed of Functionally Inter-connected Circuits
Published on: April 15, 2015
Organization of complex networks without multiple connections
S N Dorogovtsev1, J F F Mendes, A M Povolotsky
1Departamento de Física da Universidade de Aveiro, 3810-193 Aveiro, Portugal.
Physical Review Letters
|December 31, 2005
Summary
Complex random networks exhibit a novel core structure with highly interconnected vertices when connection density is high. This core
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Understanding the structural properties of complex random networks is crucial in various scientific domains.
- Previous research has explored network topology but lacked detailed characterization of core structures in specific network types.
Purpose of the Study:
- To identify and characterize a new structural feature in equilibrium complex random networks.
- To analyze the formation and properties of a highly interconnected core within these networks.
Main Methods:
- Analysis of equilibrium complex random networks, specifically excluding multiple and self-connections.
- Mathematical derivation and simulation to determine the size and characteristics of the network core.
Main Results:
- A novel structural feature, a highly interconnected core, is identified in dense random networks.
- The number of vertices in this core scales between N^(1/2) and N^(2/3), where N is the total number of vertices.
- The size-dependent cutoff of the connection distribution at the core's emergence differs from prior estimations.
Conclusions:
- The identified core structure is a fundamental property of dense random networks.
- The findings refine our understanding of network organization and provide new parameters for network models.
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