Organization of complex networks without multiple connections.

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.