Triadic closure as a basic generating mechanism of communities in complex networks.

Area of Science:

• Network Science
• Computational Social Science
• Statistical Physics

Background:

• Complex networks, including social, technological, and biological systems, exhibit universal properties like small-world, scale-free, and community structures.
• While community structures are widely observed, the underlying mechanisms that spontaneously generate them remain less understood.
• Triadic closure, a common mechanism for forming new connections, is particularly relevant in social networks.

Purpose of the Study:

• To investigate universal mechanisms for spontaneous network community generation.
• To demonstrate that triadic closure models can naturally produce community structures.
• To explore the impact of network properties and node attributes on community formation.

Main Methods:

• Modeling network growth using a simple triadic closure mechanism.
• Analyzing emergent properties such as community structure, node degree distribution, and clustering coefficients.
• Introducing fitness-based link attractivity to study phase transitions in network organization.

Main Results:

• Triadic closure models naturally generate community structures alongside fat-tailed degree distributions and high clustering coefficients.
• Community structure is more pronounced in sparser networks and diminishes with increased link density or random attachment.
• A phase transition occurs with fitness-based attractivity: communities disappear under high fitness heterogeneity, replaced by a mesoscopic organization around superhubs.

Conclusions:

• Simple triadic closure is a fundamental mechanism driving community emergence in growing networks.
• Network density and attachment randomness influence the visibility and stability of community structures.
• Node fitness heterogeneity can lead to alternative network organizations, characterized by superhub dominance rather than distinct communities.