Weighted scale-free networks in Euclidean space using local selection rule

Area of Science:

• Network Science
• Complex Systems
• Statistical Physics

Background:

• Real-world networks like the internet and airport systems exhibit complex structures.
• Existing models like the Barabási-Albert (BA) model use preferential attachment for new node connections.
• A gap exists in modeling local connection preferences in growing networks.

Purpose of the Study:

• To introduce and study a novel spatial scale-free network model.
• To investigate network properties when new nodes connect to nearest neighbors.
• To analyze the impact of spatial embedding on network characteristics.

Main Methods:

• Developing a network model where nodes appear in Euclidean space and connect to the nearest link.
• Analytically calculating link weight distribution based on Euclidean length.
• Deriving the nonlinear dependence of nodal strength on degree.

Main Results:

• The spatial network model demonstrates scale-free behavior, similar to the BA model.
• Link weights follow a power-law distribution related to their spatial length.
• A nonlinear relationship between nodal strength and degree is observed and analytically derived.

Conclusions:

• The proposed spatial network model successfully mimics key properties of real-world scale-free networks.
• Local connection preference, rather than preferential attachment, can lead to scale-free properties.
• The model provides insights into network evolution and structure influenced by spatial embedding.