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Modulated scale-free network in Euclidean space.

S S Manna¹, Parongama Sen

¹Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700098, India. manna@boson.bose.res.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 7, 2003

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This study reveals that random networks exhibit scale-free properties for specific parameter values (alpha > alpha(c)). For other values, the network

Area of Science:

Complex systems
Network science
Statistical physics

Background:

Understanding the structure and properties of complex random networks is crucial in various scientific fields.
Previous models often focused on specific network topologies, limiting generalizability.

Purpose of the Study:

To investigate the emergence of scale-free properties in a growing random network model.
To analyze the impact of node connection probability on network characteristics.
To characterize the link length distribution within the generated networks.

Main Methods:

A random network growth model was simulated on Euclidean space.
Nodes were introduced at a unit rate and connected to predecessors based on a probability function involving node degree and link length.

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Numerical simulations were employed to study the network's degree and link length distributions for varying parameter values (alpha).

Main Results:

The network exhibits scale-free behavior for alpha values greater than a critical threshold (alpha(c)).
For other alpha values, the degree distribution follows a stretched exponential decay.
The link length distribution was found to follow a power law, D(l) approximately l(delta), with an exactly calculable exponent delta.

Conclusions:

The studied random network model can generate scale-free networks under specific conditions.
The parameter alpha plays a critical role in determining the network's topological properties, specifically its degree distribution.
The link length distribution is consistently power-law-like, offering insights into spatial network organization.