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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Generalised thresholding of hidden variable network models with scale-free property.

Sámuel G Balogh¹, Péter Pollner², Gergely Palla²

¹Department of Biological Physics, Eötvös University, H-1117, Budapest, Hungary. balogh@hal.elte.hu.

Scientific Reports

|August 4, 2019

Summary

This study generalizes hidden variable models for complex networks, enabling the creation of scale-free networks with tunable properties. The research offers analytical insights and proposes methods for generating sparse scale-free networks with flexible exponents.

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Area of Science:

Network Science
Statistical Physics

Background:

Hidden variable formalisms are effective for analyzing complex network topology.
Scale-free networks are crucial in various scientific domains.
Existing models often rely on specific thresholding mechanisms for hidden variables.

Purpose of the Study:

To generalize existing hidden variable models for complex network generation.
To analytically investigate conditions for scale-free network emergence.
To explore methods for creating sparse scale-free networks with adjustable exponents.

Main Methods:

Extending connection probabilities and hidden variable distributions.
Analytical investigation of network properties.
Relaxing hard thresholding mechanisms in network formation.

Main Results:

The generalized model reproduces scale-free networks with a degree exponent of γ=2.
Analytical conditions for scale-free behavior were derived.
A relaxed thresholding approach allows for sparse scale-free networks with arbitrary scaling exponents.

Conclusions:

The proposed generalization enhances the flexibility of hidden variable models for complex networks.
The findings provide a deeper analytical understanding of scale-free network formation.
The work facilitates the generation of diverse and sparse scale-free network structures.