Analytical results for stochastically growing networks: connection to the zero-range process
1TCMP Division, Saha Institute of Nuclear Physics, 1/AF, Saltlake, Kolkata 700064, India. pk.mohanty@saha.ac.in
Summary
We developed a stochastic network model where node and connection growth is random. This model precisely maps to the zero-range process, enabling analytical calculation of network properties like degree distribution.
Area of Science:
- Network science
- Statistical physics
- Computational biology
Background:
- Growing networks are fundamental in many systems.
- Understanding network evolution requires robust models.
- Stochasticity plays a key role in network dynamics.
Purpose of the Study:
- To introduce a novel stochastic model for growing networks.
- To establish an exact mapping between this model and the zero-range process.
- To analytically determine the degree distribution and infer network evolution rules.
Main Methods:
- Development of a stochastic network growth model.
- Exact mathematical mapping to the zero-range process.
- Analytical calculation of degree distribution for arbitrary evolution rules.
Main Results:
- An exact mapping between the proposed stochastic network model and the zero-range process was established.
- Analytical formulas for the degree distribution were derived.
- The model's applicability was demonstrated on a Saccharomyces cerevisiae protein-protein interaction network.
Conclusions:
- The stochastic network model provides a powerful framework for analyzing network growth.
- The zero-range process mapping allows for precise analytical predictions of network structure.
- This approach facilitates the inference of underlying evolutionary mechanisms in real-world networks.
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