Growing multiplex networks with arbitrary number of layers
Naghmeh Momeni1, Babak Fotouhi2
1Department of Electrical and Computer Engineering, McGill University, Montréal, Québec, H3A 2A7 Canada.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2016
Summary
This study provides new mathematical solutions for the joint degree distribution in growing multiplex networks, considering heterogeneous growth and multiple layers. Findings help predict network structure over time.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Existing research on growing multiplex networks is limited to two layers and homogeneous growth.
- Previous models focused on steady-state (infinite size) conditions.
Purpose of the Study:
- To derive closed-form solutions for the joint degree distribution in growing multiplex networks with arbitrary layers and heterogeneous growth.
- To extend analysis to time-dependent distributions and arbitrary initial conditions.
Main Methods:
- Derivation of analytical solutions for steady-state and time-dependent joint degree distributions.
- Analysis of both uniform and preferential heterogeneous growth mechanisms.
- Validation through Monte Carlo simulations.
Main Results:
- Closed-form solutions for heterogeneously growing multiplex networks with multiple layers in steady-state.
- Closed-form solutions for time-dependent joint degree distributions under uniform growth.
- Demonstration of the impact of initial network conditions on transient dynamics.
Conclusions:
- The study advances the characterization of growing multiplex networks.
- Provides tools for predicting temporal variations and future structural properties.
- Offers a more comprehensive understanding beyond simplified models.
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