Analytic solutions for links and triangles distributions in finite Barabási-Albert networks
arXiv:1606.04913 · doi:10.1016/j.physa.2016.08.018
Abstract
Barabási-Albert model describes many different natural networks, often yielding sensible explanations to the subjacent dynamics. However, finite size effects may prevent from discerning among different underlying physical mechanisms and from determining whether a particular finite system is driven by Barabási-Albert dynamics. Here we propose master equations for the evolution of the degrees, links and triangles distributions, solve them both analytically and by numerical iteration, and compare with numerical simulations. The analytic solutions for all these distributions predict the network evolution for systems as small as 100 nodes. The analytic method we developed is applicable for other classes of networks, representing a powerful tool to investigate the evolution of natural networks.
References in corpus (13)
- Emergence of scaling in random networks
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Evolution of networks
- Mean-field theory for scale-free random networks
- Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
- Connectivity of Growing Random Networks
- Epidemic dynamics in finite size scale-free networks
- Epidemic threshold in structured scale-free networks
- The topological relationship between the large-scale attributes and local interaction patterns of complex networks
- Mean-field theory for clustering coefficients in Barabasi-Albert networks
- Number of loops of size h in growing scale-free networks
- Network Growth with Arbitrary Initial Conditions: Analytical Results for Uniform and Preferential Attachment