Approaching the thermodynamic limit in equilibrated scale-free networks
arXiv:0807.1874 · doi:10.1103/PhysRevE.78.061125
Abstract
We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that subleading corrections to the scaling of the position of the cutoff are strong even for networks of order 10^9 nodes. We observe also a logarithmic correction to the scaling for degenerated graphs when the degree distribution follows a power law k^(-3). We study also the distribution of the maximal degree and show that it may have a different scaling than the cutoff and, moreover, it approaches the thermodynamic limit much faster. We present also some results on the cutoff function and the distribution of the maximal degree in equilibrated networks.
9 pages, 5 figures, minor changes, figures replaced
References in corpus (29)
- Emergence of scaling in random networks
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Epidemic spreading in scale-free networks
- The spread of epidemic disease on networks
- Evolution of networks
- Critical phenomena in complex networks
- Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
- Organization of Growing Random Networks
- The statistical mechanics of networks
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- Cut-offs and finite size effects in scale-free networks
- Statistical ensemble of scale-free random graphs
- Canonical Analysis of Condensation in Factorised Steady State
- Condensation in the Backgammon model
- Finiteness and Fluctuations in Growing Networks
- Uncorrelated Random Networks
- Principles of statistical mechanics of random networks
- Complete Condensation in a Zero Range Process on Scale-Free Networks
- On large deviation properties of Erdos-Renyi random graphs
- Homogeneous complex networks
- Routes to thermodynamic limit on scale-free networks
- Phase diagram of the mean field model of simplicial gravity
- Tree Networks with Causal Structure
- A statistical mechanics approach for scale-free networks and finite-scale networks
- Organization of complex networks without multiple connections
- Finite size effects in Barabasi-Albert growing networks
- Statistical mechanics of random graphs
- A program generating homogeneous random graphs with given weights