Finite-size scaling of percolation on scale-free networks

Abstract

Critical phenomena on scale-free networks with a degree distribution $p_k\sim k^{-\lambda }$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify two distinct crossover routes to mean-field behavior: one controlled by the degree exponent $\lambda$, the other by the degree cutoff $K\sim V^{\kappa }$, where $V$ is the system size and $\kappa \in [0,1]$ is the cutoff exponent. Increasing $\lambda$ or decreasing $\kappa$ suppresses heterogeneity and drives the system toward mean-field behavior, with logarithmic corrections near the marginal case. These findings provide a unified picture of the crossover from heterogeneous to homogeneous criticality. In the crossover regime, we observe rich finite-size phenomena, including the transition from vanishing to divergent susceptibility, distinct exponents for the shift and fluctuation of pseudocritical points, and a numerical clarification of previous theoretical predictions.

arXiv comment10 pages, 9 figures

References in corpus (35)

• Power-law distributions in empirical data
• Random graphs with arbitrary degree distributions and their applications
• Critical phenomena in complex networks
• Breakdown of the Internet under intentional attack
• Generation of uncorrelated random scale-free networks
• The statistical mechanics of networks
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Percolation on complex networks: Theory and application
• Percolation Critical Exponents in Scale-Free Networks
• Cut-offs and finite size effects in scale-free networks
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Statistical ensemble of scale-free random graphs
• Non mean-field behavior of the contact process on scale-free networks
• Percolation on correlated networks
• Finite-size scaling in complex networks
• Critical phenomena in networks
• Uncorrelated Random Networks
• A new route to Explosive Percolation
• Evolution of scale-free random graphs: Potts model formulation
• Principles of statistical mechanics of random networks
• Breaking of the site-bond percolation universality in networks
• Width of percolation transition in complex networks
• Routes to thermodynamic limit on scale-free networks
• Intrinsic degree-correlations in static model of scale-free networks
• General expression for the component size distribution in infinite configuration networks
• Numerical evaluation of the upper critical dimension of percolation in scale-free networks
• Explosive Percolation Obeys Standard Finite-Size Scaling in an Event-based Ensemble
• Fundamental Structural Constraint of Random Scale-Free Networks
• Explosive percolation in finite dimensions
• Approaching the thermodynamic limit in equilibrated scale-free networks
• Scaling and universality for percolation in random networks: A unified view
• Percolation on a maximally disassortative network
• Universality of percolation at dynamic pseudocritical point
• Self-similar gap dynamics in percolation and rigidity percolation
• Crossover Finite-Size Scaling Theory and Its Applications in Percolation

Cited by in corpus (1)

• Shortest-path percolation on scale-free networks