2008/04/30 by P. L. Krapivsky, Paul Krapivsky, Dmitri Krioukov · 1 citation
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #cs.NI #physics.soc-ph
paper · pdf · doi:10.1103/physreve.78.026114
published as Phys. Rev. E 78, 026114 (2008)
openalex publication_date 2008/08/21 · arxiv created 2008/08/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing network models that perfectly match the structure of some real scale-free networks, such as the Internet. We obtain an analytic solution, supported by extensive simulations, for the degree distribution in superlinearly growing networks with arbitrary average degree, and confirm that in the true thermodynamic limit these networks are indeed degenerate, i.e., almost all nodes have low degrees. We then show that superlinear growth has vast preasymptotic regimes whose depths depend both on the average degree in the network and on how superlinear the preference kernel is. We demonstrate that a superlinearly growing network model can reproduce, in its preasymptotic regime, the structure of a real network, if the model captures some sufficiently strong structural constraints-rich-club connectivity, for example. These findings suggest that real scale-free networks of finite size may exist in pre-asymptotic regimes of network evolution processes that lead to degenerate network formations in the thermodynamic limit.