2008/10/31 by D. M. Smith, David M. D. Smith, Jukka‐Pekka Onnela +2
Mathematics · Physics and Astronomy · #Acceleration #Applied mathematics #Artificial intelligence #Bridging (networking) #Classical mechanics #Complex Network Analysis Techniques #Complex network #Computer network #Computer science #Constant (computer programming) #Contrast (vision) #Degree (music) #Graph #Graph theory and applications #Master equation #Mathematics #Node (physics) #Non-equilibrium thermodynamics #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #Random graph #Statistical physics #Theoretical computer science #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physreve.79.056101
published as Phys. Rev. E 79, 056101 (2009) · 6 pages, 1 figure, 1 table
arxiv created 2009/04/06 · openalex publication_date 2009/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous efforts at analyzing their degree distributions have employed mean-field techniques. By contrast, we show that it is possible to apply a master-equation approach to such network development. We provide full time-dependent expressions for the evolution of the degree distributions for the canonical situations of random and preferential attachment in networks undergoing constant acceleration. These results are in excellent agreement with results obtained from simulations. We note that a growing nonequilibrium network undergoing constant acceleration with random attachment is equivalent to a classical random graph, bridging the gap between nonequilibrium and classical equilibrium networks.