2001/03/31 by Güler Ergün, G. Ergun, G. J. Rodgers
Mathematics · Physics and Astronomy · Psychology · #Combinatorics #Complex Network Analysis Techniques #Computer science #Discrete mathematics #Distribution (mathematics) #Exponent #Graph #Logarithm #Mathematical analysis #Mathematics #Mental Health Research Topics #Multiplicative function #Node (physics) #Opinion Dynamics and Social Influence #Physics #Power law #Random graph #Statistical physics #Statistics #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1016/s0378-4371(01)00408-3
published as Physica A 303 (2002) 261-272 · 6 pages and 1 figure, submitted to publication
arxiv created 2001/09/14 · openalex publication_date 2002/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Three models of growing random networks with fitness dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes of connectivity k and random additive fitness η, with rate (k-1)+ η. For η>0 we find the connectivity distribution is power law with exponent γ=<η>+2. In the second model (B), the network is built by connecting nodes to nodes of connectivity k, random additive fitness η and random multiplicative fitness ζ with rate ζ(k-1)+η. This model also has a power law connectivity distribution, but with an exponent which depends on the multiplicative fitness at each node. In the third model (C), a directed graph is considered and is built by the addition of nodes and the creation of links. A node with fitness (α, β), i incoming links and j outgoing links gains a new incoming link with rate α(i+1), and a new outgoing link with rate β(j+1). The distributions of the number of incoming and outgoing links both scale as power laws, with inverse logarithmic corrections.