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Growing random networks with fitness

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  • Ergün, G.
  • Rodgers, G.J.

Abstract

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.

Suggested Citation

  • Ergün, G. & Rodgers, G.J., 2002. "Growing random networks with fitness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 261-272.
  • Handle: RePEc:eee:phsmap:v:303:y:2002:i:1:p:261-272
    DOI: 10.1016/S0378-4371(01)00408-3
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    Citations

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    Cited by:

    1. Zheng, Xiaolong & Zeng, Daniel & Li, Huiqian & Wang, Feiyue, 2008. "Analyzing open-source software systems as complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6190-6200.
    2. Behfar, Stefan Kambiz & Turkina, Ekaterina & Cohendet, Patrick & Burger-Helmchen, Thierry, 2016. "Directed networks’ different link formation mechanisms causing degree distribution distinction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 479-491.
    3. Santiago, A. & Benito, R.M., 2008. "Connectivity degrees in the threshold preferential attachment model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(10), pages 2365-2376.
    4. Kii, Masanobu & Akimoto, Keigo & Doi, Kenji, 2012. "Random-growth urban model with geographical fitness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5960-5970.
    5. Andersson, Claes & Hellervik, Alexander & Lindgren, Kristian, 2005. "A spatial network explanation for a hierarchy of urban power laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 227-244.
    6. Claes Andersson & Koen Frenken & Alexander Hellervik, 2006. "A complex network approach to urban growth," Environment and Planning A, Pion Ltd, London, vol. 38(10), pages 1941-1964, October.
    7. Wang, Jianrong & Wang, Jianping & Han, Dun, 2017. "Nonlinear dynamic evolution and control in CCFN with mixed attachment mechanisms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 120-132.
    8. Colizza, Vittoria & Flammini, Alessandro & Maritan, Amos & Vespignani, Alessandro, 2005. "Characterization and modeling of protein–protein interaction networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(1), pages 1-27.
    9. Santiago, A. & Benito, R.M., 2009. "Local affinity in heterogeneous growing networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2941-2948.

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    Keywords

    Growing network; Fitness;

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