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Mathematical Modelling of Weighted Networks

Mathematical Modelling of Weighted Networks. Orestis Chrysafis – Chris Cannings School Of Medicine & Biomedical Sciences, University Of Sheffield. The Model. Case Study. a) Strength evolution. a) Strength evolution. a) Strength evolution. Simulation parameter values:

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Mathematical Modelling of Weighted Networks

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  1. Mathematical Modelling of Weighted Networks Orestis Chrysafis – Chris Cannings School Of Medicine & Biomedical Sciences, University Of Sheffield

  2. The Model

  3. Case Study

  4. a) Strength evolution

  5. a) Strength evolution

  6. a) Strength evolution • Simulation parameter values: • Network size: N=10,000 • δ=0.5 • f(δ)=δ/(δ+1) • Propagation steps: n=3 • No of edges per new node: m=2 • Data averaged over 100 runs

  7. Simulation parameter values: • Network size: N=104 • δ=0.5 • f(δ)=δ/(δ+1) • Propagation steps: n=3 • No of edges per new node: m=1 • Data from single random realization of the network b) Strength-Degree Dependence

  8. Simulation parameter values: N=104, δ=0.5, f(δ)=δ/(δ+1), n=3, m=1 Data averaged over 100 runs c) Degree Sequence

  9. d) Joint 2-node degree sequence

  10. Parameter values: N=104, δ=0.5, f(δ)=δ/(δ+1), n=3, m=1, and the direction of the edges has been accounted for. The analytic formula does not factorise, thus nearest neighbour degree correlations form systematically.

  11. d) Joint 2-node degree sequence Theoretical expectations for a small network with maximum degree dmax=60.

  12. Simulation parameter values: N=104, δ=0.5, f(δ)=δ/(δ+1), n=3, m=2 Data averaged over 100 runs and binned logarithmically. e) Expected strength distribution

  13. f) Power-law fitting

  14. Acknowledgements Thanks to: Nick Monk David Irons The EPSRC

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