Mathematical Modelling of Weighted Networks

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Mathematical Modelling of Weighted Networks
Orestis Chrysafis Chris Cannings School Of
Medicine Biomedical Sciences, University Of
Sheffield
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The Model
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Case Study
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a) Strength evolution
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a) Strength evolution
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a) Strength evolution

• Simulation parameter values
• Network size N10,000
• d0.5
• f (d)d/(d1)
• Propagation steps n3
• No of edges per new node m2
• Data averaged over 100 runs

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b) Strength-Degree Dependence
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c) Degree Sequence
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d) Joint 2-node degree sequence
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The analytic formula does not factorise, thus
nearest neighbour degree correlations form
systematically.
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d) Joint 2-node degree sequence
Theoretical expectations for a small network with
maximum degree dmax60.
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e) Expected strength distribution
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f) Power-law fitting
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Acknowledgements
Thanks to Nick Monk David Irons The EPSRC