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Topology and Dynamics of Complex Networks

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Topology and Dynamics of Complex Networks

Topology and Dynamics of Complex Networks

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1. Topology and Dynamics ofComplex Networks FRES1010 Complex Adaptive Systems Eileen Kraemer Fall 2005

2. Based on … • Strogatz (2001), • Barabási & Bonabeau (2003), • http://powerlaws.media.mit.edu/papers/barabasi03.pdf • Wang, X. F. (2002)

3. Topology and Dynamics ofComplex Networks • Introduction • Three structural metrics • Four structural models • Structural case studies • Node dynamics and self-organization • Bibliography

4. Introduction • Examples of complex networks • Elementary features • Motivations

5. Examples of complex networks: geometric, regular

6. Examples of complex networks: semi-geometric, irregular

7. Elementary features:node diversity and dynamics

8. Elementary features:edge diversity and dynamics

9. Elementary features:Network Evolution

10. Motivations • complex networks are the backbone of complex systems • every complex system is a network of interaction among numerous smaller elements • some networks are geometric or regular in 2-D or 3-D space • other contain “long-range” connections or are not spatial at all • understanding a complex system = break down into parts + reassemble • network anatomy is important to characterize because structure affects function (and vice-versa) • ex: structure of social networks • prevent spread of diseases • control spread of information (marketing, fads, rumors, etc.) • ex: structure of power grid / Internet • understand robustness and stability of power / data transmission

11. Three structural metrics • Average path length • Degree distribution(connectivity) • Clustering coefficient

12. Structural metrics: Average path length

13. Structural Metrics:Degree distribution(connectivity)

14. Structural Metrics:Clustering coefficient

15. Four structural models • Regular networks • Random networks • Small-world networks • Scale-free networks

16. Regular networks –fully connected

17. Regular networks –Lattice

18. Regular networks –Lattice: ring world

19. Random networks

20. Random Networks

21. Small-world networks

22. Small-world networks

23. Small-world networks

24. Small-world networks

25. Scale-free networks

26. Scale-free networks

27. Scale-free networks

28. Scale-free networks

29. Scale-free networks

30. Scale-free networks

31. Case studies • Internet • World Wide Web • Actors & scientists • Neural networks • Cellular metabolism

32. The Internet

33. The Internet

34. The Internet

35. The World Wide Web

36. World Wide Web

37. World Wide Web

38. Actors

39. Mathematicians &Computer Scientists

40. Node dynamics and self-organization • Node dynamics • Attractors in full & lattice networks • Synchronization in full networks • Waves in lattice networks • Epidemics in complex networks

41. Node dynamics: individual node

42. Node dynamics:coupled nodes

43. Node dynamics and self-organization

44. Node dynamics and self-organization

45. Node dynamics and self-organization

46. Node dynamics and self-organization

47. Node dynamics and self-organization

48. Bibliography • Reviews • Barabási, A.-L. (2002) Linked: The New Science of Networks.Perseus Books. • Barabási, A.-L. and Bonabeau, E. (2003) Scale-free networks. Scientific American, 288: 60-69. • Strogatz, S. H. (2001) Exploring complex networks. Nature, 410(6825): 268-276. • Wang, X. F. (2002) Complex networks: topology, dynamics and synchronization. International Journal of Bifurcation and Chaos, 12(5): 885-916.