Collective Dynamics of ‘Small World’ Networks

1. Collective Dynamics of ‘Small World’ Networks C+ Elegans: Ilhan Savut, Spencer Telford, Melody Lim 29/10/13

2. Networks of dynamical systems

3. Networks of dynamical systems Can be represented by points (vertices or nodes) connected with lines (edges)

4. Other Networks

5. Different types of networks • ‘Collective Dynamics of Small World Networks’ Duncan Watts and Steven Strogatz, Nature 393:440-442 (1998) • Properties of networks • New type of network! • Applications Overview

6. A Regular Network

7. A Random Network

8. Fine-Tuning p Changes Network Properties • p - rewiring of regular network • Properties depend heavily on p

10. Properties of Networks • Path Length, L • Clustering coefficient, C

11. Properties of Networks • Path Length, L • “Degrees of separation” • Clustering coefficient, C • Chances that your friends are friends with each other

12. Path Length for Networks Short Long

13. Clustering for Networks Low High

14. An Example of a Regular Network

15. No Random Networks Exist in Nature

16. L and C Depend on p

17. New Type of Network • 0 < p < 1 (not fully random, not fully regular)

18. Small-World Networks • Short path length, highly clustered

19. ‘Small-world’ Network in the Middle

20. Small World Networks Are Natural • Formation of networks favors small world • Most networks built from small elements • Evolutionary and natural processes favor the formation of small-world networks

21. Many Real World Systems are Small World Networks • Collaboration graph of actors (six degrees of separation study) • Neural network of C. elegans • Power grid of Western US

22. Small World Networks Have New Properties Robustness • Resistant to random changes • Targeted ‘attacks’

23. Small World Networks Model the Spread of Disease

24. Conclusion New class of network model • Low path length • High clustering coefficient • Models many natural systems!