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

2. Networks of dynamical systems

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

4. Other Networks

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

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 o “Degrees of separation” Clustering coefficient, C o Chances that your friends are friends with each other

12. Path Length for Networks LongShort

13. Clustering for Networks HighLow

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!