Exploring Network Dynamics: Applications and Evaluations in Economic Development

1. Classes will begin shortly

2. Networks, Complexity and Economic Development Class 5: Network Dynamics

3. Classes 5-7 APPLICATIONS (Oct 21st, Nov 18 th, Nov 25 th ) 4:10pm– 5:30 pm

4. Class Evaluation

5. Community Finding Clique Percolation Methods Betweenness, Spectral Partition Methods

6. So far… We studied some basic network models: Erdos-Renyi: Random Graph. Watts-Strogatz: Small World. Barabasi-Albert: Scale-Free Networks. We also saw how to characterize the structure of networks by looking at different structural properties. Local Properties: Centrality Measures, Clustering, Topological Overlap, Motifs. Global Properties: Diameter, Giant Component, Degree Correlations.

7. We also Studied some dynamical consequences of Scale Free networks: Error-Attack Tolerance Vanishing Epidemic Threshold.

8. Vanishing Epidemic Threshold Random Network: Epidemic spreads if r > <k>/<k2> Random Network: Epidemic spreads if r >1

15. How predictable is an epidemic? Pi= 1 if is city has an infected individualand 0 otherwise. Overlap, measure similarity between the P’s describing different realizationsof the simulation

16. Heterogeneity in weight increases Predictability as there are some links That carry most of the traffic. (Effective degree is smaller) High degree nodes difficult prediction, As there are many possible paths that spreading cant take.

17. High weight – High Betweenness Low weight – High Betweenness

19. Complex Contagions and the Weakness of Long Ties D Centola, M Macy - American Journal of Sociology, 2007 Simple Contagion Process

20. Complex Contagions and the Weakness of Long Ties D Centola, M Macy - American Journal of Sociology, 2007 Complex Contagion Process

21. Complex Contagions and the Weakness of Long Ties D Centola, M Macy - American Journal of Sociology, 2007 Simple Contagion Process Watts-Strogatz type of Shortcuts increase the speed of spreading Complex Contagion Process Watts-Strogatz type of slow or stop the spreading process

22. Network Dynamics

24. CA Hidalgo C Rodriguez-Sickert Physica A (2008)

25. Persistence Perseverance

26. CA Hidalgo C Rodriguez-Sickert Physica A (2008)

27. Power-Law Decay Core-Periphery Structure T-1/4 CA Hidalgo C Rodriguez-Sickert Physica A (2008) DL Morgan MB Neal, P Carder. Social Networks 19:9-25 (1996)

28. Degree (k) Clustering (C) Reciprocity (R) CA Hidalgo C Rodriguez-Sickert Physica A (2008)

29. Multivariate Analysis (Node Level) Linear Regression p = 0.0598 C – 0.0122 k + 0.3626 r + 0.0015 Age +0.0009 Gender +0.2506 Correlations and Partial Correlations

30. Reality Test Prediction Accuracy = A/(A+B) Sensitivity=A/(A+C)

34. Mobile Phone Network Co-Authorship Network <t>=Average life-span of a community of a given size S=Size

35. Small communities that survive tend to retain its members

36. Large communities that survive Tend to change their composition More than those they do not

39. No-Invisible College Invisible College

42. Emails, Columbia

45. Many Eyes