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 individual and 0 otherwise.
Overlap, measure similarity between the
P’s describing different realizations of 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. Simple Contagion Process
Complex Contagions and the Weakness of Long Ties D Centola, M Macy - American Journal of Sociology, 2007
Simple
Contagion
Process

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

21. Simple Contagion Process Complex Contagion Process
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. Core-Periphery Structure
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 = C – k r Age Gender
Correlations and Partial Correlations

30. Prediction Accuracy = A/(A+B)
Reality
Conserved
Not Conserved A B C D
Test
Prediction Accuracy = A/(A+B)
Sensitivity=A/(A+C)

34. S=Size 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. s, Columbia

45. Many Eyes