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Networks, Complexity and Economic Development

Class 5: Network Dynamics

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

Class Evaluation

Community Finding

Clique Percolation Methods Betweenness, Spectral Partition Methods

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.

We also

Studied some dynamical consequences of Scale Free networks:

Error-Attack ToleranceVanishing Epidemic Threshold.

Vanishing Epidemic Threshold

Random Network:Epidemic spreads if r >1

Random Network:Epidemic spreads if r > <k>/<k2>

How predictable is an epidemic?

i= 1 if is city has an infected individualand 0 otherwise.

Overlap, measure similarity between the’s describing different realizationsof the simulation

High degree nodes difficult prediction,As there are many possible paths that

spreading cant take.

Heterogeneity in weight increasesPredictability as there are some links

That carry most of the traffic.(Effective degree is smaller)

High weight – High Betweenness

Low weight – High Betweenness

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

SimpleContagion

Process

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

ComplexContagion

Process

SimpleContagion

Process

ComplexContagion

Process

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

Watts-Strogatz type of Shortcuts increase the speed of spreading

Watts-Strogatz type of slow or stop the spreading process

Network Dynamics

CA Hidalgo C Rodriguez-SickertPhysica A (2008)

Persistence

Perseverance

CA Hidalgo C Rodriguez-SickertPhysica A (2008)

Core-Periphery Structure Power-Law Decay

CA Hidalgo C Rodriguez-SickertPhysica A (2008)

DL MorganMB Neal, P Carder. Social Networks 19:9-25 (1996)

T-1/4

Degree (k) Clustering (C) Reciprocity (R)

CA Hidalgo C Rodriguez-SickertPhysica A (2008)

= 0.0598 C – 0.0122 k + 0.3626 r + 0.0015 Age +0.0009 Gender +0.2506

Linear Regression

Multivariate Analysis (Node Level)

Correlations and Partial Correlations

Conserved Not Conserved

Conserved A B

Not Conserved

C D

Reality

Test

Prediction Accuracy = A/(A+B)Sensitivity=A/(A+C)

Co-Authorship Network

S=Size

Mobile Phone Network

=Average life-spanof a community of a

given size

Small communities that survive tend to retain its members

Large communities that surviveTend to change their compositionMore than those they do not

Invisible CollegeNo-Invisible College

Emails, Columbia

Many EyesMany Eyes