classes will begin shortly. networks, complexity and economic development class 5: network dynamics
TRANSCRIPT
Classes will begin shortly
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