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 Tolerance Vanishing Epidemic Threshold.

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

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

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.

High weight – High Betweenness Low weight – High Betweenness

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

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

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

Network Dynamics

CA Hidalgo C Rodriguez-Sickert Physica A (2008)

Persistence Perseverance

CA Hidalgo C Rodriguez-Sickert Physica A (2008)

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)

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

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

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

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

Small communities that survive tend to retain its members

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

No-Invisible College Invisible College

Emails, Columbia

Many Eyes