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Classes will begin shortly

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Networks, Complexity and Economic Development Class 5: Network Dynamics

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

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Class Evaluation

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Community Finding Clique Percolation MethodsBetweenness, Spectral Partition Methods

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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.

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

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

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How predictable is an epidemic? i = 1 if is city has an infected individual and 0 otherwise. Overlap, measure similarity between the s describing different realizations of the simulation

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

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High weight – High Betweenness Low weight – High Betweenness

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

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

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Simple Contagion Process Complex Contagion 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

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Network Dynamics

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CA Hidalgo C Rodriguez-Sickert Physica A (2008)

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Persistence Perseverance

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CA Hidalgo C Rodriguez-Sickert Physica A (2008)

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

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

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= 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

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ConservedNot Conserved ConservedAB Not Conserved CD Reality Test Prediction Accuracy = A/(A+B) Sensitivity=A/(A+C)

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

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Small communities that survive tend to retain its members

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

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Invisible CollegeNo-Invisible College

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Emails, Columbia

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Many Eyes

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