Classes will begin shortly

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 ) 410pm 530 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 gt1
Random Network Epidemic spreads if r gt ltkgt/ltk2gt
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
How predictable is an epidemic?
Pi 1 if is city has an infected individualand 0
otherwise.
Overlap, measure similarity between the Ps
describing different realizationsof 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
18
(No Transcript)
19
Complex Contagions and the Weakness of Long Ties
D Centola, M Macy - American Journal of
Sociology, 2007
Simple Contagion Process
20
Complex Contagions and the Weakness of Long Ties
D Centola, M Macy - American Journal of
Sociology, 2007
Complex Contagion Process
21
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
23
(No Transcript)
24
CA Hidalgo C Rodriguez-Sickert Physica A (2008)
25
Persistence
Perseverance
26
CA Hidalgo C Rodriguez-Sickert Physica A (2008)
27
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
199-25 (1996)
28
Degree (k)
Clustering (C)
Reciprocity (R)
CA Hidalgo C Rodriguez-Sickert Physica A (2008)
29
Multivariate Analysis (Node Level)
Linear Regression
p 0.0598 C 0.0122 k 0.3626 r 0.0015 Age
0.0009 Gender 0.2506
Correlations and Partial Correlations
30
Reality
Test
Prediction Accuracy A/(AB) SensitivityA/(AC)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
Mobile Phone Network
Co-Authorship Network
lttgtAverage life-span of a community of a given
size
SSize
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
37
(No Transcript)
38
(No Transcript)
39
Invisible College
No-Invisible College
40
(No Transcript)
41
(No Transcript)
42
Emails, Columbia
43
(No Transcript)
44
(No Transcript)
45
Many Eyes