Network Dynamics in Social and Economical Systems

Cesar A. Hidalgo R.1

Carlos Rodriguez-Sickert2, A.-L. Barabasi1

1 CCNRUniversity of Notre Dame, Notre Dame, IN

2 Dept. of SociologyPontificia Universidad Catolica de Chile Ann Arbor April 2007

Core-Periphery structure

The Stability of core and peripheral networks over time. David L. Morgan,Margaret B. Neal and Paula Carder, Social Networks 19 (1996) 9-25

234 widows, 1 year, 7 panels

Core = Kin

The Stability of core and peripheral networks over time. David L. Morgan,Margaret B. Neal and Paula Carder, Social Networks 19 (1996) 9-25

Another More Recent Support study

Relational Instability at the Network Core: Support Dynamics in developmentalnetworks. Jonathon N. Cummings, Monica C. Higgins, Social

Networks 28 (2006) 38-55

They analyzed 77 MBA graduates for 3 time periods and add relational content. The generating question was to name

people that have taken an active interest and concerted action in the advancement of their careers.

The conclusion is that the ties that granted psychosocial support compromised the inner core.

Yet Another Study• 42 Women Re-entering college. • Main Conclusion is that people for work support

becomes more educated as this women get educated.

Once a friend, always a friend? Effects of homophily on women’s supportnetworks accross a decade. Jill Suitor, Shirley Keeton, Social Networks

19 (1997) 51-62

Status Transition

Decay Functions

[1] Decay Functions. Ronald S.Burt, Social Networks 22 (2000) 1-28.

Bridge Decay

Bridge Decay. Ronald S. Burt, Social Networks 24 (2002) 333-363

The Persistence of Social Ties

Where? Western Country (Penetration >100%)

Share of the Market ~ 25%

Nodes = 1.950.426Edges = 7.948.890 (Voice Calls)

April 16 to April 30 2004 yes

May 1 to May 15 2004 no

May 16 to May 31 2004 yes

June 1 to June 15 2004 no

June 16 to June 30 2004 yes

July 1 to July 15 2004 no

July 16 to July 31 2004 yes

August 1 to August 15 2004 yes

August 16 to August 31 2004 no

September 1 to September 15 2004 no

September 16 to September 30 2004 yes

October 1 to October 15 2004 yes

October 16 to October 31 2004 no

November 1 to November 15 2004 no

November 16 to November 30 2004 no

December 1 to December 15 2004 no

December 16 to December 31 2004 no

January 1 to January 15 2005 yes

January 16 to January 31 2005 no

February 1 to February 15 2005 no

February 16 to February 28 2005 yes

March 1 to March 15 2005 no

March 15 to March 31 2005 yes

Mobile Phone Network

Persistence

Perseverance

Core-Periphery Structure Power-Law Decay

Pij, i and k

Pij, i and C

Pij and <reciprocity>

Pij, i, Gender and Age

Gender And Age

F

M

F M

1-M/F

= 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

P = 0.09C + 0.002k + 0.15r – 0.03 Gender -0.002Age + 0.35 R + 0.56TO +0.16

Linear Regression

Multivariate Analysis (Tie Level)

Correlations and Partial Correlations

Conserved Not Conserved

Conserved A B

Not Conserved

C D

Reality

Tes

t

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

Conclusions

• Quantitative Sociology can be performed using mobile phone billing data.

• As an example we studied the persistence of ties and showed that is strongly coupled to the topology of the network.

• This coupling is strong enough to make relatively accurate predictions about the existence of ties in the future.

The Product Space and its Consequences for Economic

Growth

Cesar A. Hidalgo R.1

Bailey Klinger2, A.-L. Barabasi1, R. Haussman2

1CCNR, Dept of Physics, University of Notre Dame2CID, Kennedy School of Government, Harvard University

Area of countries proportional to ppp (GDP per Capita). Source: worldmapper.org

Share of the ith product on the basket of country c at time t

Share of the ith product on the basket of the world at time t

ij=P(RCAi|RCAj)ij=P(RCAi|RCAj)

ij = min{P(RCAi|RCAj),P(RCAj|RCAi)}

B. Balassa, The Review of Economics and Statistics 68, 315 (1986).B. Balassa, The Review of Economics and Statistics 68, 315 (1986).

Feenstra’s Trade Flows(1)

(1) Feenstra, R. R. Lipsey, H. Deng, A. Ma and H. Mo. 2005. “World Trade Flows: 1962-2000”NBER working paper 11040. National Bureau of Economic Research, Cambridge MA.

sitc-4 import and export data.

Threshold = 0.55

Number of Links = 1525

MALAYSIA

Malaysia 1975

Malaysia 1980

Malaysia 1985

Malaysia 1990

Malaysia 1995

Malaysia 2000

Density

j = Fraction of the product space

that seems to be developed fromthe jth product perspective

TN

TH N

Tk

kj

T

k

kj

j

1

1

Discovery Factor

Hj = Increase in density betweentransition product and undeveloped

products.

Discovery Factor

Density

P(transition | closest developed product is at proximity )

Denotes where region has RCA

KEY

ConclusionWe showed:

• Product space is heterogeneous• Constrains the development of RCA• Rich and poor countries are located in

distinct places of it

• Development Strategies should be different for rich and poor countries

• The structure of the space preventseconomical convergence

Acknowledgments

• A.-L. Barabasi

• B. Klinger

• R. Hausmann

• C. Rodriguez-Sickert

• Kellogg Institute