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NETWORK INDICATORS: A NEW GENERATION OF MEASURES?
EXPLORATORY REVIEW AND ILLUSTRATION BASED ON ESS DATA
Elsa Fontainha
ISEG Technical University of Lisbone-mail: [email protected]
Edviges CoelhoStatistics Portugal (INE)
e-mail: [email protected]
Brussels
18-20 February 2009
NTTS 2009
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Aim of Research
To illustrate how to construct indicators of cohesion and convergence across Europe and to identify the roles (e.g. centrality, reciprocity) performed by several entities (countries, regions, institutions, individuals, enterprises, etc.) in European networks mapped by demographic, economic, financial and communication flows or links.
To attain that goal we adopted network analysis, derived from graph theory, to explore data from the European Statistical System (ESS) The proposed indicators can be produced on a regular
basis and complement the current indicators.
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Attribute and Relational Data
Attribute Data
Gross Domestic Product (GDP)
Population growth Student/Teacher ratio
...
Relational Data
Foreign Direct Investment
Immigration Emigration Tourism flows ...
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How to study relational data?
Matrix format Eurostat
• geo/partner• input-ouput analysis
From matrix format to network graph…A
E
D
C
A B C D E
A - 0 1 0 0
B 0 - 0 0 0
C 0 0 - 1 0
D 0 1 0 - 0
E 0 0 0 0 -
B
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From matrix format to network graph…
AE
D
C
A B C D E
A - 0 1 0 0
B 0 - 0 0 0
C 0 0 - 1 0
D 0 1 0 - 0
E 0 0 0 0 -
Links are directed (represented by arrrows)E is an isolated node (ex: country)There are no reflexive links
From adjacency matrix to network graph…
B
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Network AnalysisLinks and Nodes
Network analysis Describes the structure of relations
(represented by links, oriented or not) between agents (represented by nodes/egos)
e.g. Nodes Countries
Links Immigration flows among countries
Applies quantitative techniques to compute measures which improve the knowledge of
the characteristics of the whole network (e.g. EU) the position of nodes (e.g. countries) in the network
structure.
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Network and Node Indicators (computed from flow matrices)
Indicators
Network
Size Centrality Density Cohesion Reciprocity …
Indicators
Node/Ego
In-degree Out-degree Power Isolated …
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Computing Network Indicators from ESS:some illustrations
Data: ESS
Immigration by country of previous residence (migr_immiprv)
Immigration by citizenship (migr_immictz) EU direct investment flows, breakdown by partner
country (bop_fdi_flows) Socrates-Erasmus student and teacher mobilityProblems encountered
Data • (e.g. missing information for some countries
and/or years ( -> imputation ) Methodology: limits imposed by methodology
• (e.g. n x n matrix)
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Methodology: main steps(for each indicator)
1. Selection, filtering and weighting original data (ESS)
2. Construction of the adjacency (association) matrix
3. Construction of network graphs from matrix( all links and only strongest links)
4. Computation of indicators (for nodes and network) from adjacency matrix
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intra-EU Immigration 2002 251 ties, 17 nodes
ATCY
CZ
DE
DK
ES
FI
IT
LT
LV
NL
PL
PT
SE
SI
SK
UK
Blue arrows = reciprocal linksRed arrows=Non reciprocal
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intra-EU Immigration 2006 267 ties, 17 nodes
AT
CY
CZ
DE
DK
ES
FI
IT
LT
LV
NL
PL
PT
SE
SI
SK
UK
Blue arrows = reciprocal linksRed arrows=Non reciprocal
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intra-EU Immigration 200227 ties, 17 nodes (only strong links)
AT
CY
CZ
DE
DK
ES
FI
IT
LT
LV
NL
PL
PT
SE
SI
SK
UK
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intra-EU Immigration 200636 ties, 17 nodes (only strong links)
AT
CY
CZ
DE
DK
ES
FI
IT
LT
LV
NL
PL
PT
SE
SI
SK
UK
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Immigration(residence)
Immigration (ctz)
FD Invest.
Students Teachers
N countries = = = = =
Network size = = = = =
N of Ties
Network Centr. (Outdegree) %
Network Centr.(Indegree) %
Outdegree Mean (StdDev)
Indegree Mean (StdDev)
Network Density
Indicators – NetworksImmigration, Foreign Investment, Teachers and
Students (Year t - 2006)
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Immigration(origin residence)
Foreign D Investment
2006 2002 2006 2002
Size in 16(except CY,
SI)
16(except CY, LT, LV, PL, PT, SI, SK)
NL(10)PT (7)SE (7)
BE (11)SE (11)
Size out 16(except FI, LT, LV, SI)
16AT, DE, ES, NL, PL, SE,
UK
FR (14)NL (9)
AT (13)FR (13)IT (13)NL (13)UK (13)
In-degree DE (1578)UK(1082)ES(577)
DE (1153)UK (298)ES (280)
BE (60)NL (47)
FI (49)NL (46)
Out - degree PL (701)SK(613)
SK (551)PL (310)
FR (48)ES (42)
UK (47)SE (37)
Indicators – Node (Countries)Immigration and Foreign Investment
2002-2006
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Student mobility
2006/7 2004/5
Size in 26BE ES FR IT DE EE
26BE DE ES FR IT PT FI SE UK LV LT AT PL FI25BE CZ DE EE ES FR IT LV LT AT PL FI
Size out 25BE CZ DE EE ES FR IT LV LT AT PL FI
25BE DE ES FR IT NL AT PT FI UK
In-degree ES (26992)FR (20140)DE (16683)
ES (25217)FR (20200)DE (16688)
Out - degree DE (2715)FR (21213)ES (20568)
DE (2715)FR (21213)ES (20568)
Indicators – Node (Countries)Student mobility (Socrates-Erasmus)
2004/5 – 2006/7
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Conclusions and future research
1. It is possible to compute network indicators from the ESS data. They are useful for the understanding of the relations among countries and the network diffusion mechanisms.
2. There is, in general, an increase in the density of the network (EU countries) across time regardless of the phenomena under analysis (migrations, capital flows, etc.). Cohesion is increasing. EU recent enlargements are reflected in that increase.
3. The role of each country inside the network remains stable across time in some cases but changes in others. For example, with regard to immigration, Spain has increased its position as a destination country since 1998.
4. The results suggest that geography and language still matter for several EU networks of people, goods, services, capital and knowledge. Explanation for this is beyond this paper’s goals but could contribute to a greater understanding of EU networks.