Dr. Abonyi János MTA-PE „Lendület” Complex Systems Monitoring Research Group Department of Process Engineering at the University of Pannonia www.abonyilab.hu janos@abonyilab.hu

Gadár László MTA-PE Budapest Ranking Research Group Innopod Solutions Kft.

Dr. Kosztyán Zsolt Tibor MTA-PE Budapest Ranking Research Group Department of Quantitative Methods at the University of Pannonia

Measurement of regional attractiveness based on company-ownership networks

Is the settlement structure reflected in personal investments?

How are company ownerships distributed in the geographical space?

Is physical proximity significant factor in investment decisions?

Can we characterize the attractiveness of economic regions?

Measurement of regional attractiveness based on distance-dependent network modularity

Internal and external linking probabilities

Community structure based on null models

Key research questions

𝑎𝑖,𝑗 > 𝑝𝑖,𝑗

LAU-21 LAU-22

LAU-23

LAU-11

NUTS-31

LAU-12

NUTS-32

NUTS-33

LAU-24

Owner

Company

LAU-25

NUTS-21

LAU-13

LAU-26

LAU-27 LAU-28

LAU-14

Company ownership relations connect the elements of settlement hierarchy and form a weighted directed network of settlements (LAU 2), sub-regions (LAU 1) small regions (NUTS 3), regions (NUTS 2)

Network model

Analized network

Town-level (LAU 2)

Sub-region level (LAU 1)

County-level (NUTS 3)

Region-level (NUTS 2)

Number of nodes (N) 3111 175 20 7

Number of internal connections 797 492 846 309 893 559 969 995

Number of external connections 279 598 230 781 183 531 107 095

Vislualized edges: more than 10 connections

Internal densities and openness

Densities inside towns/regions can highlight the modular structure

Smaller locations are more closed than larger ones

Openness values reflect higher attractiveness

Bigger regions have higher openness

𝐷𝑖[𝑛𝑘,𝑖𝑛]

=𝑎𝑖,𝑖[𝑛𝑘]

𝑛𝑖[𝑛𝑘,𝑝]𝑛𝑖[𝑛𝑘,𝑐𝑜]

𝑂𝑖[𝑛𝑘]=𝐷𝑖[𝑛𝑘,𝑒𝑥]

𝐷𝑖[𝑛𝑘,𝑖𝑛]

Community model based methodology

Model

Network

Communities Extracted

knowledge

𝑀𝐶 =1

𝐿 𝑎𝑖,𝑗 − 𝑝𝑖,𝑗(𝑖,𝑗)∈𝑪𝒄

𝑎𝑖,𝑗

𝑝𝑖,𝑗 𝑎𝑖,𝑗 − 𝑝𝑖,𝑗

𝑀𝐶 = (fraction of edges within communities) – (expected fraction of such edges)

𝑝𝑖,𝑗 = 𝑔 𝐼𝑖 , 𝐼𝑗 , 𝑑𝑖,𝑗

What determines the attractivity?

What is the effect of the distance?

𝐼𝑖 𝐼𝑗 𝑑𝑖,𝑗

Expected number of connections

Number of connections Communities + Modularity

unmodeled effects/cohesion

L: number of connections

Town of the owners

Town of the owned companies

Modularity of the towns and regions …

Modularity at a given hierarchy level [nk]

in the same … town (nk=1, LAU-2); region (nk=2, LAU-1) ; county (nk=3, NUTS-3 )

𝑀𝐶[𝑛𝑘] =

1

𝐿 𝑎𝑖,𝑗

[1]− 𝑝𝑖,𝑗[1]

(𝑖,𝑗)∈𝐶𝑐[𝑛𝑘]

𝑎𝑖,𝑗[1]

# of connections between town i and j

The model … estimated number of town-town connections

Random configuration model (PNG):

Attractiveness-related node importance:

Extended with deterrence function (PSPA):

Parametric SPA (P,):

Gravity type models (PGRAV):

𝑝𝑖,𝑗[1]=𝑘𝑖[1,𝑜𝑢𝑡]𝑘𝑗[1,𝑖𝑛]

𝐿

𝑝𝑖,𝑗[1]= 𝛾𝐼𝑖

𝑜𝑢𝑡𝐼𝑗𝑖𝑛

𝑝𝑖,𝑗[1]= 𝛾𝐼𝑖

𝑜𝑢𝑡𝐼𝑗𝑖𝑛𝑓(𝑑𝑖,𝑗)

𝑝𝑖,𝑗[1]= 𝛾 𝐼𝑖

𝑜𝑢𝑡 𝛼 𝐼𝑗𝑖𝑛 𝛽𝑓(𝑑𝑖,𝑗)

𝑝𝑖,𝑗[1]=𝛾 𝐼𝑖𝑜𝑢𝑡 𝛼 𝐼𝑗

𝑖𝑛 𝛽

𝑑𝛿

Town of the owners

Town of the owned companies

𝐼𝑖 𝐼𝑗 𝑑𝑖,𝑗 Towns are equally important Number of investors and companies Modified random configuration model Number of inhabitants Total Domestic Income (TDI)

𝐼𝑖 = 𝐼𝑗 = 1

𝐼𝑖 = 𝑛𝑖[𝑛𝑘,𝑝] 𝛼

𝐼𝑗 = 𝑛𝑗[𝑛𝑘,𝑐𝑜] 𝛽

𝐼𝑗 = 𝑘𝑗𝑖𝑛 𝛽 𝐼𝑖 = 𝑘𝑖

𝑜𝑢𝑡 𝛼

Dependence on distance

Nonparametric deterrence function

Modifications of gravity law

𝑝𝑖,𝑗[1]= 𝛾𝐼𝑖

𝑜𝑢𝑡𝐼𝑗𝑖𝑛𝑓(𝑑𝑖,𝑗)

𝑓 𝑑 = 𝑎𝑖,𝑗

[1]𝑖,𝑗|𝑑𝑖,𝑗=𝑑

𝐼𝑖𝑜𝑢𝑡𝐼𝑗𝑖𝑛

𝑖,𝑗|𝑑𝑖,𝑗=𝑑

𝑓 𝑑 =1

𝑑𝑖,𝑗𝛿

𝑓 𝑑 = 𝑒𝑥𝑝 −𝑑𝑖,𝑗𝛿

𝑓 𝑑 = 𝑑𝑖,𝑗−𝛿𝑒𝑥𝑝 −

𝑑𝑖,𝑗𝜅

Actual and degree based estimated values (LAU 2)

Comparison of the number of internal connections and their estimated values at town (LAU 2) hierarchy level when Ii

out = ki[1,out], Ij

in = kj[1,in]

There are more inner-connections than expected

Actual and degree based estimated values (LAU 1)

Comparison of the number of internal connections and their estimated values at town (LAU 1) hierarchy level when Ii

out = ki[1,out], Ij

in = kj[1,in]

Actual and gravity null model based estimated values

Comparison of the number of internal connections and their estimated values at town (LAU 1) settlement hierarchy level when Ii

out= TDIi, Ijin = TDIj

Community detection based ”tomography”

PNG, Ii = kiout, Ij = kj

in PGRAV, TDI-based importances

Number of incomming and outgoing investments

Cost of connections: Distance dependence

Similarity of the regions (development level)

Conclusions

Personal investments link geographic locations

Network based measures can evaluate the attractiveness of towns/regions

Small and less competitive regions have less internal connections

Larger cities are much more opened

Significant dependence on distance

The attractiveness of Budapest is high connections are much less distance dependent

Different null models and node importance measures can be used to explore regional similarities

PGRAV with TDI importance: Budapest forms cluster with county centers and competitive touristic regions, while remaining small clusters are less attractive regions

Structure of the company—ownership network

In-strength distribution (LAU 2) Local clustering coefficient

vs. degree (LAU 2)

Scale-free

Hiearchical

Slightly disassortative

Relations of the regions

Interlinking communities Gain of the merged modularity Δ𝑀𝑖,𝑗

[𝑛𝑘]=1

𝐿𝐴𝑖,𝑗[𝑛𝑘]− 𝑃𝑖,𝑗[𝑛𝑘]+ 1

𝐿𝐴𝑗,𝑖[𝑛𝑘]− 𝑃𝑗,𝑖[𝑛𝑘]

Compulsory condition

Normalization

𝑃𝑖,𝑗[1]

𝑖,𝑗

= 𝐴𝑖,𝑗[1]= 𝐿

𝑖,𝑗

𝐼𝑖𝑜𝑢𝑡

𝑖

= 1

𝐼𝑗𝑖𝑛

𝑗

= 1