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EUROPEAN COMMISSION

Eurostat

Directorate E: Sectoral and regional statistics

Unit E-4: Regional statistics and Geographical Information

Labour Market Areas

Study on applicability of Labour Market Areas in Hungary

Hungary

Agreement number: 08141.2015.001-2015.500

Methodological Report, version 1.0

Prepared by

András Kezán, HCSO (project leader)

Dániel Szilágyi, HCSO

József Gerse, HCSO

Balázs Jankó, HCSO

János Pénzes PhD, University of Debrecen

Ernő Molnár PhD, University of Debrecen

Gábor Pálóczi, University of Debrecen

EUROSTAT/Contract No.:Agreement number: 08141.2015.001-2015.500

Doc. No.:1.0

Issue/Rev.:1.0

Date:2017-06-30

Table of contents1 Introduction52 Definition framework63 Functional delineation73.1 Purpose of functional delineations73.2 Methods of functional delineation83.3 Functional delineations in Hungary94 Settlement and commute specialty of Hungary104.1 Settlement network104.2 Nature and correction of commute data124.2.1 Features of commute data induced by employment124.2.2 Correction of commute database225 Comparing deterministic and non-deterministic spatial delineations265.1 Delineation of Local Labour Systems (LLS)265.1.1 Methodology of the delineation of LLS265.1.2 Results of the LLS delineation275.2 Spatial distribution methods based on complex network analysis285.2.1 Network analysis and spatial research285.2.2 Structural equivalence calculation295.2.3 The clique percolation algorithm315.2.4 The Louvain method325.2.5 CURDS method345.2.6 Euro method405.3 Comparing the different methods435.3.1 Conceptual comparison of the methods435.3.2 Comparison of results446 The possibilities of selecting optimal parameters in EURO method476.1 The first steps of optimisation476.2 Systematic sampling486.3 Application of country level (global) indicators496.4 Introduction of the applied country level indicators496.5 Evaluation of the applied country level indicators506.5.1 Q modularity556.6 Descriptive data of LMAs556.6.1 Examined principles and applied indicators556.7 Characteristics and limits of descriptive data576.7.1 Utility of size and self-containment measures576.7.2 Well-measurable aspects586.7.3 Measures with limited objectivity616.7.4 Well-measurable though arguable aspects626.8 Aspects used in selecting optimal parameters627. Interpreting results of the EURO method637.1 Multivariate statistical models to define optimal parameters637.2 Barriers with the use of Smart measure657.3 Selecting optimal parameters in the EURO method667.3.1 Evaluating LMAs667.3.2 Sorting LMAs out727.3.3. Complying with spatial criteria of the LMAs, final LMA delineation757.3.4 Specifics of the optimal delineation, commute relations778 Summary859 References87

1 Introduction

The ‘Study on applicability of Labour Market Areas in Hungary’ project financially aided by Eurostat lasted for the time period December 2015 – June 2017. Our project tested the applicability of EURO method in the delineation of Labour Market Areas in Hungary. There was a multi-domain expert participation in the project. The experts represented the areas of regional statistics as well as methodology and scientific research.

The results of our project were as follows:

· Feasibility of implementation of the EURO method

· LMAs based on EURO method

· Exchange knowledge and best practice

· Disseminate and share the results

The action established the system of LMAs mainly for statistical purpose. In order to adapt the system of Labour Market Areas and also EURO method in Hungary this system should be approved and supported by main stakeholders, from the side of decision makers and the scientific community. The main goal of the project was to set up a system that is acceptable to all local stakeholders.

The outcome of the project was the list of the Labour Market Areas and a study about the application of EURO method as well as a working paper focusing on the properties of the final LMAs.

List of participants involved in the execution of the project:

András Kezán, HCSO (project leader), Dániel Szilágyi, HCSO, József Gerse, HCSO, Balázs Jankó, HCSO, János Pénzes PhD, University of Debrecen, Ernő Molnár PhD, University of Debrecen, Gábor Pálóczi, University of Debrecen

2 Definition framework

The concept of functional urban regions was created in the 1950s by American researchers (Keserű 2013). In spite of having a long history, the concept lacks clear definitions (OECD 2002; Antikainen 2005), as statistical databases differ, and the settlement network is different in each country (Keserű 2013). Functional urban region adds the limitation regarding the quality of a core (size, employment functions, institutional infrastructure) and consequently the character of spatial flows or interactions organising the region. In this case a core should have an urban character (Klapka–Halás–Tonev 2013). Delineation is primarily based on work-related commuting, and each municipality is joined to that center, where the most commuter travel to, without any threshold. However, a center should be viewed as an urban one only if it have at least 15-20 000 employed persons (Drobne–Konjar–Lisec–Pichler Milanović–Zavodnik Lamovšek 2010).

The definition of functional regions is complex, as it is used for territories characterized by a high frequency of intra-regional economic interaction, including services, commerce and work-related commuting (Karlsson–Olsson 2006). In spite of that, most study leaned on work-related commuting for delineation (Cörvers–Hensen–Bongaerts 2009). Functional regions can be further classified by commuting orientation (Klapka–Halás–Tonev 2013). The OECD-delineation for functional regions was created only to the narrower areas of cities with at least 100 000 inhabitants. High population density was emphasized (OECD 2012).

The European Commission launched its functional urban area concept under the ESPON 1.1.1. project, it is basically the travel-to-work area of commuters. In this delineation, each municipality is joined to that center, where the largest proportion of its workers commute to. In many international studies, a commuting-flow threshold of either 15 or 20 percent is used to determine whether a municipality is attached to a particular center or not (Antikainen 2005). This filtering method results different interpretations with the functional urban area-concept (Drobne–Konjar–Lisec–Pichler Milanović–Zavodnik Lamovšek 2010). More threshold values can be applied during the delineation, such as the minimal number of jobs and the percentage of residents of an area working in the same area. The latter value can be modified based on the number of population. It is important to note that threshold values can differ in different countries, and several alternative approaches have been conducted (Cörvers–Hensen–Bongaerts 2009).

Beside the travel-to-work area concept, the Local Labour Market Area expression is also often cited in professional literature. The difference between them is that the first one includes weekly commuting. In Local Labour Market Areas daily commuting is the cornerstone, and interactions don’t necessarily need to be oriented at any core (Klapka–Halás–Tonev 2013). These delineations have common properties: they cover territories characterized by intensive interactions, and exclaves may emerge.

Hungarian researchers of the VÁTI-institute (a non-profit urban development organization) delineated Local Labour Systems (LLSs) under the RePUS (Regional Polycentric Urban System) project, using work-related commuting data from the 2001 census (Radvánszki–Sütő 2007). The procession of the 2011 census data was carried out with this (slightly corrected) method (Pénzes–Molnár–Pálóczi, 2014). The next phase of the research focused on combining these zones with microregions, and this created the Functional Urban Districts (Sütő 2008). To mention yet another research in Hungary, Faluvégi Albert delineated functional district by using commuting data (Faluvégi 2008). These two analysis used the same data with a two-step model: centers were identified first, then their catchment areas. VÁTI-researchers chose lower values (1000 person) to appoint employment centers, but a requirement was for these municipalities to have at least one municipality for which that is the primary connection. Every municipality was joined to an employment center. The other approach consisted of two type of employment centers, urban (above 5000 person) and rural (between 1200 and 5000 person) ones. Due to the threshold criteria several municipality was not joined to any district.

Functional Economic Areas (FEAs) are also based on the concept of work-related commuting (Kristensen 1998). This approach has different method and purpose compared to the previous ones (see chapter 3.1).

As Hartshorne claimed (quote from Paasi 2009: 4736):

‘The problem of establishing the boundaries of a geographic region presents a problem for which we have no reason to even hope for an objective solution. The most that we can say is that any particular unit of land has significant relations with all the neighbouring units and that in certain respects it may be more closely related with a particular group of units than with others, but not necessarily in all respects’.

The purpose of the delineation of functional regions is to maximize the intra-regional flows, and minimize the flows amongst regions. Therefore the research is based on relational database (Haggett 1965). Horizontal functional interactions should be maximized within the region, while interactions across borders should be minimized during the process so that to have internal cohesion and external distinction (Smart 1974; Karlsson–Olsson 2006; Farmer–Fotheringham 2011; Klapka–Halás–Erlebach–Tonev–Bednář 2014).

Administrative and spatial-political delineations are not flexible enough to follow the quick changes of phenomenon, thus properly delineated functional regions could be more suitable for dedicated purposes than administrative regions (Haggett 1965).

Travel-to-work (sometimes also called journey-to-work) flows (especially daily flows) are the most often utilized tools for functional delineations. Commuting is one of the most common and regular periodical movement of people (Bujdosó 2009; Bodor–Pénzes 2012). Functional regions based on these relations and flows are called local labour market areas (LLMA) or travel-to-work areas (TTWA).

3 Functional delineation3.1 Purpose of functional delineations

Regionalization processes always serve a defined target, which specially illustrate the system of territorial units, or even make it unique. The clarification of the standards and the purpose of a particular delineation is always needed (Szabó 2015).

In spite of attempts towards objectivity, functional regions are always abstract concepts, and their development method is strongly affected by the targets. The territorial units are joined and separated based on the targets and the suitable method during the delineation process.

The most common target of these functional regions is to create territorial units where its units are linked by spatial interactions. Available statistical data limit the amount of interactions could be used for research, and this affects the feasibility of the delineation.

According to the general approach, functional territorial units are kind of statistical territorial units, which function as an alternative or a complement to the administrative (often NUTS-related) territorial units. Their benefits then appear in scientific spatial research.

A couple of delineation based on work-related commuting serve such purposes. Special spatial interactions can provide proper foundation for spatial research about the labour market and the economy. A research in Denmark attempted to delineate functional economic areas (FEA), and the hypothesis was that it is possible to have territorial units with local economic sustainability even without an urban centre. Nevertheless, these units are mainly around a certain center (Kristensen 1998).

Some functionally created territorial units are integrated into the administrative nomenclature in a country, thereby original functional interactions may be complemented with – „top-down” – institutional and other roles.

Statistics in the European statistical system are primarily refer to administrative territorial units in member countries. The comparability of these units is provided by population intervals fixed in Regulation (EC) 1059/2003 of the European Parliament. However, there are no common standards for territorial units in Europe outside of the NUTS-system, thus the comparability of statistics aggregated on lower administrative levels is limited between countries. The Commission aims to resolve the problem by producing statistics for territorial (grid) units with same size and by delineating functional areas with common methods to achieve comparability. One of the tools of the latter aim is to create labour market areas, which has already been applied in some member countries. The application of labour market areas is a bit more than a pure statistic domain, as examples in member countries show that they can serve political decisions, strategies. Our research and study aimed to examine the applicability of the EURO method and its problems in member countries. The method was recommended by the Commission, and it was finetuned by the DevStat research group (Coombes–Casado-Díaz–Martínez-Bernabeu–Carausu 2012) and a working group set up for this special purpose.

3.2 Methods of functional delineation

Functional regions are abstract concepts, so there isn’t any perfect method to delineate them, and that’s the reason why methods based on the exact same database may result significantly different outcomes (Laan–Schalke 2001).

Applicable methods are limited by main types of flows in a certain area (Figure 1). Applying methods with pre-defined centers can be misleading in cases where spatial flows are not nodal.

Figure 1: Examples of functional regions

Source: Klapka–Halás–Tonev 2013, 97. p.

The three way the most often implemented to delineate functional regions are the followings in professional literature:

· clustering methods with numerical classification (e.g. Smart 1974; Kristensen 1998)

· methods with graphs (e.g. Nystuen–Dacey 1961; Karlsson–Olsson 2006; Benassi–Deva–Zindato 2015)

· multi-step (rule-based) methods (e.g. the method developed by CURDS – Centre for Urban and Regional Development Studies in Newcastle, U.K. More information: Coombes – Green–Openshaw 1986; Coombes–Bond 2008)

The method developed by CURDS has become one of the most successful and appreciated way for functional delineation. Several studies have been conducted by it about european countries: about Italy (Sforzi 1997), about Slovakia (Bezák 2000; Halás–Klapka–Bleha–Bendář 2014), about Spain (Casado-Díaz 2000; Flórez-Revuelta–Casado-Díaz–Martínez-Bernabeu 2008), about Belgium (Persyn–Torfs 2011), about Poland (Gruchociak 2012), about the Czech Republic (Klapka– Halás–Tonev–Bendář 2013; Tonev 2013).

The method deployed by Smart (1974) is one of the most often used one, as it provides an appropriate way to relativize statistical data about interactions and make them symmetric. CURDS-researchers applied this method for the second and third version of their algorithm (Coombes–Green–Openshaw 1986; Coombes–Bond 2008).

The second method of interactions was developed by Coombes and his colleagues (Coombes–Dixon–Goddard–Openshaw–Taylor 1982). The second version of this algorithm was applied for studies in the Czecz Republic (Halás–Klapka–Tonev–Bednář 2015) and in Slovakia (Halás–Klapka–Bleha–Bednář 2014), details are discussed in chapter 5.. In this case international results and methods are more comparable, and potential centers can be discovered. The newest version of the method doesn’t provide the latter benefit (Coombes–Bond 2008).

3.3 Functional delineations in Hungary

The method of our research had a unique approach, which can be deemed innovative in the topic of spatial research and delineations in Hungary. However, previous researches produced remarkable results in the last couple of decades.

Dusek Tamás (2004), Nemes Nagy József (2009), and Barancsuk–Gyapay–Szalkai (2013) discussed the general philosophy of delineation.

The concept of functional regions emerged in Hungarian social geography in the 1960s (Mendöl 1963). The following researches concentrated on primarily to delineate catchment areas of major cities (Beluszky 1967) – work-related commuting was not included in that approach though. Lackó–Enyedi–Kőszegfalvi (1978) created functional urban zones for the whole territory of Hungary based on commuting, an each municipality was joined to a center. The researchers considered the hierarchy levels mentioned in the official development document of the settlement network. A delineation was made for the whole territory of Hungary based on the public transport system (Szónokyné Ancsin–Szinger 1984). Work-related commuting was the base for researches about the dynamics of catchment areas (Erdősi 1985; Nagy 1988), or about spatial classification. Researches have been conducted with functional approach about smaller areas – mainly about cities and their catchment areas –, and sources were for example phone calls (Tóth 1974) and commercial relations (Kovács 1986). Timár (1983) and Bujdosó–Dávid–Uakhitova (2013) applied complex approach.

Under the RePUS (Regional Polycentric Urban System) project, Local Labour Systems were delineated based on the 2001 census data about work-related commuting (Radvánszky–Sütő 2007). Functional urban areas were also created by combining delineated units and microregions (Sütő 2008). The update of the LLS-system mentioned above was also carried out based on 2011 census data (Pénzes–Molnár–Pálóczi 2014). This model included two-steps: centers were identified first (employment centers), then their catchment areas (municipalities with the most intensive commuting flows to those centers). The method introduced here is capable of discovering the nodal regions (Klapka–Halás–Erlebach–Tonev–Bednář 2014). Another study was conducted with a complex, gravity model-based method (Hardi–Szörényiné Kukorelli 2014).

Others went deeper beyond work-related commuting data. A study analysed the agglomeration of Budapest and the inter-municipality relations by using data about commuting to schools (Keserű 2013). Inter-municipality relations can be also explored by using traffic data of roads (e.g. Szalkai 2010 and Tóth 2013). Other researchers attempted to delineate functional regions by the online social network system (Lengyel–Varga–Ságvári–Jakobi–Kertész 2015).

4 Settlement and commute specialty of Hungary4.1 Settlement network

The settlement network of Hungary has been permanent since the 19th century. There has been some unions and disjunctions of certain settlements, but they did not have an outstanding effect on the whole system.

There is a significant difference between the settlement networks of the two main areas of Hungary: Trans Danubia and the Great Plain. This could be seen from the variance of the settlement density. In the Great Plain the value of the indicator is 1.3-1.4 (there is 1.3-1.4 settlement per 100 km2), while this value is five times higher in Trans Danubia. The main reason for the difference is the distinct natural conditions, and the role of historical factors. In Trans Danubia the relief (hills, mountains) is favourable to dense settlement network. The historical factor is that during and after the Ottoman dominion the small villages which existed earlier, were not re-established in the Great Plain. The new settlement network was different from the former one: loose network of crowded market-towns and huge villages came into existence. There is another special settlement type in the Great Plain, these are farms whose origin is in connection with the agriculture. Farms are not essential part of the settlements but these are a common unit from the public administration’s point of view. The brightest period of the farms was in the second half of 19th century, and the first part of 20th century. In 1940 approximately 1 million people lived on farms. During the 1960s the structure of the agriculture had changed and because of this the number of the farms started decrease. The number of the population on farms was 200 thousand people in 1990 (Beluszky 1999).

Substances of settlements was considerably not changed since 1990. There was a little increase in the number of settlements while their number increased from 3108 to 3155 because of secede and divide between 1993 and 2014. But the legal status of settlements changed significantly. The number of towns in 1990 was only 164 which increased more than double to 2015 (346 towns). There was 3155 settlement in Hungary on 31 December 2015. Tenth of this was town (Table 1, Figure 2)

Population size

Legal status of settlements

Capital

Towns of county rank

Other towns

Great villages

Villages

Country

- 499

1127

1127

500 - 999

653

653

1000 - 1999

7

14

614

635

2000 - 4999

93

72

304

469

5000 - 9999

104

16

8

128

10000 - 19999

84

1

85

20000 - 49999

5

34

39

50000 - 99999

11

11

100000 -

7

7

Budapest

1

1

Country

1

23

322

103

2706

3155

Table 1: Number of settlements of Hungary by population size and legal status

Figure 2: Population size category of settlements

4.2 Nature and correction of commute data4.2.1 Features of commute data induced by employment

Commute is a special form of internal migration which means a periodic movement with daily weekly or rarely incidence between habitation and workplace. Features of social-economic and related settlement systems development now and then create spatial separation of employment demand and supply. This procession can moderate stress devolved due to bigger concentrate of population and stabilize the demographical situation of villages (Perczel 2003).

Commute as a multitudinous phenomenon in Hungary primarily was generated by the first wave of the forced industrialization in 1950s. The significant increased (54%) number of commuters in 1960s was related with agricultural collectivization (Table 2). In 1970s the number of commuters increased further (240 thousand people – 25%) although the sum of employees was less (1. 5%) increased. This phenomenon due to then settlement development among others was connected with the broadening of employment facilities and evolving of new country centers. This new centers was created leaning on resource of a group of settlements not one settlement. The decentralization of industrialization this time reached also the small and medium cities and created the “hick town compromise” of spatial development of economy (Pirisi-Kiss-Máté 2016). In many cases smaller settlements turned into objective of commute for the population of surrounding villages. Indicators of commute were relative stabile in 1980s (Lakatos 2015.).

Economy processions in the follower decade of regime changed generated fluctuations not only in employment and structure of national economy but also in spatial structure of workplaces. Because of stopping big factories some part of the country dynamically reduced the work facilitation. Especially in the undeveloped areas the labour force request was bigger the demand. This effected one side a bigger option for employers other side an effacement of comfort aspects - like the vicinity of home and work place, reach easy and quick- for employees in the decision of accepting a work facility. Employees became mobile according to 2001. Census data. The economy processions affected principally the chance of finding a workplace in place. The number of employees reduced with almost fifth between 1990 and 2001. Including this the number of employees at the residing place felled of almost 25 percent but the number of daily commuters only with 4 percent. While in 1990 75 percent of employees worked at his residing place and only every fourth was commuter until then in 2001 the rate of daily commuters was 30 percent (Lakatos 2015.).

The big (8.7 percent) increase of the number of commuters in the last two decades is not only an effect of the economic changes. Especially in 2000s a lot of people moved from big cities to agglomeration mostly families being in easy circumstances with employed member and enough income. Their work place is usually in that city, where the family lived before the moving. That’s why since that they go to the work day to day as an extern.

Denomination

thousand people

distribution %

1960

Residing and working at the same place

4 124

86.6

Daily commuter

636

13.4

Sum

4 760

100.0

1970


4 012

80.4

Daily commuter

977

19.6

Sum

4 989

100.0

1980


3 849

76.0

Daily commuter

1 217

24.0

Sum

5 066

100.0

1 990


3 380

74.7

Daily commuter

1 145

25.3

Sum

4 525

100.0

2001


2 589

70.1

Daily commuter

1 102

29.9

Sum

3 690

100.0

2011


2 545

64.6

Daily commuter

1 341

34.0

Sum

57

1.4

Sum

3 943

100

Table 2: Number and distribution of employees by commute[footnoteRef:1] [1: The Census data between 1960–1990 contains only the active employees without workers by child-care or pension.]

Since 2001 the resident population data in the Census - based on international accepted methodology - contains also people temporary residing abroad, some of whom are employed. In the course of commute monitoring number of employees does not contain temporary resident population (Lakatos 2015).

In 2011 every third employees (1 million 341 thousand people) commuted daily in Hungary. It means 34 percent of all employees. This number contains also employees worked on inconstant settlement (agents, vendors etc.). Employees commuted 2-3 daily but regularly are counted also as commuters. But the number of commuted doesn’t contains employees who are living far from their families and go home weekly or monthly. 87 percent of commuters travel every day to the same Hungarian settlement. Their number increased with 246 thousand since 2001. The number of employees on inconstant settlements (153 thousand) decreased and number of commuters abroad daily – because of the accession to EU – quintuplicated since the millennium (Lakatos 2015.).

The impact of economic change reflects best in content of sectors because the distribution of employees between the sectors is a characteristic indicator of structural rates. Processes started in 1980s and continued faster after regime change was a little bit others by commuters as by the sum of employees (Table 3). In 1980s decreased with more than a quarter the number of employees in agriculture. Due to this the participation of primer sector relapsed significantly. The decrease of rate this time didn’t appeared by commuters yet.

In 1990s the number of employed people fell extremely (with more than two-third) in agricultural sector. The cooperation’s transformed, farmed in smaller ranges that’ why they could less commuter employing. The family farms worked with small headcount and didn’t employed workers from other settlement. That’s why in 1990s the number of commuters fell significant (76 percent) compared to all agricultural workers.

In the industrial sector the number of employees decreased with near one fifth between 1980 and 1990. In 2001 was only near two-third of the 1990 data. The decrease of employees touched a wide scope of daily commuters because in industry and building-trade there are a higher number of commuters than the average. But the data shows that the increase is bigger in that group who stayed and worked in place (staying in workers’ hostel, far from family, rarely travelling home).

It follows from the above that between the employees residing and working at the same place increased the rate of working people in service sector than between commuters. But in such service sectors where a lot of private entrepreneurs and privately owned companies are (education, personal

Like 2001 also in 2011 workers in industry and building-trade sector has higher proportion between daily commuters than between workers residing and working at the same place but the proportion of workers is service sector is lower between commuters. Workplaces in service sector are more consistently distributed in the country than in industry and building-trade sector. Previous can find in every settlement but industry and building-trade not. Commute in service sector is not so important also because there are a lot of sole proprietorship in this sector (like in trade, hospitality, economic or personal service).

Denomination

Agriculture, forestry

Industry, building-trade

Service sector

Sum

1990


15.1

35.3

49.8

100.0

Daily commuter

16.4

45.7

38.0

100.0

Sum

15.5

37.9

46.6

100.0

2001


6.1

27.5

66.4

100.0

Daily commuter

4.0

45.4

50.5

100.0

Sum

5.5

32.9

61.6

100.0

2011


4.9

22.8

72.3

100.0

Daily commuter

3.7

38.4

57.8

100.0

Sum

4.5

28.3

67.2

100.0

Table 3: Distribution of employees by contracted national economy sector and daily commute (%)

The main direction of worker’s movement is determined by local situation of bigger companies. They are usually in big cities that’s why the orientation of worker’s movement shows from settlements to cities (Table 4). According to 2011 Census data 37 percent of commuters are travelling from settlements to cities but only 7 % in the other direction. Including this 41 % of commuters was appealed by capital and cities with county right 32% by other cities and 14% by settlements in 2011 (the rest 13% of commuters occurred in inconstant settlement or abroad – HCSO 2016).

Work place, resident place

To capital

To towns of county rank

To other city

To settlement

To abroad

To inconstant settlement

Sum

person

From capital

–

4 823

37 023

6 057

1 399

29 379

78 681

From towns of county rank

22 356

8 738

38 345

22 721

7 521

22 087

121 768

From other city

136 788

109 084

116 292

66 918

7 942

50 151

487 175

From settlement

66 374

195 562

234 301

94 911

10 266

51 793

653 207

Sum

225 518

318 207

425 961

190 607

27 128

153 410

1 340 831

distribution %

From capital

–

0.4

2.8

0.5

0.1

2.2

5.9

From towns of county rank

1.7

0.7

2.9

1.7

0.6

1.6

9.1

From other city

10.2

8.1

8.7

5.0

0.6

3.7

36.3

From settlement

5.0

14.6

17.5

7.1

0.8

3.9

48.7

Sum

16.8

23.7

31.8

14.2

2.0

11.4

100.0

Table 4: Daily commuters by settlement rights and direction of commute, 2011

Figure 3: Distribution of resident, extern and commuted employees by resident place and population size of work place 2011

74 percent of commuters are travelling to a more populous settlement than his/her resident place. Growing the number of inhabitants grows the rate of extern workers and decreased the rate of commuters (Figure 3). In settlements having more than 10000 inhabitant third-quarter of commuters was employed while just third of commuters resides in such settlement size. The differences are quite big between the different settlement types and population size categories (HCSO 2016). The long term decrease of significance of the rule as commute center of little towns are notable: also the centers out of agglomeration areas has a growing commute deficit on long term as long as the surplus of little town’s consist mainly of some industry or tourism centers (Pirisi-Kiss-Máté 2016.).

Commute with employment purpose is nodal in Hungary. So mainly of commuters are traveling to a bigger center. From this point of view is also very different the Great Plain from the other part of Hungary. For Great Plain is characteristic the big size of settlements. Intensive commute evolved only near to the biggest cities. Figure 4 shows the strength and direction of commute connections between settlements. The plan shows order of connections by number of commuters from settlements.

Figure 4: Employment indicated commute out from settlements by order of intensity 2011

Figure 5: Settlements with positive commute balance and their employees (without Budapest) 2011

Based on 2011 Census data 374 settlement had positive employment balance because of commute (Figure 5). Lot of them aren’t still nodes because they employed less than 500 workers. This settlements through has local employment significance but attracts only workers from nearby settlements.

The settlement network has a lot of differences in Hungary that’s why is also very different the commute on the two different area. In Great Plan commute is less characteristic. It shows also the index-number of commute intensity.

, where

Ii means the degree of commute intensity to i settlement. Tij means the number of commuters from i settlement to j settlement. Tji means the number of commuters from j settlement to i settlement. Tii is the number of employees residing and working at the same place (by Pénzes–Molnár–Pálóczi 2014).

When calculating intensity of commute was taken in account only commute to a definite settlement without commute to different settlements and abroad. The differences between the two areas are explicable with specialties of settlement network and economic differences. The Great Plain’s multiple system with boroughs, giant villages and farmsteads don’t subserve commute. Here is a high rate of agriculture which causes also high rate of employment in resident place because agriculture connected to house. Besides industrialization after the Second World War and the complex system of institutions and service supply is enough to employ resident population but not enough to attract workers from villages also if they have a positive commute balance.

Intensity of commute increased with 10 percentage point during a decade to 2011 in Hungary (49.6% in 2001; 59.7% in 2011). Considering territorial aspects it is an increase firstly in north (Figure 6. and 7.). Comparison of the two maps confirm the above mentioned facts that also the suburbanization assisted commute because moving to agglomeration didn’t effected movement of work places. Inhabitants of agglomeration has to commute. This is typical firstly of big cities in Trans Danube.

Figure 6: Commuting intensity, 2001

Figure 7: Commuting intensity, 2011

Based on internal employment rates of LAU1 the current administrative units can be considered as more or less independent employment units (leaving out of consideration the direction and concentration of commute connections). It’s not a coincidence because during creating LAU1 researchers considered commute connections besides other factors (like functions, optimization of travel distances, etc.). We can see on maps a very high scope of internal employment rate in both of supply and demand part of employment rates (Figure 8 and 9). The extremely low rates are characteristic to Budapest and big cities. The reason of this is that LAU1 units was set up firstly for administrative purposes. That’s why during their creation were taken into account accessibility and reduction of differences because of size.

Figure 8: Internal employment rate of demand by LAU1 units 2011

Figure 9: Internal employment rate of supply by LAU1 units 2011

Employment rates in case of counties (NUTS3) have smaller scatter than in districts (Table 5). Hungarian counties have usually high internal employment rate (Figure 10 and 11). The only exception is Budapest and the agglomeration. Budapest has an attraction impact not only on Pest County but also on surrounding counties. But also this impact can’t decrease the rate under international accepted value which is appropriate to characterize separate labour market districts. Certainly is the situation other if we are considering near employment rates also interactions between settlements (measure, direction) in the course of adjudicate on insertion of labour markets and administrative unit’s scope. The problems of insertion appear rather on NUTS2 than on NUTS3 level (Chapter 5.2.4.).

AVDSC

AVSSC

MINDSC

MAXDSC

MINSSC

MAXSSC

NUTS3

0.95

0.93

0.77

0.99

0.60

0.99

LAU1

0.85

0.75

0.41

0.96

0.37

0.97

Table 5: Characteristic indicators of employment rates of NUTS3 and LAU1 units 2011

Figure 10: Value of employment rate on demand by counties (NUTS3) 2011

Figure 11: Value of employment rate on supply by counties (NUTS3) 2011

4.2.2 Correction of commute database

There was presented in the previous chapters the way how HCSO surveyed employment indicated commute of population during Census 2011 (more Kiss-Szalkai 2014). Census questionnaire was created in accordance with census decree and international methodologies. Direction of commute is derivable from questions of resident place and workplace. We didn’t need to research microdata because aggregate data of commute database on settlement level completed. Data of settlement commute matrix could be used directly but some correction was needed.

Some correction was needed to enable the matrix for research purposes. People working abroad (83 822) or inconstant settlement (153 410) were removed from database because they couldn’t connect definitely to commute relation (Figure 12). District of Budapest and their commute relations were contracted.

Employed

(3 942 723)

Living abroad temporarily

(56 694)

Living in Hungary

(3 886 029)

Daily commuter

(1 340 831)

Working in the locality of residence

(2 545 198)

Working in various

settlements

(153 410)

Commuting to other

settlement

(1 160 293)

Commuting abroad

(27 128)

Figure 12: Employment, commute date, Census 2011

Database also contains such relations which - because of big geographical distance or not appropriate transport connections (like in Czech data – Tonev 2013) - certainly not or only under certain conditions satisfied the definition of daily commute. The applied indicators don’t defined the self-reliance connection of settlements (workers at the same place) that’s why the diagonal of matrix is zero. It is necessary to review the related literature in the interest of eliminate this mistakes and resulted distortions.

Time of daily commute has a typical distribution which can be considered as constant in time and in spatial since Neolithic (Marchetti constant) irrespectively of place, type of travel or other living specialty. Regional scale studies define the most characteristic travel time in 1.1 - 1.3 hour (e.g. Zahavi 1976). Following this the increase of travel speed didn’t result time saving just increase of travel distance. Last results seems to confute theories of travel time costs (Barthélemy 2011). Consequently there can’t be define unequivocally one universal travel distance or time over this can’t realize daily commute.

International literature define commute with very big distance or time requirement as extreme commuting. It’s different in every country who means extreme commuter. The limit of this is in USA 100 mile (167 km) in UK 50 mile (83 km) in Sweden and Norway and also in European commute study 100 km (Vincent–Geslin–Ravalet 2016). According to a survey 5-10 % of European active population are commuting more than two hours at least three day in a week (Lück–Rupperthal 2010).

Hungarian literature is mentioned more limits. According to A study of unemployed commute cost limit jobseekers can undertake at most 45 km commute without their income after travel cost will be smaller than social aid (Bartus 2012). But disadvantages groups has even low threshold (Alpek 2017).

It’s important to highlight that in our model the travel time is shorter than in reality because we calculated with maximum speed allowed by Road Traffic. Usually this is reduced by infrastructure and traffic. Commuters using public transport (except train) should be calculated also more time than in our model.

To separate daily and weekly commute we are inspected relative frequency distribution of commuter’s number and relations between settlements functioned by travel time and travel distance. We can see on Figure 13 a craggy maximum of distribution in the point of 5 minutes distance then after a steep decrease the curve is flattened in the point of 40 minutes. Commute become equable in the point of near 90 minutes.

Figure 13: Relative frequency distribution of travel time and number of connections

Source: Pálóczi–Pénzes–Hurbánek–Halás–Klapka 2016

Figure 14: Relative frequency distribution of travel time and number of commuters


According to Figure 14 mass of commute decreased dramatically between 15 and 20 minutes. After 40 minutes become marginal. This sign the agglomeration of employment in Hungary which generally holds the isochrones of 20 minutes. We are thinking that the less intensive but having significant number of relations commute between 40 and 90 minutes are also relevant. Supposing that they have daily frequency we have taken into account also this so-called “weak bonds”. We are supposing that commuters travelling more than 3 hours aren’t daily commuters.

Figure 15: Relative frequency distribution of travel distance and number of connections


Figure 16: Relative frequency distribution of travel distance and number of commuters


Next to travel time we are looking into the role of travel distance. Based on distribution of connections similar to previous distribution is drawn. The function maximum is 10 km distance. Then after a steep decrease the rate of connections between 50 and 100 km is also considerable (Figure 15). Taken into account also number of commuters it’s clearly visible that number of commuters farther than 50 km in one direction is negligible (Figure 16).

Because of all these we realized a relatively concessive screening on data. Commuters more than 90 minutes and 100 km aren’t regarded as daily commuters. Consequently from 1 160 293 internal commuters who commutes in 85 100 relation (there and back means two 1+1=2) was filtered out 17 792 relation (20.91 % of all relation). In this near 18 thousand relation realized only 4 % of all commute (46 276).

Daily and non-daily commuters should be severance with the aim of Census microdata. This work would have passed the frame of this research. In our opinion corrected commute data matrix in this form is more available to carry out tests because filtering extreme connections reduces possible distortions at the same time sufficiently represents real commute connection system.

5 Comparing deterministic and non-deterministic spatial delineations

Chapter 2. and 3. contains the conceptual framework of functional delineations and the purpose, methods of delineation of labour market areas, plus researches in Hungary in this topic. This chapter presents methods profoundly which are suitable for such type of functional delineation, and details how the method chosen by the Commission and used in the feasibility study differs from other similar non-deterministic methods. At the end of the chapter we discuss that how the results of methods with different algorithms and measures can be compared.

5.1 Delineation of Local Labour Systems (LLS)

5.1.1 Methodology of the delineation of LLS

The method to be described in the following was the first analysis that processed the commuting data of the 2011 census, the approach of which although differs considerably from the EURO underlying the present research, many important findings can be made in the light of the results, and, therefore, it is worth mentioning it as a part of the comparative study as well.

Hungarian researchers of the VÁTI-institute (a non-profit urban development organization) delineated Local Labour Systems (LLSs) under the RePUS (Regional Polycentric Urban System) project, using work-related commuting data from the 2001 census (Radvánszki–Sütő 2007). ). The next phase of the research focused on combining these zones with microregions, and this created the Functional Urban Districts (Sütő 2008).

The practice of defining centers embedded in the settlement network in the study of Radvánszki–Sütő, 2007 is more flexible, more adaptable to the heterogeneity of the settlement system, and the delineation of the catchment area allows the repeat-free coverage of the whole territory of the country. Pénzes–Molnár–Pálóczi prepared their study of 2014 by adopting or partially modifying the methodology of the first study. The analysis was prepared for the commuting data of the 2011 census and, retrospectively, for those of the 2001 census as well (Pénzes–Molnár–Pálóczi 2014).

The commuting catchment areas were defined by using a two-step model. In line with the methodology, centers were identified first, during which the following were takin into account:

· All settlements with more than 1,000 persons employed locally were taken into account (328 settlements in 2001 and 348 settlements in 2011). The threshold applied was taken from the work of Radvánszky and Sütő.

· Then, only those settlements were left among the centers that attracted at least one settlement from where the most commuters went to work in the given center (205 settlements in 2001 and 197 settlements in 2011). This selection method was also included in the original methodology.

· The next step was to remove those settlements from the range of centers from where more than 10% of employees commuted to another center (their earlier review of scientific literature included similar thresholds). Although the threshold is arbitrary, they found it to be suitable to filter the range of employment centers (if 10% of a settlement’s employed people commute to a single place, it means an external attachment which is strong enough to question that the settlement is an independent center). In order to reduce the anomalies resulting from the application of the method, they have made an exception in two cases. On the one hand, in case of some settlements mutually attracting each other, center-pairs have been designated (Keszthely and Hévíz, as well as Balatonboglár and Balatonlelle both in 2001 and 2011 and Siklós and Harkány in 2001). On the other hand, in the surroundings of larger towns, the settlements from where the proportion of people commuting was less than 20%, the number of people employed locally was more than 5,000 (also called urban centers in the scientific literature - Faluvegi (2008), and there was a positive daily labour force account were considered independent centers, despite gravitating towards larger centers. In the surroundings of Budapest, Vác met the criteria both in 2001 and 2011 and Százhalombatta in 2001. In 2011, Bonyhád, Hatvan, Kazincbarcika and Körmend could also be separated from the hinterland of the nearby large towns with this method. Accordingly, 141 centers or center-pairs were designated in 2001 and 123 in 2011.

· Although when selecting the methodology, the primary aim was that the delineation of centres should be able to manage the spatial heterogeneity of the country‘s settlements (employment centers of different sizes, labour movement of different intensity) – these circumstances must be taken into account in LMA delineation as well –, catchment areas within catchment areas cannot be displayed with the method applied. Therefore, corrections described in the third point were necessary to manage very extreme cases. The examination of the still remaining secondary catchment areas, especially in the capital region, was considered justified, but their detailed presentation is not possible due to the limited size of the study. The method applied could not really handle the self-employing settlements either, as it is also shown by a few examples in the study.

As a second step, the designation of centers was followed by creating catchment areas around the centers on the basis of the following principles:

· On the one hand, irrespective of the intensity of attraction, the settlements where the most important destination of commuting of employees was the central settlement in question were determined (and assigned to the selected center).

· Centers strongly linked to another center (that is, from where more than 10% of employees commuted to the center in question) were merged and brought their entire catchment area determined with a similar method.

· Finally, further settlements were assigned (indirectly) to the designated centers according to the affiliation of their most important center of attraction.

· The spatial continuity of catchment areas formed in this way was also a viewpoint, because of which some settlements were re-assigned to the secondary or tertiary center of attraction (however, this was not applied in case of the catchment area of Miskolc).

5.1.2 Results of the LLS delineation

The system of LLSs formed as a result of the delineation was suitable for the static and dynamic analysis of both the clearly designated centers (and co-centers) and their catchment areas (the study cited could be based on the processing of the commuting data of the 2001 census as well).

Figure 17: Local Labour Systems in 2011

Source: Pénzes–Molnár–Pálóczi 2014, 486 p., Figure 4

After Budapest, the units integrating the largest number of settlements (more than 100) were Pécs, Miskolc, Zalaegerszeg and Győr (Figure 17). In line with settlement geographical differences, the zone of dominant large centers and their catchment areas are sharply separated from smaller units that represent a fragmented structure characteristic in regions having marked small centres farther away from larger centres. In peripheral regions more or less marginalised in respect of work-related commuting, the distant center, which, however has a significant catchment area, has an unrealistically extended effect (e.g. in case of Miskolc). This is one of the forms of peripherality, the other one is the separation of small centers far away from larger centers (only slightly connected to them) with strongly local catchment areas, which are not able to integrate more considerable areas. So, the methodology can only slightly handle the sharp differences in the settlement network in Hungary, and so, the size of the formed districts shows a significant standard deviation (the LLS method resulting in a spatial distribution with high extremities, e.g. compared to the EURO method, is shown in the study cited as well – Pénzes–Pálóczi 2017).

Mainly due to the generally increasing importance of commuting, the trend between the two censuses points to the disappearance of microregions on national level. This has also the consequence that in the delineated LLSs, the declining importance of the center and the development of units with several sub-centers is an observed trend. All these findings are useful experiences in the evaluation of the results of the EURO method.

5.2 Spatial distribution methods based on complex network analysis

5.2.1 Network analysis and spatial research

The application of network analysis in spatial research can be considered as a kind of renaissance. In the 1960s and 1970s studies were already prepared on the analysis of spatial interactions based on graph theory (Klapka–Halás–Tonev–Bednář 2013; Dusek–Kotosz 2016).

In the last decades, network research developed in many disciplines (in many cases in parallel) according to the challenges in the disciplines concerned. In addition to physics, medicine, biology, ecology (Szabó–Novák–Elek 2012) and sociology (Letenyei 2005), the methodology of network analyses gains more and more space also in the domestic scientific literature of human geography and regional science. In the Hungarian scientific literature, it has already been used in the analysis of scientific cooperation (Vida 2012), tourism (Madarász–Papp 2013), interbank settlement (Pál 2014), formation of polycentric urban regions (Fleischer 2009), transport (Géber 2007; Pálóczi–Pénzes 2011, Szabó et al. 2013), as well as microregional commuting connections (Letenyei 2000).

In network analysis, the techniques suitable for spatial distribution are collectively called locally dense subgraph search (Tibély 2011), or simply community detection (Kovács–Orosz–Pollner 2012). Hereafter, the terms subgraph search and community detection are used as synonyms for each other. The generally accepted precise definition of network nodes (or groupings, clusters, modules, communities) is not known (Tibély 2011), but it could be described as the ‘dense’ subgraphs of the network, within which the nodes are connected to each other more frequently and, in case of weighted networks, more intensively than to the other parts of the network (Derényi–Farkas–Palla–Vicsek 2006).

Within community detection, three main categories – local, global and based on the similarity of vertices – can be distinguished (Fortunato 2010). In the local approach, the attention is focused on the nodes of the subgraph and their direct neighbours, while the rest of the graph is ignored. The global definition manages the subgraphs as the structural units of the graph; it should be imagined so that the distinctive features of the graph become recognisable if the subgraph is compared with the whole graph. The definition based on the similarity of vertices chooses the subgraph as a group of similar vertices. The measurement criterion of similarity is the existence or absence of the edge between the vertex-pairs (De Montis–Caschili–Chessa 2013).

The result of the subgraph search performed in case of unweighted graphs can only be the identification of modules based on topology. On the other hand, when analysing weighted networks, besides topology, the weight of individual edges affects the clusters, so it is worth considering the commuting system as a weighted network.

Numerous methods and algorithms are known in the scientific literature for searching the groups of vertices. The systematization of Fortunato distinguishes three main types (Fortunato 2010):

· divisive algorithms;

· optimization methods;

· spectral analysis.

Other methods, which cannot be classified in the above categories, such as the Q-state, Potts model, clique percolation: Derényi–Farkas–Palla–Vicsek 2006), random walk, Markov cluster algorithms, maximum likelihood and L-shell method (Fortunato 2010) are also known.

5.2.2 Structural equivalence calculation

Structural equivalence calculations can be used to identify the members of the commuting network with the same roles. With the help of the method, it is possible to identify groups in approximately the same situation in respect of the network. Two settlements are structurally equivalent with each other if they have relations of similar intensity with the same settlements. In the commute matrix, this appears so that the columns and rows of the two settlements are the same. If the two actors are structurally equivalent, they can be optionally interchanged or merged and so, the complex network can be made more transparent (Kürtösi 2005) (Figure 18).

Figure 18: Structurally equivalent actors

Source: Kürtösi 2005

In case of real networks, a perfect identity of relations between two actors can be observed only in exceptional cases, but, by calculating correlation between the columns and rows of the actors, such groups can be identified whose members’ relations are more similar to each other. As can be seen in the study of Pénzes-Pálóczi published in 2015, one of its possible method is that the Pearson's correlation coefficient between the columns and rows of settlements is calculated in pairs. If two actors are structurally equivalent, the correlation coefficient will be 1. As a next step of the examination, the authors chose the so-called interactive CONCOR (CONvergence of iterated CORrelations) operation controlled by the analyst to organize the actors into groups. Using the correlation matrix of the calculated relations, the software calculated again correlations. By the permutation of the columns and rows of the correlation matrix observed among correlation coefficients, the basic population is separated into two blocks. By repeating the operation, further subgroups can be defined within the groups. The significant disadvantage of the method is that it is only suitable for double breakdowns, i.e. it always offers groups of even numbers, which does not necessarily reflect the reality. For the detailed description of the method see Kürtösi Zsolt (2005).

The method is theoretically suitable for separating settlement groups that are connected to similar employment centers with similar intensity, i.e. it can be assumed that their employment situation, the number of jobs available by commuting may change similarly at times of recession and boom. (Obviously, the qualification and sectoral attachment of the employed add further shades to the picture).

Figure 19: Tree diagram of structural units in the study area in north-eastern Hungary

Source: Pálóczi–Pénzes 2015, 335 p., Figure 2

Figure 20: Structural units in north-eastern Hungary

Source: Pálóczi–Pénzes 2015, 336. p., Figure 3

The study area consisted of the settlements of three counties in north-eastern Hungary. By performing the calculation with the commuting data of these settlements, 10 groups could be created with the help of the software using the method. The largest group consisting of 457 settlements is the 1.1.1.1.1 block named ‘Other’ (Figure 19). Those settlements belong to this group whose relations are so diverse that the algorithm used could not define further groups. This group includes also the most influential members of the network, thus, the naming settlement is not included in any of the other groups identified by the name of the settlement (Ózd, Kazincbarcika, Miskolc, Tiszaújváros, Sárospatak, Sátoraljaújhely, Debrecen, Nyíregyháza).

After the first step of grouping, a settlement group dominated by Miskolc was separated from the basic population which does not include Miskolc. As shown on the map (Figure 20), a group with internal relations 2.1.2 (Miskolc) and two groups in peripheral position dispersed in space can be distinguished.

Based on the results of the study (Pálóczi-Pénzes 2015), it can be stated that the method is not really suitable for the analysis of a complex, diverse system of relations such as commuting. Although it detected the intensive catchment area of major employment centers and revealed their internal relations, the method could not typify a significant part of the settlement network. The number of groups created depends on the subjective decision of the researcher, which can significantly influence the outcome (Pálóczi–Pénzes 2015). Furthermore, in networks with a larger number of elements, such as the national level examination, the method can only be run with a more significant IT background. However, the method may be suitable for agglomeration research, and it also provides an opportunity to further analyse the internal structure of larger areas created with other methods.

5.2.3 The clique percolation algorithm

The clique percolation algorithm is searching for groups among which overlapping is allowed. This process creates groups from the densest elements of the network, from cliques. Within a cliques, each vertex is connected to all other vertices, and the clusters are the coherent chains of these cliques (for the description of the method see: Derényi–Farkas–Palla–Vicsek 2006).

In the case of real networks, overlapping obviously occurs among groups. If we search for clusters free from overlapping, the designated cluster may include such members which ‘do not know each other’ (false positive); however, a number of vertices may be included in other cluster (false negative) despite the obvious coherence. The clique percolation algorithm is in principle capable of avoiding such mistakes. For this reason, the commuting data set was analyzed using the above mentioned method. However, the results did not live up to the expectations, since the algorithm identified more than 5,000 groups. Although when running it on a weighted network, the number of groups was reduced, but we did not consider it suitable for analyses in spatial research, so we do not present the results.

5.2.4 The Louvain method

The Louvain algorithm optimization process (Blondel–Guillaume–Lambiotte–Lefebvre 2008) has already been successfully applied in the topic of commuting (De Montis–Caschili–Chessa 2013).

The method is based on maximizing the objective function called modularity (Qw) (Newman-Girvan 2004). The value of the function shows the number of edges for a certain subgroup within the community compared to the number of edges outside the community. The value of the function makes it comparable how a subgraph meets the criteria compared to all the other possible variations, and its value may vary between -1 and +1. The value is zero if no further subgraph can be created within a given subgroup. The negative value indicates that there is no point in further breakdown of the network: the group in question is the best breakdown. For weighted networks it can be defined as follows:

where is the weight of edges connected to i and j vertices,

(strength of vertex) is the sum of weights of edges connected to i vertex,

is the sum of weights of all edges, and is a function, which equals one if i and j vertices belong to the same community and are not at all connected to any other one.

The significant advantage of the Louvain method is that, as opposed to other clustering approaches, the number of subgraphs follows from the algorithm, i.e. there is no set value at baseline, so the subjectivity of the researcher can be eliminated. The algorithm is based on the following iterative steps (Table 6):

Step

Task

1

Each vertex belongs to a unique group.

2

The adjacent vertices of each target vertex belong to the same community if the variable of modularity ( is positive.

3

This merging process lasts until the modularity function reaches its maximum.

4

Those vertices belong to the new network which were identified in step 3. The pairs of subgraphs are connected to each other if the vertices belonging to the subgraphs were connected earlier – the weight of edges equals the sum of weights of edges connected to the vertices of the particular subgraph.

5

Performing the first step on the last network.

Table 6: Iterative steps of modularity optimization

Source: Pálóczi 2016, 131 p., Table 2 – on the basis of Blondel–Guillaume–Lambiotte–Lefebvre 2008 and De Montis–Caschili–Chessa 2013

The ΔQ function measures the degree of change associated with the given vertex’s separation from or connection to the C community.

Pálóczi published his examinations performed with the Louvain method in his study published in 2016. The calculations were carried out on a symmetric, undirected graph (Link 1) with a software called Pajek. Along with the original algorithm, the software makes it possible to regulate the level of resolution of communities with the help of the so-called resolution parameter (for the description of the method see: Arenas et al 2008). If the resolution is 1, the algorithm runs in an unchanged form, if its value is increased, the software continues the iteration and more and smaller modules are created, and if its value is decreased, fewer but larger modules are formed.

On the basis of the experiences, the single run of the algorithm often results in an unstable modular structure, i.e. along with the same parameters there may be significant differences among the modules. Accordingly, the algorithm was run several times with the same resolution value. The distributions belonging to the same resolution value were tested with the recommended correlation test. As a final result, the stability of the modules belonging to the 0.2 and 1.0 resolution values was higher than the 0.99 Cramer’s V-value (Figure 21, 22). Based on the results, it is obvious that the methodology delineated professionally evaluable, spatially contiguous settlement groups, so its application is relevant in regionalization based on commute connections.

Figure 21: Settlement groups identified with the help of the Louvain modularity optimization in each county (resolution=0.2)

Source: Pálóczi 2016, 132 p., Figure 4

Figure 22: Settlement groups identified with the help of the Louvain modularity optimization in each county (resolution=1)

Source: Pálóczi 2016, 134 p., Figure 6

The results highlight that labor market settlement groups are not in line with the NUTS2 level regions of Hungary (Figure 20, 21). The most significant deviation is caused by the diverse and intensive relations of Budapest which determines Central Hungary. Interestingly, the spatial extension of module 2 (Figure 20) is considerably smaller in the direction of west, which is the result of the more significant employment role of north-western Hungary.

Based on the results it can be stated that the settlement groups (regions) based on employment relations, i.e. formed by regionalism, fit less to the NUTS2 regions and better to the county boundaries. The deviations from the county system are not one-off deviations resulting from the methodology, but they reflect the real commute connections which can be verified by the findings of the related studies.

In the study cited (Pálóczi 2016), a comparison with the earlier described LLS delineation, which is based on the fitting and hypothetical aggregation of the boundaries of territorial units was also made. In this way, the different delineations can be compared.

The modularity optimization performed using the Louvain method proved to be suitable for delineating larger territorial units. The method can be applied to determine the hierarchical order of LLSs, as well as to examine additional spatial interactions.

5.2.5 CURDS method

The so-called CURDS method is a possible application of algorithms based on relativization indicators already partially described. The results are available in the Czech (Halás–Klapka–Tonev–Bednář 2015) and Slovak (Halás–Klapka–Bleha–Bednář 2014) case studies already cited and most recently also on Hungary (Pálóczi–Pénzes–Hurbánek–Halás–Klapka 2016) as well. The method developed by Coombes based on common theoretical and relativization methodologies (referred to as the CURDS method) is somewhat different from the EURO methodology. The following overview summarizes this procedure.

The algorithm can be divided into three steps, within which it can be divided into 4 steps and different operations (Klapka–Halás–Erlebach–Tonev–Bednář 2014):

a, determination of proto-regions

1. determination of potential centres

2. determining multiple centres using the critical value of the interaction indicator

b, Assignment of the remaining areas

3. assigning regions to proto-regions by maximizing the interaction indicator

c, assessing the validity of the solution

4. The constraint function and the iterative break down of regions if they do not meet the constraint function defined by the criteria.

The starting territorial unit (in this case the settlement level) must meet two characteristics to be considered as a potential regional centre, one such condition is the "job ratio" function (ratio of outward and inward commuting):

The other criterion is the self-containment value of the supply side (or residence-based supply side) (the proportion of locally employed and total commuters):

If the potential centre j does not meet the criterion of sufficient self-containment:

then the potential groups of j centres are identified based on the mutual link between them and the interaction indicator values.

The criterion for the value of the interaction indicator was 0.01 in case of the Smart measure (and 0.2 in case of the original CURDS measure) ( Klapka–Halás–Erlebach–Tonev–Bednář 2014). The resulting cores and multiple cores are considered as proto-regions.

In the next step, the remaining i territorial units (settlements) are sorted in descending order by number of persons employed and assigned to the proto-region to which they are most strongly related according to the interaction indicator.

If i is associated with j proto-region, then each flow is recalculated and a new interaction matrix is created. This step is repeated until no more i settlement is left.

In the next step, we use a constraint function to determine a minimum size and self-containment criteria (internal employment rate) for the resulting regions. The regions are sorted in descending order by the value of the constraint function and the last region, which does not meet the condition of the constraint function, is broken down into its settlements. The settlements that become "free" again are connected to another region in accordance with step 3. This operation is repeated iteratively until all regions correspond to the constraint function.

As discussed in the above points, the role of the constraint function is critical in terms of the pattern of the resulting regions. The constraint function performs optimization between two parameters of the resulting regions. Basically, this means that the rate of self-containment must reach a higher level in the smaller regions, while in case of larger regions a lower level of self-containment is acceptable.

In the regionalization procedure, the constraint function is responsible for two important factors - size and self-containment - as well as the optimization between the two. While self-containment is a critical parameter and cannot fall below 0.5 (that is, more than half of the starting points and destinations of the flows belonging to each region must be a settlement in the given region), the minimum size can be adjusted according to the specified practical goals and the subject of the research.

The minimum size of a region can be defined by different criteria. The most common feature of a region is its population, which is a standard, simple and easily accessible criterion. Nevertheless, if we want to use this indicator to the regionalization procedure, there are three options:

1. the sum of outbound and internal flows (number of people living in the region; this largely corresponds to the economically active population – It can be defined differently by country, depending on the laws and regulations of the given country);

2. the sum of inbound and internal flows (number of people working in the region; number of jobs in the region);

3. the sum of internal flows (number of residents and workers in the region, internal flow).

The choice of criteria depends on the type of the task to be solved. In case of a general purpose regionalization task, the use of the number of workers living in the region seems to be the most convenient solution, because this correlates best with the population of the region. If the regional labour market and the size of the full economic potential are emphasized, then a better choice is the combination of options 2 and 3 (Halás–Klapka–Tonev–Bednář 2015).

The number of employed population was () used in the study cited. (Pálóczi–Pénzes–Hurbánek–Halás–Klapka 2016).

The relative value of self-containment in a region is the primary criterion for determining functional regions. In the second variant of the CURDS algorithm, the self-containment rate was defined as follows:

which is the ratio between internal flows and the maximum number of economically active persons or jobs (the value of the counter is divided by the larger of the two values). The lower-value job-based and residence-based self-containment can be termed as the index of unidirectional self-containment. In our study, the alternative approach of self-containment was defined as follows:

which is able to determine the self-containment rate of a region by taking into account the flows into and out of the region. This is a much more complex examination of self-containment and therefore it can be called as the index of total self-containment. (In the denominator, is included both in the values of and , therefore the value must be deducted from their sum.)

Figure 23: Index of unidirectional self-containment (the value of the index is the same in both cases) (a); and the index of total self-containment (the value of the index is the same in both cases) (b).

Source: Halás–Klapka–Tonev–Bednář 2015

Both concepts have advantages and disadvantages. The index of unidirectional self-containment cannot distinguish between the following two cases: the volume of flow (inflow or outflow) is large in one direction while low in the other or both directions are high (Figure 23 (a)). In both cases, the index shows the same numeric value.

By contrast, the full internal self-containment rate cannot distinguish between the two cases when the volume of one direction is large and the other is small, as well as when the volume of both directions is moderate (Figure 23 (b)). Again, in both cases, the index will provide the same numeric value.

The values provided by the two self-containment determinations are significantly different. A Czech case study has shown that when the unidirectional self-containment rate was less than 0.66, the regionalization algorithm also produced results that did not correspond to the concept of a functional region. The overall self-containment rate has always produced good results (Halás–Klapka–Tonev–Bednář 2015), thus it was also used in the cited Hungarian study (Pálóczi–Pénzes–Hurbánek–Halás–Klapka 2016).

The constraint function is an important part of the regionalization algorithm, as it determines which regions will break up while running the algorithm and which will appear as a result. The constraint function performs optimization between the pre-defined minimum size and the value of the self-containment rate. As a result, it expects higher self-containment rates for smaller regions, while in case of larger regions it allows a lower self-containment rate. The CURDS algorithm published in 1986 defines a linear line and four limit values (upper and lower limits, upper and lower self-containment rates) for optimization (Figure 24: dashed line). Papps and Newell (2002) solved the optimization of size and self-containment with a very slightly curved function instead of the straight line used earlier (Halás–Klapka–Tonev–Bednář 2015).

According to Halás and his co-authors (Halás–Klapka–Tonev–Bednář 2015), the constraint function can be given by a single regular curve, expressed as follows:

Where β1, β2, β3, β4 are the limit values of the optimization between region size and self-containment rate (Β1 and β2 are the lower and upper limits of self-containment; Β3, β4 are the lower and upper limits of the size). They can be controlled without recalculations and any limit can easily be changed to any logical value. Α7 (0 <α7 <1) determines the curve of the function optimizer part. The closer α7 is to 1, the curve is closer to one. Conversely, if α7 is approximated to zero, the optimization will increasingly follow the arc of a curve.

Figure 24: Continuous constraint function - the dashed line is the line of the constraint function used in the original CURDS algorithm

Source: Halás–Klapka–Tonev–Bednář 2015

This function can be called a continuous constraint function. The values of the parameters determine where the continuous constraint function intersects the original function. Α8 (0 <α8 <1) determines how the function optimizing part curves. The closer α8 is to 1, the closer the curve is to one. Hence, α8 = 0.09 and the continuous constraint function intersects the β1-β2 line at sections 1/10 and 9/10 of the original function as well as it intersects the β3-β4 line at sections 1/10 and 9/10. The continuous constraint function has been designed to approximate the size and the lower limit of the self-containment rate asymptotically.

The position of each region can be represented on an x-y plot diagram where the axes represent the size of the regions and the value of the self-containment rate. The regions and constraint curves are located at the top right of the chart, which sector was highlighted in Figure 25. Although the algorithm and its application are relatively an exact research method after the parameters have been determined, the results are still significantly dependent on the predetermined parameters. Charting the regions provides a refinement opportunity to determine even more suitable parameter values.

In all cases, it is better to start testing with a lower size and minimum self-containment rate. Of course, in this case, the algorithm defines several regions, but their position on the x-y chart and the knowledge of the settlements and the regional system of the given field of study can help to identify which regions should be broken up by increasing size and self-containment parameters. Of course, we also know the opposite of this effect, when we cannot find such region among the results that should have appeared. Graphical analysis of results helps to determine the curve and position of the constraint function. If there is a significant gap in the points field, then this is a sign that the continuity of size and self-containment has been interrupted, or more precisely - there is a significant gap between the optimization of these parameters.

Figure 25: Use of constraint function on the point diagram of the FRD-1 and FRD-2 variants


Figure 26: Functional regions according to the FRD-1 delimitation


The following parameters were used for the version illustrated in Figures 25 and 26; the self-containment rate had a minimum value of β1 = 0.60 and a maximum value of β1 = 0.65, while the size had a minimum value of β3 = 3000 and a maximum value of β4 = 20000.

When comparing to the results of the EURO method, we will return to the further comparison of the results and the methodology.

- 999Employed persons working in the locality of residenceEmployed persons commuting to work in other localities by residenceEmployed persons commuting in the locality from other localities by place of employment262958156084490411000 - 4999Employed persons working in the locality of residenceEmployed persons commuting to work in other localities by residenceEmployed persons commuting in the locality from other localities by place of employment8403034491111739685000 - 19999Employed persons working in the locality of residenceEmployed persons commuting to work in other localities by residenceEmployed persons commuting in the locality from other localities by place of employment80350630569323968720000 - 49999Employed persons working in the locality of residenceEmployed persons commuting to work in other localities by residenceEmployed persons commuting in the locality from other localities by place of employment46756912012918864650000 - Employed persons working in the locality of residenceEmployed persons commuting to work in other localities by residenceEmployed persons commuting in the locality from other localities by place of employment74150481373283433BudapestEmployed persons working in the locality of residenceEmployed persons commuting to work in other localities by residenceEmployed persons commuting in the locality from other localities by place of employment77018947903225518

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