Acta Universitatis Danubius. Œconomica, Vol 12, No 4 (2016)

The Determination of Spatial Interdependencies in the European Union

Cătălin Angelo Ioan, Gina Ioan

Abstract. The article deals with neighborhood ties to European Union countries in terms of graph theory. It is determined the minimum distance between states - the number of links in a graph and then their degree of connectivity to the Union. It also studied the link between the degree of connectivity with low GDP per capita considering that the development of the relatively isolated states can not grow without the development of communications infrastructure.

Keywords: graph; globalization; Bellman

1. About Globalization

The concept of globalization emerged in a more serious form somewhere at the end of World War I, is one that arises heated arguments for it or against it. The current period governed by the existence of the Internet (with all that it implies – e-mail, social networking sites, sites with statistical data more than enough etc.), a ready means of locomotion, a television increasingly more aggressive, a culture of increasingly standardized, but more pervasive, all of this born discussions leading to hopes or fear.

Benefits of globalization consists, according to the authors, in the faster spread of scientific achievements, faster implementation of new technologies and, especially, the rapid exchange of information. If until the 9th decade of the last century the information circulated through personal and scientific journals, symposia, exhibitions, media (as they addressed the public), since that time, the Internet has produced it almost instantaneous propagation.

As disadvantages, globalization brings, primarily uniformity. In terms of cultural, influence of powerful nations is to the full felt. Importing a way of life, often a foreign to the receptor, leads to paradoxical situations and sometimes frictions which generating pain. The best example in this respect are American cinema (with superheroes who struggle alone with armies, preferably Russian ...), Spanish (the passion for a beautiful lady lead to violent crimes) or Indian (in which, this time, the noble evil is defeated by a pair of beautiful singing and waving their hands gracefully behind a tree).

The Anglo-Saxon rhythms are already indisputable masters of modern music, despite symptomatic poverty or feelings expressed lyrics. It can thus continue to analyze other areas of arts (literature phenomena of Harry Potter or Dan Brown's writings, sculpture, painting, etc.). Also, information flows faster, a bit too quickly, the planet's population no longer having time to think, taking it in pure form, being at the same time led by superficiality and, not incidentally, to manipulation.

On the other hand, globalization is a very effectiveness phenomena especially for educated man. Information that is rapidly distributed nourishes him with data and/or allowing new ideas, in turn, disseminate their own results.

A problem that the authors face it is that if the European Union (obviously this study could easily extend to the entire earth) globalization extends through modern methods or classics that include the displacement of populations between regions and, once with them, the transmission of information.

To study this, the authors turned to the graph theory.

2. Bellman-Kalaba Algorithm

Considering a graph whose set of nodes is A={x₁,...,x_n}, n2 and arches - U subset of Cartesian product AA, assign each arc (x_i, x_j)U the effective distance from x_i to x_j.

Let D₁=(d_ij)M_n(R) the matrix where, if there isn’t an arc between x_i and x_j (or edge in non-orientate graphs) are considered d_ij= (on implementation on computer, a great value), and d_ii=0 i= .

3. Determination of Minimum Length of Roads between EU Countries

In this section we will determine the minimum lengths of the roads between EU countries for the purposes of considering only the existence arcs (actually the edges, since this is an undirected graph) between them, and not the actual distance (which would involve determining the “center” of a country - otherwise a complicated endeavor even if mathematically it is possible). So either graph links between countries:

Figure 1.

Note: 01 – Austria, 02 – Belgium, 03 – Bulgaria, 04 – Croatia, 05 – Cyprus, 06 - Czech Republic;

07 – Denmark, 08 – Estonia, 09 – Finland, 10 – France, 11 – Germany, 12 – Greece, 13 – Hungary;

14 – Ireland, 15 – Italy, 16 – Latvia, 17 – Lithuania, 18 – Luxembourg, 19 – Malta, 20 – Netherlands;

21 – Poland, 22 – Portugal, 23 – Romania, 24 – Slovakia, 25 – Slovenia, 26 – Spain, 27 – Sweden;

28 - United Kingdom.

Edges between nodes (figure 1) indicates the existence of common borders between countries (usually on land, the only exceptions being made for linkages United Kingdom, Malta, Cyprus with other neighboring countries - because of their insularity and pairs Denmark- Sweden, Finland-Estonia, Greece-Italy to nearby maritime each other). The length of each edge is unitary. The matrix of the graph in figure 1 (symmetrical because it is non-oriented) where in the rows and columns there are countries with relevant coding above:

Applying the Bellman-Kalaba algorithm, finally gives the matrix of minimum distances between countries:

The data in Table 2 shows the minimum number of arcs necessary for the transition from one country to another. For example, on line 1 and column 9 we have a value of 4 which means that the shortest path (not necessarily unique) from Austria to Finland passes through four countries (except the one starting): Germany-Denmark-Sweden-Finland .

Because the effect of one state against another is inversely proportional to the distance (reasonable assumption), we shall reverse matrix values above (replacing 1/0 with 1 – because we shall assume that the effect of one country on itself is maximum). So we get:

In table 3, how much will be small the distance between two states, a greater value will be allocated.

The data obtained in Table 3 can not be used in their raw form, benefiting countries form Centre of European Union which, geographically, have the most connections between them. For this reason, we normalize these values by dividing each line distances to the sum of its elements. Following this approach, the normalized matrix is not symmetrical, depending from the links neighboring third countries. So we get in the end:

Noting with D – “distances” in the normalized matrix – meaning the matrix of degree links to a specific country with all the others, result that elements of D² by multiplying the lines of D with its columns, these would provide the degree of connection of a country to another, passing binding by one of the other EU countries. Similarly, elements of Dⁿ will provide a degree of connection with another country, at least in passing binding “n” EU countries.

Numerical data analysis reveals that (aside from the inherent rounding) elements of B⁸ columns differ by less than 0.0001, significant results being accurate to 4 decimal places.

Therefore, we get finally degrees of connection (in terms of distance) of countries in the European Union:

4. The Relationship between the Degree of Connection and Size of the Countries GDP per Capita

In the following we will investigate the dependence of GDP per capita of EU countries, of which we excluded Luxembourg because the gap is very large compared to the rest of the data (in 2013 it has a GDP/capita of 83,400 euros to the following: Denmark - 44,400 euros) which affects the state diagram in figure 2.

For an accurate graphical representation, we determined the values maximum for each year and we computed the ratio of GDP/capita to the maximum value divided after by 15 (for comparability in absolute degree of connection).

The analysis reveals the following:

• Countries with a high GDP/capita are generally those with a large number of close connections (in terms of neighborhood relations) with European countries: Germany, France, Austria, Italy, Belgium, United Kingdom, Netherlands, Denmark,

• There are a limited number of countries whose GDP/inhabitant is very high: Sweden, Finland and Ireland which are relatively isolated geographically but whose economic policies have overcome the barriers of distance.

• Symptomatic are former socialist countries: Czech Republic, Poland, Hungary, Slovenia, Slovak Republic, despite their geographical placement, pay still errors of the past.

• Countries such as Greece (the situation here is somewhat special in recent years), Lithuania, Croatia, Romania, Bulgaria, Latvia, Estonia have economies resettlement on new bases, but they face barriers metric which requires the development of a strong infrastructure of telecommunications which will blur their relative geographic isolation.

5. Conclusions

The above analysis establishes a new approach to economic relations within the European Union in terms of neighborhood relations. Multiple links between states favor the exchange of goods more quickly, the migratory movement of the population - especially in contiguous areas, globalization - as a complex phenomenon can lead to economic developments but which, unfortunately, can deep differences within the Union. European countries were disadvantaged by geographical location as a chance to build economic development and/or amplification of a communications infrastructure that will alleviate the barriers of distance.

6. References

Ioan, C.A. & Ioan, G. (2012). Methods of mathematical modeling in economics. Galati: Zigotto Publishers.

Ioan, C.A. (2001). Determining the minimum effective way with Bellman-Kalaba algorithm. The Annals of Danubius University, Fascicle I, Economics.

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