The Journal of Accounting and Management, Vol 6, No 2 (2016)

Aspects 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 and the consequences, in terms of minimum distance, of leaving the European Union by one country or another.

Keywords: graph, European Union, Bellman

1 Introduction

2 The analysis 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, where: 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.

Figure 1

Source: Ioan C.A., Ioan G. (2016),

The determination of spatial interdependencies in the European Union,

Acta Universitatis Danubius. Oeconomica, to appear

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 is, after [1]:

Table 1

Applying the Bellman-Kalaba algorithm, finally gives the matrix of minimum distances between countries ([1]):

Table 2

The data in Table 2 shows the minimum number of arcs necessary for the transition from one country to another. The last column is the sum of all distances in the appropriate row, that is the d_i – indicator. We can easily see that =60 corresponds to Germany that is this country is the center of the European Union from the point of view of distances in a graph.

In what follows we shall exclude, successively, one country (in order) and we shall inquire which country will be the center and how much the distance will be modify.

Table 3

We see from this analysis that beyond the economic implications of the withdrawal of one country or another, may outline new poles (in terms of graph theory), namely in the case of Austria-exit the new pole being France and in the case of Germania-exit the new pole being Italy. In the other cases, the center of the graph will remain Germany but with an increasing of the distances in the case of Denmark or Poland and with a big decrease in the case of France, Greece, Spain or United Kingdom.

Also we can remark that in the case of France-exit the graph will have two connected components, one containing the pair (Portugal, Spain) and the other the rest of the countries.

In the case of Greece-exit, Cyprus becomes isolated, the other countries remaining with links and if Italy will exit EU, Malta becomes isolated, the other countries remaining with links.

In the case of Spain-exit, Portugal becomes isolated, the other countries remaining with links and also if United Kingdom exit EU, Ireland becomes isolated, the other countries remaining with links.

3 Conclusions

The above analysis shows that, in terms of distances, European Union countries are highly interconnected, having a stable center (Germany).

Any departure from the European Union by one country preserves as the current center the actual pole or moves it to the most advanced countries on the continent.

The decrease of the minimum distance from the center to other countries can not be done unless the output of major EU countries (except Greece) which obviously is unacceptable.

We should note also the special places of France or Spain, whose output would cause a break of European Union in two connected components would cause a malfunction particularly high.

4 References

Ioan C.A., Ioan G. (2016), The determination of spatial interdependencies in the European Union, Acta Universitatis Danubius. Oeconomica, to appear

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

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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