Method

In the original formulation proposed by Nyusten & Dacey (***) a spatial unit is dominated by as spatial unit  j if and only if two conditions are fulfilled : (a) the maximum flow send by i is directed toward j and (b) the total sum of in-flows from j is greater than the total sum of in-flows from i.

Let us take some example to illustrate the application of the rule :

• Italy: if we consider the matrix of total trade in 2004-2006, the maximum export flow of Italy is directed toward Germany (47 685 M$) and the total import of Germany  (767 524 M$) is greater than the total import of Italy (376 023 M$). The rules (a) and (b) are therefore fulfilled and we will consider that Italy is dominated by Germany for export trade.
• Germany: In this case, the maximum export flow of Germany is directed toward France (88 409 M$) but the total import of France (492 856 M$) is lower than the total import of Germany. Therefore, Germany is not dominated and is considered as a terminal node or dominant country.

The result of the analysis is the building of an oriented graph that produces a strict hierarchy of countries. For example, Bosnia is dominated by Croatia, which is dominated by Italy, which is dominated by Germany. We can derive from this graph a typology of countries:

• Dominant countries (Germany) are the top level of hierarchy as their main flow is directed toward a country of lower level.
• Intermediate countries (Italy, Croatia) are at the same time dominated and dominant.
• Dominated countries (Bosnia) are dominated by a country but are not dominating others and are therefore located at the bottom level of the hierarchy.

Results

Export vs. Import dominant flows on manufacturing goods (2004-2006)
↓ Click to enlarge ↓

Dominant import flows (2004-2006) ι Dominant export flows (2004-2006)

Regarding trade, we can produce two different graphs of domination according to the direction of flows. Left figure is related to the domination of export countries by import countries and reveals the power of the client that can decide to restrict its import by means of different tools (protection of internal market, external tariff, rules and norms, etc.). Right figure is related to the domination of import countries by export countries and reveals the power of the supplier that can decide to restrict its export, for example in the case of high level technological products able to produce weapons. A good example of this difference is provided by Gabon. In terms of export, this country is dominated by USA because the majority of exports are based on oil that is bought by American companies. But in terms of import, the dominant country for Gabon is France that has inherited from the colonial period a strong position in the provision of manufacturing goods. Thus, we can observe that concerning the importation of manufacturing goods, USA is the most dominant country of the World and even dominate all the countries with the 'dominant flows method' with the strange exception of Arabic Gulf and Oceanian countries. Germany and China are the two most important relays which dominate, it, respectively most of the European countries for the first and East Asian countries for the second. The pattern of the exportation is a little bit reversed concerning the dominant countries. Germany and China, in red, form now the two most dominant countries in terms of exportations. The area of influence of Germany gathers most of the European and African countries whereas China dominates via the relays of USA and Japan, American, Asian and Oceanian countries.

Dominant directed financial flows
Click to enlarge ↓

The dominant flows method has also been applied to the matrix of cross-listings in the framework of the global financial integration of the stock-exchange industry. Firstly, the choice of the original method seems relevant as far as it highlights the preferred choice of corporate issuers to get their shares listed on foreign markets. Nevertheless, the testing did not provide a perfect tree: the thirteen countries of issuers that send very few cross-listings to foreign markets often present ex-aequo dominant outflows. For instance, amongst the two Nigerian issuers that list their shares abroad, one lists its shares on South African market (Johannesburg Stock Exchange), while the other one prefers the International market of the London Stock Exchange. To get round this bias and to get a clearer partition of the world, we decided to keep only the link sent to the country of destination gathering the highest in-degree volume of cross-listings. As far as the results are concerned, the figure 3 points out different groups, related to six dominant states. The most important core (in-degree expressed in volume: red countries on the graph) is the United States, despite the fact that the listing place of London collects more links (in-degree expressed in volume). According to this method, The United Kingdom takes then the role of a relay core. Three other relays of the United States appear: Singapore, Switzerland and Spain. Those mainly collect listings in their regional area. Singapore market quotes shares of Malaysian or Thai issuers. As far as the other dominant states are concerned, the regional partition of the world remains conclusive, especially for El Salvador the stock market of which attracts cross-listings shares of Guatemalan, Honduran or Costa Rican firms. Similarly, the United Arabian Emirates markets list many shares of the Gulf States issuers, especially equities that are relevant to the Islamic finance. The matrix has also been applied to the bilateral variation of the dominant flows method which includes probability indicators. On the whole, we can observe very few changes related to the fact that the probability indicators widen the financial context of relationships: Luxembourg becomes a dominant state; an inversion occurs: France becomes a relay for the United States, surpassing Spain in the hierarchy of the graph; and lastly, the regionalization process is reinforced in Southern Africa.