A Small World Perspective on Urban Systems - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 24

Fig. 2.4 Hierarchy of European cities according to their control of multinational firms from 1990

to 1996

positions, such as the node degree (number of links), reachability (distance to all
other points), betweenness centrality (number of shortest paths passing through a
point), or generalized Strahler index ( Auber, Delest, & Chiricota , 2004 ; Delest &
Auber , 2003 ), measuring how many trees can be built from a node; every measure
can be weighted or not ( Wasserman & Faust , 1994 ; Newman , 2003 ; Brandes &
Erlebach , 2005 ). These indexes are all very useful to compare node positions
in a graph or even the position of the same node in different graphs (multiplex
graph).

￿ Dependencies and power: this characteristic is considered when social or eco-

nomic networks are oriented either reflecting ownership between enterprises,
decision-making, or hierarchy. The balance between incoming links (in-degree)
and outgoing links (out-degree) can be a measure of such dependencies or power.
For example, this method can be used to easily identify cities of power in
multinational-firm networks according to the opposition between headquarters
and subsidiaries (Fig. 2.4 ). Links are oriented and the centrality in the graph is
calculated based on the share of the number of headquarters (representing the
out-degree) relative to the number of subsidiaries (in-degree). Between 1990
and 1996, the graph has spread all over Europe, particularly areas like southern
and eastern Europe. London, with a high share of headquarters/subsidiaries, is
the most central, with many American headquarters controlling subsidiaries in
the continent. However, Paris seems to be much more connected to other larger
European cities.
Also, one can identify dual positions in which some cities are only linked
to one other. According to Nystuen and Dacey's methodology ( 1961 ), one can
build a conceptual hierarchy with the highest link of each city going to a bigger
city. All of these links create some “regional systems”. Therefore, a hierarchy
can also emerge from non-oriented links according to weighted dependencies.
Figure 2.5 shows this construction applied to connections among European cities
using complete graphs built inside each firm of a sample of 100 groups in 1996
(Fig. 2.5 ). The first link of the majority of the analyzed European cities is oriented
to Paris, the most connected city according to this kind of graph of firms.