A Small World Perspective on Urban Systems - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 25

Fig. 2.5 Hierarchy of European cities according to their positions in multinational firms in 1996

￿ Equivalence and structural equivalence: organizational structure is viewed as

a pattern of relations among positions. White, Boorman, and Breiger ( 1976 )
and Burt ( 2000 ) have developed positional theories of structural equivalence.
According to Monge and Contractor ( 2003 , p. 19), this theory “argues that
people maintain attitudes, values, and beliefs consistent with their organizational
positions irrespective of the amount of communication that they have with
others in their organizational networks”. From a geographical perspective, we
could argue that places like cities are formed by tangled and overlapped social,
economic and institutional networks that also put them in equivalent positions.
For example, cities of the same country are equivalent with respect to their
political national capital in many ways, from hierarchical administration to
hierarchical economy and culture. In contrast, national capitals are in structural
equivalence with their respective national urban systems, although some national
networks are more hierarchical than others.
Bridge cities can be identified by confronting the weighted degree and
betweenness centrality of each city at every level ( Barrat, Barthélémy, & Vespig-
nani , 2005 ; Guimerà, Mossa, Turtschi, & Amaral , 2005 ). In fact, degree and
betweenness centrality are very correlated, although they have different natures:
local (for degree) and global (for betweenness centrality). However, a low
degree with a high betweenness centrality especially shows the role of bridges
between clusters (Fig. 2.6 left), and the threshold to apply these measures must