Conclusion - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 203

were air transportation networks (Chap. 9 ), and collaboration between researchers
(Chap. 11 ). These two examples illustrated that certain distant cities were highly
connected, while other closer cities were less connected. Thus, space and territories
are more influenced by the density of networks compared to physical distance.
However, unlike such domains as sociology, the concepts and applications of
graph theory could not be directly applied to geography. Studying geographical
networks requires conceptual adaptations that extend beyond a strict topological
description that focuses on the orientation of the links, weights, positions and
attributes of nodes (Sect. 3.4.3 ). Gleyze argued that the concept of “reachability”,
which corresponds to the geographical concept of “accessibility”, is not necessarily
revealed by high density in the graph. Moreover, when networks are aggregated
by geographical proximities, non central territories inherit centrality properties,
dependencies and powers from institutions as firms, although these properties may
not have existed prior to aggregation.

2 Transformation of Space By Networks

Networks create new territory properties by transforming the proximities of spaces.
Networks reduce the distance of paths along links that are used to locate individuals
based on their relative positions in the network. In Chap. 6 , Lambert, Bourqui and
Auber detailed general methods of network visualisation for graph layouts based on
attractive forces. The process of moving individuals with more interactions closer to
each other transforms geographical space into topological space. Network topology
may sometimes coincide with geographical distance. However, networks often
distort space, and cohesive territories or communities are not based on geographical
proximity. The topological proximity of Malta and UK in the Eurovision network
provides a typical example (e.g., Gleyze's example of votes for Eurovision songs in
Sect. 3.4.3 ).
In Chap. 4 , Alain L'Hostis considered the time-distance relationship and de-
scribed the spatial inversion phenomenon and the time-space contraction created
by transportation networks' selection of a limited number of places. This inversion
is difficult to represent by maps, which preserve the order of spatial proxim-
ities because they adopt Euclidean principles for representing distance in two
dimensions. Abandoning Euclidean space and the rule that the shortest path is
represented as a straight line, Alain L'Hostis introduced the “shrivelling” of maps
that create new spatial terrain through “time-space” peaks and valleys. This process
is similar to the approach adopted in astrophysics, where the space-time of the
universe is deformed by general relativity in crumpled spaces ( Luminet , 2001 ).
Applied to terrestrial transport, this “crumpling” generates new connections and
new proximities that allow new properties of geographical space to emerge. Tunnel
effects that reflect the nonaccessibility of the space between two nodes eliminate
part of the space between two linked nodes, and geographical distances are no
longer symmetrical between places. Space is transformed by conditional relative