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The small-world phenomenon has been already the subject
of a huge variety of papers, showing its appeareance in a variety of
systems.
However, some big holes still remain to be filled,
as the commonly adopted mathematical formulation is valid only
for topological networks.
In this paper we propose a generalization of the theory of small worlds
based on two leading concepts, efficiency and cost, and valid also for
weighted networks.
Efficiency measures how well information
propagates over the network, and cost measures how expensive it is
to build a network. The combination of these factors leads us to
introduce the concept of economic small worlds , that
formalizes the idea of networks that are “cheap” to build, and
nevertheless efficient in propagating information, both at global
and local scale.
In this way we provide an adequate tool to quantitatively analyze the
behaviour of complex networks in the real world. Various complex
systems are studied, ranging from the realm of neural networks, to
social sciences, to communication and transportation networks. In
each case, economic small worlds are found. Moreover, using the
economic small-world framework, the construction principles of
these networks can be quantitatively analyzed and compared,
giving good insights on how efficiency and economy principles
combine up to shape all these systems
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