Physics – Physics and Society
Scientific paper
2010-05-11
Physics Letters A, Volume 375, Issue 15, p. 1626-1629. 2011
Physics
Physics and Society
Scientific paper
10.1016/j.physleta.2011.03.006
Since its recent introduction, the small-world effect has been identified in several important real-world systems. Frequently, it is a consequence of the existence of a few long-range connections, which dominate the original regular structure of the systems and implies each node to become accessible from other nodes after a small number of steps, typically of order $\ell \propto \log N$. However, this effect has been observed in pure-topological networks, where the nodes have no spatial coordinates. In this paper, we present an alalogue of small-world effect observed in real-world transportation networks, where the nodes are embeded in a hree-dimensional space. Using the multidimensional scaling method, we demonstrate how the addition of a few long-range connections can suubstantially reduce the travel time in transportation systems. Also, we investigated the importance of long-range connections when the systems are under an attack process. Our findings are illustrated for two real-world systems, namely the London urban network (streets and underground) and the US highways network enhanced by some of the main US airlines routes.
Costa Luciano da F.
Viana Matheus P.
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