Urban Heartbeats (Daily Cycle of Public Transport Intensity) - Geoinformatics for Intelligent Transportation - page 197

the small-world behaviors existed in that system. In another study Sen et al. [ 18 ]
found that India s railway network exhibited small-world properties and predicted

that railway networks in other countries would also exhibit small world properties.
Similar properties were reported by Seaton and Hackett [ 11 ] who calculated the
clustering coef

'

cient, path length and average degree vertex of the rail systems in
Boston, US and Vienna, Austria.
Also, Musso and Vuchic [ 19 ], Vuchic and Musso [ 20 ] focused on evolution and
characteristics of subway networks. Derrible [ 21 ] was interested in network cen-
trality of 28 worldwide metro systems, where he studied the emergence of global
trends in the evolution of centrality with network size and examine several indi-
vidual systems in more detail. Sienkiewicz and Holyst [ 22 ] have analyzed the bus
and tram networks of Polish cities finding that some systems appeared to show a

scale-free behavior, with scaling factors. A very similar analysis was offered by Xu
et al. [ 12 ] focusing the complexity of several bus networks in China.
However, as far as the bus, subway, or tram sub-networks are not closed sys-
tems, the inclusion of additional sub-networks has signi

cant impact on the overall
network properties as has been shown for the subway and bus networks of Boston
[ 13 , 14 ]. Latora and Marchiori [ 13 ] introduced the related concept of ef

ciency,
which measures how easily information is exchanged over the network. They
showed that small-world networks are highly ef cient. Soh et al. [ 16 ] examined

Singapore public transportation system where they focused on the degree, strength,
clustering, assortativity and eigenvector centrality characteristics of the transpor-
tation networks.
Lu and Shi [ 23 ] analyzed the public transport networks in three Chinese cities
and they found that the public transportation networks have the characteristics of
complex networks. In addition, the urban transportation network parameters all
signi

cantly affect the accessibility, convenience, and terrorist security capability of
the urban public transportation network. Von Ferber et al. [ 15 , 24 ] used complex
network concepts to analyze the statistical properties of public transport networks of
several large cities, looking at all technologies and accounting for the overlapping
property of transit systems, notably

finding a harness effect. They also attempted to
model system based on number of stations and lines.
On the other site we do not register many authors who deal with evolving
transport networks, especially public transport networks. Albert and Barab si [ 3 ]

brought fundamentals of evolving networks. If new nodes and edges appear while
some old ones disappear, we can talk about evolving networks. The Barab

á

á si -

-

Albert model was the first model to derive the network topology from the way the

network was constructed with nodes and links being added over time. From there
they were derived many other evolving network models. Evolution models are
often used primarily to study social networks for instance Snijders et al. [ 25 ], Xu
and Hero [ 26 ]. Nevertheless we register some examples. Zi-You and Ke-Ping [ 27 ]
investigated the emergence of scale-free behavior in a traf c system by using the

NaSch model to simulate the evolution of traf flow. Xie and Levinson [ 28 ]

describe generally evolving transportation networks. In this publication they tried to
understand the process of network growth by identifying and quantifying its

c fl