IEEE Circuits and Systems Magazine - Q4 2019 - 59

J. Node and Edge Weights
In generating weighted networks, a weight (w) is either
added to a node, an edge, or both. Weighted transport
networks are still relatively less explored, despite their
obvious practical significance in quantifying the relative
importance of nodes and edges in relation to the level of
service and performance provided by a public transport
network. In this section we discuss a few weight metrics
commonly employed in the topological analysis of various public transport networks.
Node weight can be assigned to reflect the relative
importance of a node (station). For instance, a weight
can be assigned to a station or a link according to the
number of routes servicing it (degree) [12], [26], or according to the sum of weights of the adjacent edge
weights (weighted degree) [27]. Edge weight may be assigned according to the morning peak hour capacity of
the vehicles carrying the traffic [12], the minimum geographical distance between any two nodes [10], [21], the
number of overlapped bus routes between two stations
[11], [21], [27], or the number of common stops serviced
along a route in C-space [20]. Furthermore, dynamic
edge weights may also be assigned according to the average travel time between two nodes [19], which have
been found to be very useful in analyzing the dynamic
behavior of PTNs, especially in describing the varying
behavior during peak- and off-peak hours.
In our recent work [13], we proposed a static demand estimation approach to assign node weight
which reflects the demand centrality of a node, i.e.,
the capability of a node in serving the static demand
by considering the number of points of interest (POIs),
and the number of people accessing a specific station
(node occupying probability). A POI can be a hospital,
hotel, office, school, sports arena, cinema, shopping
complex or the residential apartment. The crux of this
demand estimation approach is that the real-world usage of a bus stop should be strongly dependent on the
presence of POIs around the bus stop and the number of people accessing it. Using the information on
POIs and node occupying probability (NOP), the node
weight is evaluated as
wi = c1 e

m=1

d m o + c 2 Pi + c 3 k i

V. Notable Contributions to Public
Transports Network Analysis
In this section, we discuss a few notable contributions in
the field of PTN analysis in addition to the applications
of network metrics in the study of PTN topologies.
i) The usual procedure for generating the topology of
a PTN is based on some available online dataset.
Kurant and Thiran [15] made a novel attempt to
extract real physical topology of a network by
considering the time-tables of the mass transportation systems. Despite the different terminologies adopted (space-of-changes for P-space
representation, space-of-stations for L-space representation and the other being space-of-stops
representation), the representations proposed by
Kurant and Thiran [15] are generally consistent
with the representation types discussed in Section III. Essentially, a multilayer framework had
been adopted considering the actual mapping
of logical graphs on physical graphs, where the

(22)

where wi is the weight of node i, dm is the number of POIs
of category m (emergency, recreation, education, etc.) located around node i within a radius of 100 m, Pi is the total number of passengers accessing node i, ki is the node
degree, c1, c2, and c3 are scaling factors. Certain POIs
which are equidistant to multiple stops are allocated to
the nearest node with the least distance. Fig. 6 shows the
heat map indicating the nodes serving high demand in
FOURTH QUARTER 2019

Hong Kong. In a comparison between the nodes serving
high demand areas and the nodes with high centrality
values, we notice about 60% similarity of the nodes being
compared, indicating that nodes of high topological centrality are also serving relatively higher demand areas.
However, the remaining 40% nodes, though are topologically central, are serving low demand areas. This shows
that merely considering topological features but ignoring their actual usage might lead to unrealistic conclusions, and such information is important information to
operators to carefully design and optimize the network.
Fig. 7 shows the comparison of highly central nodes versus nodes serving high demand areas. Thus, the demand
estimation method would address the practical usage of
topologically central nodes.

Figure 6. Heat map showing the nodes serving higher demand areas (red) in Hong Kong.

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IEEE Circuits and Systems Magazine - Q4 2019

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