IEEE Circuits and Systems Magazine - Q4 2019 - 42

with respect to the locations of public transport stops
or routes, missing information in the sequence of stops
along a route, allocation of multiple id's to a specific stop
or route, missing information on the geographical location of a few stops, etc.
Step 2: Process the crude data obtained in Step 1
to permit further analysis. This involves the following procedure:
i) Since PTNs belong to the category of spatial networks,
understanding the topological behavior along with
spatial information will facilitate better network
analysis. The spatial information of public transport
stops listed in the datasets are either easting-northing or latitude-longitude. However, since many of
the network visualization tools adopts latitude and
longitude information for displaying the spatial locations of the stations, it is useful to convert easting
and northing data to latitude and longitude using
tools like ArcGIS [8]. Before the conversion, a suitable global coordinate system (e.g., WGS84) should
be chosen based on the information about local
coordinate systems (e.g., OSGB36 for London and
HK1980 for Hong Kong) provided by the local survey departments [9].
ii) In some datasets, the numbers assigned for the
stops are typically non-sequential in nature, posing
computational challenges to analysis, e.g., in generating adjacency matrix as discussed in Step 3. Thus,
it is necessary to map the list of id's (both routes

and stops) extracted from the database with sequentially mapped numbers. This mapping of
original stop id's with sequentially mapped id's
makes it less arduous to further process the data.
iii) The concept of short distance station pairs (SSPs)
has been commonly adopted to represent a group
of stations as a single (merged) station [10]-[12].
Assigning new id's to such SSPs according to
the sequential mapping carried out in Step 2 is
recommended to facilitate identification of SSPs
in a network. The clustering of multiple stations
into one station can be based on geographical
closeness, similar names for nearby stations, stations within a specific walkable catchment, etc.
Although different terminologies have been used,
the essential idea of SSPs has been reported in
several sources [10], [11], [13]. The idea behind
identifying SSPs is to establish a virtual connectivity among the nodes, especially when a large
number of SSPs are observed in the network [10],
[13]. However, as discussed in ref. [13], when combining multiple nodes as a single node based on
their geographical closeness, the actual definition of geographical closeness is always a matter
of choice. A distance threshold ^d th h is needed to
define the closeness of two nodes and can be chosen judiciously by observing the distribution pattern of geographical distances between successive stations (d ij) in a network. However, it should

Table I.
Graph type and space of representation used in various PTN analyses.
Directed

Undirected

Weighted

Unweighted

References

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[15] [16] [17]

Bus Transport Network
L-space

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[11] [18]
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*

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[12] [19]
[20] [21]
[10] [13] [22]

P-space

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*

*

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[16] [17] [23]

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*

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*

[10] [20] [22] [26]

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*

*

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[17]

*

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*

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[27]

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[28] [29]
[30] [31]

[18] [24] [25]
C-space

Metro Transport Network
L-space

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✓

*

[32]
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IEEE CIRCUITS AND SYSTEMS MAGAZINE

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[33] [34] [35]

FOURTH QUARTER 2019
IEEE Circuits and Systems Magazine - Q4 2019

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