IEEE Circuits and Systems Magazine - Q4 2019 - 60

logical layer is the real-world traffic flow layer and
the physical layer is the topological representation based on space-of-changes, space-of-stations
and space-of-stops. A node load was estimated
based on the weighted combination of four load
estimators, namely, node degree, betweenness, restricted betweenness, and simple load (origin-destination pair), assuming the combined estimation
would aid in revealing some hidden network information which only degraded the performance of
the best involved estimator (simple load). Moreover, Kurant and Thiran [15] also acknowledged
the fact that only the OD-pair information would
not suffice to carry out node load estimation without additional information like the traffic pattern.
ii) A rare but insightful attempt was made by Haznagy
et al. [12] to apply the page ranking concept in a PTN
analysis. The public transport stops are ranked, in a

Nodes With High Centrality Values (Topologically)
22.6

Latitude

22.5
22.4
22.3
22.2
22.1
113.8

114

114.2
Longitude
(a)

114.4

114.6

Nodes With High Centrality Values (Real-World Usage)
22.6

Latitude

22.5
22.4
22.3
22.2
22.1
113.8

114

114.2
Longitude
(b)

114.4

114.6

Figure 7. Hong Kong bus transport network with highly central nodes evaluated using (a) different centrality measures;
and (b) static demand estimation method (nodes with high
centrality or high node weight are the nodes with the normalized value greater than or equal to 0.8.)
60

IEEE CIRCUITS AND SYSTEMS MAGAZINE

similar manner as in web page ranking in a search
engine demonstrated earlier by Larry Page [64]. The
idea behind evaluating the pagerank is to identify
the key nodes in the network that have significant
impact in analyzing the transport efficiency.
iii) Spatial embedding networks (SENs) have been introduced by Yang et al. [10] to demonstrate the effectiveness in capturing the topological properties
alongside with the underlying spatial characteristics of a network. It has been demonstrated that,
considering the underlying geographical feature is
as important as considering the network topology
in PTN analysis. A concept of extended space (ES)
model was adopted to represent the L-space (ESL),
P-space (ESP) and networks with SSPs (ESW) representation. A flexible transfer algorithm using the
extended model was also proposed to evaluate the
cost of a transfer plan (cd) taking into account factors like transfer time, walking distance, and distance to taking buses. Such analysis has practical
significance as it provides the passengers a list of
top minimum cost transfer path routes.
iv) A simple network evolution model using a quasicontinuous approximation model was proposed
by Chen et al. [23]. In their work, the number of bus
routes a stop joins, R, and the bus stop's degree,
k, are the key parameters. Based primarily on the
preferential attachment, a simple BTN model was
organized by adding one new route at a time. It
was demonstrated empirically that a strong linear correlation exists between R and k, and this
formed the basis for the evolution model [23].
v) A new P-space representation that considers the
uplink and downlink routes separately for the bus
routes in Harbin (a northeastern Chinese city) was
proposed by Feng et al. [26]. Essentially, the representation introduced a duplication factor DFRl which
is the ratio of repeated stations to unique stations
for a given route Rl This parameter provides practical useful information about the bus route's spatial
availability, and DFRl was found to exceed 36%. In
the new representation, the adjacency matrix element aij is assigned a value 1 if the node is a part of
both uplink and downlink routes, and 0.5 if the node
is a part of either uplink or downlink route. This representation readily captures the richness of a node
in terms of the degree, weighted degree, average
shortest path length, and node weight (weighted degree/degree). The basis for evaluating the richness
parameter is the so-called rich-club phenomenon,
i.e., the correlation probability of nodes having high
richness parameter (hub nodes). An exponential
distribution was observed by probing the rich-club
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IEEE Circuits and Systems Magazine - Q4 2019

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