IEEE Circuits and Systems Magazine - Q4 2019 - 52
the scale-free behavior for three cities, and it was very interesting to observe that the Hong Kong network plausibly
exhibited the scale-free property with the supernode representation, as shown in Fig. 2. In other words, a slight modification in the topological representation permitted the
exposition of an important network property which otherwise was undetected under conventional graph representation. Therefore, the effect of supernodes in analyzing the
public transport networks should not be overlooked.
Finally, it is very interesting to observe the scalefree property (sometimes called the 80/20 rule) in public transport networks. This demonstrates the fact a
myriad number of stops carry 20% of the network load,
and a countable number of stops carry 80% of the load.
Public transport networks having such a property are
free of any scaling applied to them. The mechanism of
passenger flow in a scale-free network is an important
research topic from the perspective of a transport engineer, similar to the study of information spread or
disease spreading by network engineers and biologists.
Another core research area of practical importance is
robustness analysis which aims to study the network
functionality upon removal of a certain set of target
nodes. It has been shown that scale-free networks are
more prone to targeted attacks, in contrary to random
networks which end up merely at network fragmentation on targeted attacks.
C. Network Cohesiveness
The extent to which the immediate neighbors of a node
are connected to each other is examined through a property called clustering, which defines the level of cohesiveness
in a network. Clustering, also known as the transitivity,
is a local property dealing with node level information
in network theory. The cohesiveness of nodes is evaluated at local level through a parameter called local clustering coefficient, which is given by
/ a ij a ih a jh
Ci =
/ / (a ij + a ji) (a jh + a hj) (a hi + a ih)
Ci =
2 [k i (k i - 1) - 2k i)]
;
(8)
100
Empirical Value
Estimated Value
10-1
Pr (K ≥ Kmin)
Pr (K ≥ Kmin)
h
i!j
10-2
10-2
10-3
10-3
101
(K)
10-4 0
10
102
101
(K)
102
100
100
Empirical Value
Estimated Value
Empirical Value
Estimated Value
10-1
Pr (K ≥ Kmin)
10-1
Pr (K ≥ Kmin)
j
k i) = / a ij a ji
Empirical Value
Estimated Value
10-1
10-2
10-2
10-3
10-3
10-4 0
10
(7)
k i (k i - 1)
for undirected networks, and
100
10-4 0
10
j, h
101
(K)
(a)
102
10-4 0
10
101
(K)
102
(b)
Figure 2. Power law fit for (a) in-degree distribution; (b) out-degree distribution under regular (upper) and supernode (lower) representations.
52
IEEE CIRCUITS AND SYSTEMS MAGAZINE
FOURTH QUARTER 2019
IEEE Circuits and Systems Magazine - Q4 2019
Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q4 2019
Contents
IEEE Circuits and Systems Magazine - Q4 2019 - Cover1
IEEE Circuits and Systems Magazine - Q4 2019 - Cover2
IEEE Circuits and Systems Magazine - Q4 2019 - 1
IEEE Circuits and Systems Magazine - Q4 2019 - Contents
IEEE Circuits and Systems Magazine - Q4 2019 - 3
IEEE Circuits and Systems Magazine - Q4 2019 - 4
IEEE Circuits and Systems Magazine - Q4 2019 - 5
IEEE Circuits and Systems Magazine - Q4 2019 - 6
IEEE Circuits and Systems Magazine - Q4 2019 - 7
IEEE Circuits and Systems Magazine - Q4 2019 - 8
IEEE Circuits and Systems Magazine - Q4 2019 - 9
IEEE Circuits and Systems Magazine - Q4 2019 - 10
IEEE Circuits and Systems Magazine - Q4 2019 - 11
IEEE Circuits and Systems Magazine - Q4 2019 - 12
IEEE Circuits and Systems Magazine - Q4 2019 - 13
IEEE Circuits and Systems Magazine - Q4 2019 - 14
IEEE Circuits and Systems Magazine - Q4 2019 - 15
IEEE Circuits and Systems Magazine - Q4 2019 - 16
IEEE Circuits and Systems Magazine - Q4 2019 - 17
IEEE Circuits and Systems Magazine - Q4 2019 - 18
IEEE Circuits and Systems Magazine - Q4 2019 - 19
IEEE Circuits and Systems Magazine - Q4 2019 - 20
IEEE Circuits and Systems Magazine - Q4 2019 - 21
IEEE Circuits and Systems Magazine - Q4 2019 - 22
IEEE Circuits and Systems Magazine - Q4 2019 - 23
IEEE Circuits and Systems Magazine - Q4 2019 - 24
IEEE Circuits and Systems Magazine - Q4 2019 - 25
IEEE Circuits and Systems Magazine - Q4 2019 - 26
IEEE Circuits and Systems Magazine - Q4 2019 - 27
IEEE Circuits and Systems Magazine - Q4 2019 - 28
IEEE Circuits and Systems Magazine - Q4 2019 - 29
IEEE Circuits and Systems Magazine - Q4 2019 - 30
IEEE Circuits and Systems Magazine - Q4 2019 - 31
IEEE Circuits and Systems Magazine - Q4 2019 - 32
IEEE Circuits and Systems Magazine - Q4 2019 - 33
IEEE Circuits and Systems Magazine - Q4 2019 - 34
IEEE Circuits and Systems Magazine - Q4 2019 - 35
IEEE Circuits and Systems Magazine - Q4 2019 - 36
IEEE Circuits and Systems Magazine - Q4 2019 - 37
IEEE Circuits and Systems Magazine - Q4 2019 - 38
IEEE Circuits and Systems Magazine - Q4 2019 - 39
IEEE Circuits and Systems Magazine - Q4 2019 - 40
IEEE Circuits and Systems Magazine - Q4 2019 - 41
IEEE Circuits and Systems Magazine - Q4 2019 - 42
IEEE Circuits and Systems Magazine - Q4 2019 - 43
IEEE Circuits and Systems Magazine - Q4 2019 - 44
IEEE Circuits and Systems Magazine - Q4 2019 - 45
IEEE Circuits and Systems Magazine - Q4 2019 - 46
IEEE Circuits and Systems Magazine - Q4 2019 - 47
IEEE Circuits and Systems Magazine - Q4 2019 - 48
IEEE Circuits and Systems Magazine - Q4 2019 - 49
IEEE Circuits and Systems Magazine - Q4 2019 - 50
IEEE Circuits and Systems Magazine - Q4 2019 - 51
IEEE Circuits and Systems Magazine - Q4 2019 - 52
IEEE Circuits and Systems Magazine - Q4 2019 - 53
IEEE Circuits and Systems Magazine - Q4 2019 - 54
IEEE Circuits and Systems Magazine - Q4 2019 - 55
IEEE Circuits and Systems Magazine - Q4 2019 - 56
IEEE Circuits and Systems Magazine - Q4 2019 - 57
IEEE Circuits and Systems Magazine - Q4 2019 - 58
IEEE Circuits and Systems Magazine - Q4 2019 - 59
IEEE Circuits and Systems Magazine - Q4 2019 - 60
IEEE Circuits and Systems Magazine - Q4 2019 - 61
IEEE Circuits and Systems Magazine - Q4 2019 - 62
IEEE Circuits and Systems Magazine - Q4 2019 - 63
IEEE Circuits and Systems Magazine - Q4 2019 - 64
IEEE Circuits and Systems Magazine - Q4 2019 - 65
IEEE Circuits and Systems Magazine - Q4 2019 - 66
IEEE Circuits and Systems Magazine - Q4 2019 - 67
IEEE Circuits and Systems Magazine - Q4 2019 - 68
IEEE Circuits and Systems Magazine - Q4 2019 - Cover3
IEEE Circuits and Systems Magazine - Q4 2019 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021Q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q1
https://www.nxtbookmedia.com