IEEE Circuits and Systems Magazine - Q1 2023 - 29
The removal or malfunction of some nodes will cause greater
damages than modifying other nodes.
robustness optimization; and 4) exploring more realworld
applications.
A. Weighting the Attacks
The currently widely-used a posteriori robustness
measures assign unique weights for each single attack
in the attack sequence, assuming equal contributions
of all the remaining network functionalities to the calculation
of the overall robustness. As shown in Eq.
(1), when wNi =1/ , it means that fi
() and fj ji() ≠()
are equally important to the overall network robustness.
Although the importance of attacking nodes
i and j can be partially reflected by the different
values of fi
() and fj
many scenarios.
(), this is clearly insufficient in
Practically, the removal or malfunction of some
nodes will cause greater damages than other nodes. If
such important nodes are attacked at the very beginning,
the robustness measure should be different from
the scenario that these important nodes can be protected
until the later stages. The robustness measure can be
delicately adjusted for different applications, by setting
proper configuration of wi . Meanwhile, if important
nodes can be attacked at the beginning, more credits
should be assigned to the attack strategy; otherwise, it
means that the attack strategy is less efficient.
Moreover, the network robustness under different
attack strategies can be weighted, depending on the
specific situation and concern. Weighting values can
be added into Eq. (16), where its current form implies
Table 4.
Robustness ranks of the 6 undirected 4-node networks, using 4 a posteriori measures and 10 a priori measures.
Undirected 4-Node
Networks
FUL
R1 (Eq.(2))
R15 (Eq.(22))
R3 (Eq.(6))
R7 (Eq.(12))
R1 (Eq.(2))
R15 (Eq.(22))
R3 (Eq.(6))
R7 (Eq.(12))
R1 (Eq.(2))
R15 (Eq.(22))
R3 (Eq.(6))
R7 (Eq.(12))
EFF
NB
EB
CC
AS-SR
AS-SG
AS-NC
LS-AC
LS-NS
LS-ER
FIRST QUARTER 2023
1
1
1
1
1
1
1
1
1
1
1.5
1
1
1
1
1
1
1
1
1
1
1
LOP
2
2
4
2
2
2
4
2
2.5
2.5
4
2
2.5
2.5
2.5
4.5
3
2
3
2
2.5
2
STR
4.5
4.5
5
4
5
5
5
5
5
5
5
5
4
4
4
4.5
4
4
4
3.5
4.5
4
CTS
3
3
2
3
3.5
3.5
2.5
3.5
2.5
2.5
1.5
3
2.5
2.5
2.5
2
2
3
2
3.5
2.5
3
CHA
4.5
4.5
3
5
3.5
3.5
2.5
3.5
4
4
3
4
5
5
5
4.5
5
5
5
5
4.5
5
6
6
6
6
6
6
6
6
6
6
6
6
6
NA
NA
4.5
6
6
6
6
6
NA
IEEE CIRCUITS AND SYSTEMS MAGAZINE
29
ISO
A Priori Measures
MBTA
A Posteriori Measures
MDTA
EXA
IEEE Circuits and Systems Magazine - Q1 2023
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