IEEE Circuits and Systems Magazine - Q1 2023 - 25

Figure 5. Network robustness in terms of the number of connected components (nNCC), controllability (nD), connectivity (nL), and
communication ability (nCM), together with the threshold of destruction T. Here, δ represents the portion of nodes removed from
the network. Node MDTA is implemented.
Figure 6. Network robustness in terms of the number of connected components (nNCC), controllability (nD), connectivity (nL), and
communication ability (nCM), together with the threshold of destruction T. Here, δ represents the portion of edges removed from
the network. Edge MBTA is implemented.
consistently later than the turning points of these
curves. This means that, under node MDTA, Eq. (21)
suggests a good threshold for the network destruction
in terms of controllability robustness, but not for
connectivity and communication robustness. In contrast,
as shown in Fig. 6, the vertical green lines match
the turning points of the connectivity and communication
curves better than the controllability curves.
This implies that, under edge MBTA, Eq. (21) suggests
a good threshold for connectivity and communication
robustness, but not for the controllability robustness.
FIRST QUARTER 2023
This means that there is no turning point in the controllability
curve under edge MBTA; the turning point
only appears under node MDTA.
Table 2 shows the comparison of robustness performance
under two measure schemes, namely the complete
disconnection (CD) scheme as described by Eq.
(1) and the thresholdbased disconnection (TD) scheme
as described by Eq. (20). In the table, the numbers in
parentheses represent the corresponding ranks of
robustness. It is clear that, under different schemes,
the robustness performance can be measured very
IEEE CIRCUITS AND SYSTEMS MAGAZINE
25

IEEE Circuits and Systems Magazine - Q1 2023

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