Robustness Analysis of City Road Network at Different Granularities - Space-Time Integration in Geography and GIScience - page 135

the information provided by L is useless to the entire network. Different from L and
S , the change of C shows significant differences between different attack strategies.
The changes of C under random attacks display a minor decrease while changes of
C under degree based attacks display a remarkable decrease and changes of C under
betweenness based attacks display a noticeable increase. This proves that different
attack strategies targets to road with different importance and cause various damages
to the network. The third stage contains the final changes of the network. Although
the network is not totally destroyed, it has malfunctioned and become valueless to
this research.
The inflections to divide the stages occur at different removal rate of nodes. The
shorter the first stage is, the faster the network becomes malfunction. Compare with
the three attack strategies, we can find out that all dual graphs are robustness to
random attacks but vulnerable to intentional attacks especially betweenness based
attacks. According to the red points in Fig. 8.6 , the network only malfunctions
once more than 50 % of the nodes are removed. However, degree-based attacks
are more dangerous, especially to local efficiency. According to the green points,
although removal of nearly 20 % of the nodes will cause fragmentation, local traffic
in the attacked area will soon become paralyzed. As blue points show, attacks on
nodes with high betweenness cause the network to split after only several nodes
are removed. This is because the attack strategy targets on nodes with a high
betweenness, such as bridges or cloverleaf junctions in the city. These nodes hold
the whole network together, and when they are removed the city will separate into
several parts. Local efficiency under betweenness attack increases with the removal
of high betweenness nodes.
Comparing the results of the three types of dual graphs under attacks, we
can see some structure differences and how the differences affect the network
vulnerability under attack. In Fig. 8.6 a-c, the green points referring to network
performances under degree based attacks are similar with red points referring to
network performances under random attacks. This means the network represented
by segment-based dual graph lacks of sensitivity under degree based attack. Stroke-
based network performances under attacks are shown in Fig. 8.6 d-f. Unlike other
two dual graphs, the first stage in successive intentional attacks is so short that
is difficult to observe. This finding indicates that the network represented by
stroke-based dual graph splits at the very beginning of the attack procedure. Thus
robustness of stroke-based dual graph is tolerant under random attacks yet fragile
under target attacks including degree based attacks as well as betweenness based
attack. Community based dual graph under attacks in Fig. 8.6 g-i shows a clear
three stage procedure and sensitive to both intentional attacks. It implies that
community-based network can capture the structural diversity from the modular
perspective of the road network. The structural diversity makes the community-
based city road network sensitive to intentional attacks than the other two models
of road network and provides a more reliable robustness evaluation of network
structure.