Robustness Analysis of City Road Network at Different Granularities - Space-Time Integration in Geography and GIScience - page 133

evaluate the importance of a node. Based on these analyses, we choose one random
attack strategy and two intentional attack strategies: a degree-based attack strategy
and a betweenness-based attack strategy.
After determining the attack strategies, the performances of network under attack
should be measured. Since the performances under attack are difficult to judge with
single measurement, we argue that the concept of robustness is based on two types
of performance of networks to attacks: efficiency behavior and fragmental fraction.
To provide a comprehensive perspective on the network efficiency behavior, we
evaluate the efficiency from both global and local views. The global efficiency of
urban road networks can be reflected from average path length L introduced in
formula ( 8.1 ) while clustering coefficient introduced in formula ( 8.2 )isusedto
evaluate the local efficiency. Network fragmentation is also an important property to
show the performance of city road network under attacks. We use the relative size of
the largest connected component S which is shown as a fraction of the total network
size to investigate the impact of attacks on the network structure.
Single attack targeting on certain node can only provide the network performance
when the observed node is removed. However, the robustness of the entire network
does not depend on only one node. To quantitatively measure the overall road
network robustness under pressure, we used a successive attack strategy to destroy
the network until the capacity reaches its maximum and record the network
performance during each attack.
For the random attack strategy, we randomly choose one node at each step and
delete the node and all edges linked to it from the network. The loop is performed
until the whole network collapses when S 0 where the network is isolated
into single nodes only. The performance of a network under attack, measured as
efficiency and fragmentation, is quantified at each loop to observe the reaction of
the revised network.
For the degree-based attack, we remove the node that has the highest degree at
each step, calculate the parameters L , C , S and recalculate the degree of each node.
The removal procedure is repeated until the network collapses. The betweenness-
based attack is similar, except we remove the node that has the highest betweenness
and recalculate the betweenness for each node at every loop.

8.4 Experiment Results

8.4.1 Network Performances Under Successive Attacks

In this section, we study the performances of the Beijing road network under
successive random attacks in three dual graphs. Figure 8.6 shows the changes of
L , C and S during the attacks.
In Fig. 8.6 , the x axis shows the fraction of the removal nodes while the y axis
shows the change of L , C or S . Figure 8.6 a-c show the changes of the Beijing road