Intentional Attacks on Complex Network
Speaker: Shin-Ming Cheng
Advisor: Kwang-Cheng Chen
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Outline
 Introduction
 Intentional attack
- Cascade-based attack
- Analytical model
- Numerical result
 Attack with global information
 Attack with local information
 Conclusion
 Reference
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Introduction
 Intentional attack
- Is an attack that aim at bringing down network nodes in decreasing order of nodal
degrees
 Whether the fragility indeed exists in Internet?
- Doyle and his colleagues [1] argued that, as a result of careful design for maximizing
network throughput, the hub nodes at the router level are typically the edge nodes
with a large number of low-capacity connections.
- The removal of these hub nodes, though disastrous to the large number of lowcapacity users connected to them, will not bring down the Internet
 Is the retrieval of global information in Internet possible?
- Internet is too large for anyone to obtain their global topology information, which
means an accurate, intentional attack is hardly feasible.
- Distributed attack by using local information
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Traditional Intentional attack
 Cascading Failures on Power Transmission Grid Systems
- Each node deals with a load of power
- Removal of nodes can cause redistribution of loads over all network
- A cascade of overloading failure is triggered.
- On August 10, 1996, a 1300-mw electrical line in southern Oregon sagged in the summer heat
resulting in break-up into four islands, with loss of 30,390 MW of load affecting 7.49 million
customers in western North America [2]
- On August 14, 2003, an initial disturbance in Ohio triggered the largest blackout in the U.S.’s
history in which millions of people remained without electricity for as long as 15 hours
 Cascading Failures on Internet
- Traffic is rerouted to bypass malfunctioning routers
- Eventually leading to an avalanche of overloads on other routers that are not
equipped to handle extra traffic.
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Input Parameters and Output Measure
 The load at node i is defined as the total number of shortest paths
passing through this node.
 The capacity of a node is the maximum load that the node can handle.
 The capacity Ci of node i is proportional to its initial load Li
- Ci  (1   ) Li
- where the constant 
 0 is the tolerance parameter.
 The removal of nodes in general changes the distribution of shortest
paths.
 Cascading failures can be conveniently quantified by the relative size of
the largest connected component
- G  N' / N
- where N and N’ are the numbers of nodes in the largest component before and after
the cascade, respectively.
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Before the attack
 Degree distribution: P(k )  ak 
 Load distribution: L(k )  bk 
- where k is the degree variable, and a and b are positive constants.
 Thus, we have

kmax
1
P(k )dk  N

k max
1
P(k ) L(k )dk  S
- where kmax is the largest degree in the network and S is the total load of the network.
 Then we have a 
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(1   ) N
S
,
and
, where       1
1
b


(k max  1)
a (1  k max )
6
After the attack
 Degree distribution: P' (k )  a' k  '
 Load distribution: L' (k )  b' k  '
 Since only a small fraction of nodes are removed from the network, we
assume that P' (k )  a' k  and L' (k )  b' k 
 Then a' 
(1   ) N
S '
b
'

, and
1
(k max'
 1)
a' (1  k max' )  
 For the node with k links, the difference in load before and after the
attack can be written as L(k )  (b'b)k   [(b' / b)  1]L(k )
 The maximum load increase that the nodes can handle is C (k )  L(k ) L(k )
 Thus, the nodes still function if   [(b' / b)  1]
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 The critical value of the tolerance parameter
1

 k max'
 1  1  k max'
b'

ac   1   1

b
k

1
1

k
max
 max


 1  k max'
 

 1  k max
 S ' 
   1
 S 
 S ' 
 S' 


   1  1  (k max
 k max'
)   1
S
 S 



 k      S ' 

 max   1    1
 1  k max'
 k max' 
  S 

 When N   (i.e., infinite scale-free network),
-  c  0 , which indicates that the network cannot be brought down by a single attack
if   0
 For a finite size network

- k max'
 0 , thus  c  0 , suggesting that breakdown can occur for    c
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Numerical Results
Cascading failure in scale-free networks
 In the case of the removal of the node with the highest degree,  c  0.1
 This phase transition phenomenon seems to be robust for different
sizes of network
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Numerical Results
Cascading failure in scale-free networks
 Removal of a single node chosen
- at random (squares), or among those with largest degrees (asterisks), or highest loads
(circles)
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Numerical Results
Cascading failure in homogeneous networks
 All nodes are set to have the same degree k=3 and N=5000
 In the inset, k≥2, γ=3, and N=5000. The resulting average degree [k] ≈3.1
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Numerical Results
Robustness of the scale-free network
(a) Barabási-Albert (BA) model
(b) real-world Internet model by the NLANR Project
 Internet hubs are of very high degrees.
- The nodal degree of the biggest hub is 1458, whereas in the BA model, it is only 386.
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Numerical Results
Robustness of the scale-free network
 Greedy sequential attack:
- chooses the largest-degree, live node adjacent to the node crashed in the last step as its
next-step target.
 Coordinated attack:
- Searches through all the live nodes adjacent to any crashed node and selects among them
the largest-degree node as its next-step target.
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Conclusion
 The scale-free network has “robust yet fragile” property, whereas the
random graph is robust to both random and intentional attacks.
- Internet is vulnerable to intentional attack.
- However, a random attack does not significantly affect the network performance.
 Performance of attacks based on incomplete/inaccurate networktopology information and local information
- Incomplete information can degrade the efficiency of an intentional attack
significantly, especially if a big hub is missed.
- Distributed attacks can be highly effective, sometimes almost as efficient as an
accurate global information-based attack.
 Connection with current works?
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Reference
1. J. C. Doyle et al., “The ‘Robust Yet Fragile’ Nature of the Internet,” Proc. Nat’l. Acad.
Sci., vol. 102, no. 41, Oct. 2005, pp. 1497-1502.
2. D. N. Kosterev, C. W. Taylor, and W. A. Mittelstadt, “Model validation for the August
10, 1996 WSCC system outage,” IEEE Transactions on Power Systems, vol. 14, no. 3,
Aug 1999, pp. 967-979
3. A. E. Motter and Y.-C. Lai, “Cascade-based attacks on complex networks,” Phys. Rev. E,
vol. 66, p. 065102(R), 2002.
4. L. Zhao, K. Park, and Y.-C. Lai, “Attack vulnerability of scale-free networks due to
cascading breakdown,” Phys. Rev. E, vol. 70, p.035101(R), 2004.
5. P. Crucitti, V. Latora, and M. Marchiori, “Model for cascading failures in complex
networks,” Phys. Rev. E, vol. 69, p. 045104(R), 2004.
6. Y. Xia and D. J. Hill, “Attack Vulnerability of Complex Communication Networks,” IEEE
Transactions on Circuits and Systems, vol. 55, no. 1, Jan. 2008, pp. 65-69
7. S. Xiao, G. Xiao, and T. H. Cheng, “Tolerance of intentional attacks in complex
communication networks,” IEEE Communication Magazine, vol. 46, no. 1, Jan 2008, pp.
146-152
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