MAE 298, Lecture 4
Jan. 16, 2008
We are living in a connected world.
Networks permeate every aspect of
our lives. Our consciousness is based
on the network of neurons in our brain. Our
society is formed by various social, economi-
cal and political networks. The Internet,
which is profoundly changing the way we
live, is nothing but a network of information
resources. Our overall well-being depends to
a large extent on the stability and health of
many networks. Yet we live in a constantly
changing and often hostile environment. It
is therefore important to understand how
robustly these networks respond to disrup-
tions. On page 378 of this issue, Albert, Jeong
and Barabási1address this problem in a
simple and elegant way. They find that the
tolerance of networks to different types of
perturbation depends critically on the net-
work structure.
Given a set of nodes and links, a simple
network can be built by linking pairs of
nodes at random until we use up all the
available links2. Such a random network
belongs to the class of ‘exponential net-
works’ because each node has roughly the
same number of connections (it is statis-
tically homogeneous) and the frequency
of highly connected nodes decreases expo-
nentially. But most naturally occurring
networks have much more intricate hierar-
chical structures; for example, the frequency
of highly connected nodes often decays as a
simple power law. Power laws are found in
many areas, from the distribution of popu-
lation sizes to the frequency of scientific
citations. Networks that follow power laws
are called ‘scale-free networks’ because they
are not tied to a specific scale. This means
they are extremely inhomogeneous: where-
as most nodes have one or two links, a few
highly connected nodes will have a large
number of links and so play a key role in the
behaviour of the network.
Albert and co-workers1wisely simplify
their study of network tolerance by focusing
on these two classes of network structure: the
random, exponential network and the self-
organized, scale-free network. To measure
the quantitative performance of a network,
the authors use the average distance between
two nodes in the network, where distance is
defined by the minimum number of links
between these two nodes. The authors also
consider two types of destructive perturba-
tion: randomly occurring error, which is due
to random malfunction of the nodes; and
an intentional attack, which is aimed at the
most connected nodes.
For an exponential network, Albert and
co-workers find that the accumulation of
random errors has a deteriorating effect on
the network performance. This decrease in
network performance occurs because each
deletion of a node destroys some local
paths, which leads to an increase in the dis-
tance between the nodes involved in these
paths. The above argument seems quite
reasonable and general. But in the case of a
scale-free network, Albert and co-workers
make a surprising discovery: they find that
the performance of the scale-free network
is almost unchanged by the random removal
of nodes up to a large deletion rate.
The immunity of this network’s perfor-
mance to random error suggests two features
about the network structure: first, most of
the nodes are just ‘end users’, the removal
of which does not affect the paths between
other nodes; second, there are ‘degenerate
paths’ between nodes, which implies the
existence of highly connected nodes. These
two competing requirements have apparent-
ly found the perfect balance in the scale-free
network. Further study is needed to under-
stand this network’s immunity to random
error — one can only speculate that the
reason lies deep in the scale-free nature of
the network structure.
However, the structure that makes the
scale-free network superior to the exponen-
tial network in the case of random error
becomes its Achilles’ heel under hostile
attack. The most effective way of destroying
a network is to attack its most connected
nodes. For the scale-free network, in which
there are nodes of high connectivity, the
effect of targeted attack is much more severe
NATURE
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VOL 406
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27 JULY 2000
|
www.nature.com 353
news and views
How robust is the Internet?
Yuhai Tu
Figure 1 What does the Internet look like? No map exists of the entire Internet, but these lines show
the paths an e-mail might take across some of the largest networks. The lines branch at each network
router, or node, along the way. Colours were assigned according to the geographic domain (for
example, .se for Sweden) where each network router was registered. The map was created using the
skitter tool (developed by D. McRobb at CAIDA)7, which sends out small packets of data from a
source to many destinations through the Internet. The data collected by skitter give a snapshot of
the Internet at a particular moment. (Graph created by B. Huffaker using graph layout code provided
by B. Cheswick and H. Burch.)
CAIDA
Switzerland
Germany
Spain
Italy
Japan
Netherlands
Russian
Federation
Sweden
UK
USA
Unknown
Complex systems, such as the Internet, are surprisingly resistant to random
errors. But a new study warns against complacency — the feature that
makes the Internet immune to accidents also makes it vulnerable to attack.
© 2000 Macmillan Magazines Ltd
“Exploring network robustness”
