Information Technology Reference
In-Depth Information
It is worth stressing that there exists another proposal regarding how to create a scale-
free network with
3[
29
]. The authors of that model propose that the number of new
links arriving is a fluctuating rather than a fixed quantity.
α<
6.2.3
Web failures
We have all experienced failure in grades, in sporting events, or in our love life.
This is part of the unpredictability of the world's complex social webs and how we
humans interact with and within them. These setbacks are part of what we learn as
we grow older; love is lost when our overtures no longer match the needs of the
pursued and tests are blotched when the interests of the professor are not taken into
account during preparation. These losses are devastating when they occur, but they
rarely have long-term negative effects, and they prepare youth for the challenges of
future responsibility. Of course, there are more elaborate social networks in which
failure has more dire outcomes than a bruised ego, such as failure due to attacks
on computer networks by malicious hackers and on social organizations by terror-
ists. The latter can unravel the very fabric of society, unless thoughtful people can
determine how complex webs respond to attacks or even to unintentional forms of
failure.
We discussed failure and survival previously in a manufacturing context and learned
that the probability of failure of a given fraction of a large number of manufactured
widgets is given by an exponential. A single parameter characterized the fraction of
widgets lost and that was the constant rate of failure during the manufacturing process.
In this simple manufacturing model the exponential predicts that the same fraction of
widgets fail in every equal interval of time. Knowing this failure pattern enables the
industrialist to plan for the future. Why do simple networks respond to failure in this
way and how are complex networks different?
There are two general classifications of internally generated failure, namely failure
that is local in space and time, and failure that is catastrophic. Local failure can be
the loss of a single circuit in a large switching network that has essentially no effect
on the functioning of the web. Catastrophic failure spreads over vast physical regions
such as the failure of the power grid we discussed earlier and/or extends over long
times such as an economic depression. The extent of web damage caused by failure is
a consequence of how the elements of the web are interconnected. A random web has
all the nodes more or less connected so that the loss of any particular node causes the
same damage as the loss of any other node. On the other hand, in a scale-free network
the connectivity of the nodes can be quite different, so the aggregated damage due to
failure of a particular node depends on the properties of that node. Not all nodes are
equal.
Another kind of failure is caused by external disruption, whether it is the human body
or a computer web being invaded by viruses, or social/political organizations being
attacked by terrorists. We want to know how robust the biological or social web is
with respect to such disruption. One measure of the degree of breakdown of the web is
the loss of ability to support and transport information. Put somewhat differently, the
