Information Technology Reference
In-Depth Information
The web proposed by the authors of [
11
] with
α
≈
1 is expected to generate the
smallest size possible (
L
=
2). Figure
6.24
illustrates the relation between
α
and
L
in
these various domains.
6.4
Reflections
In this section we considered whether there exists a connection between the topology
of the web and its efficiency. The
small-world experiment
by Milgram [
24
,
32
] sug-
gested that the structure of a social network is such as to make it very efficient for
the transport of information. In the experiment, Milgram sent several packages to 160
random people living in Omaha, Nebraska, asking them to forward the package to a
friend or acquaintance whom they thought would bring the package closer to a partic-
ular final individual, a stockbroker in Boston, Massachusetts. The letter included this
specific condition: “If you do not know the target person on a personal basis, do not try
to contact him directly. Instead, mail this folder to a personal acquaintance who is more
likely than you to know the target person.” The outcome of the experiment revealed
that, without any global network knowledge, letters reached the target recipient using,
on average, 5
2 intermediate people, demonstrating that social acquaintance networks
were indeed small worlds.
Here we point out that the scale-free structure may be hidden and that finding the
shortest path connecting two generic sites,
i
and
j
, may require a special algorithm.
After all, from [
32
] we learn that the participants were given, in addition to his name and
address with the prescription of not sending the letter directly to the target (or of doing
that only if the participant knew the target), his occupation and place of employment,
his college and year of graduation, his military service dates, and his wife's maiden
name and hometown. Then the participants were asked to make sure that each of the
following recipients of the letter recorded their name. This was to prevent looping. If
we activate random walkers of the same kind as those described earlier, the instruc-
tion of not visiting nodes that have already been explored, except for the purpose of
avoiding localization, is probably easy to implement. The choice of the nodes, on the
basis of their social condition, is, on the contrary, something much more difficult to
assign to the random walker, being closely connected to what we define as human
intelligence. Anyway, this experiment certainly established that a given social web is
complex.
There are many open questions. What
.
is the relation between the topological
efficiency and the dynamical efficiency?
In the last chapter we discussed dynamical efficiency, with a special focus on the issue
of social consensus. Here we limit ourselves to noticing that both random and com-
plex webs have a small length, but the random webs have small clustering coefficients,
whereas the real webs have large clustering coefficients. We think that this fact can be
explained by our conjecture that the topology of a real web is created so as to facilitate
global consensus. In fact, the large clustering corresponds to communities of strongly
interacting individuals, who debate issues and eventually reach local consensus. The
