Information Technology Reference
In-Depth Information
Fig. 9.3 An example small
network. Nodes are agents.
Solid lines are solid
connections. Dashed lines are
weaker connections
7
13
6
14
Mathematically, this problem is well defined. The answer is the maximum
length of a path between every pair of nodes in a network. A more complete
answer is the distribution of path lengths, that is, what are all the paths lengths for
the network. Some networks, linearly connected, would have the longest average.
These would be like telegraph stations in the old west. Networks that are com-
pletely connected, where every node knows every other node, like a grade school
classroom, would have a maximum length of 1. Unconnected nodes would have
either an undefined answer or infinity as their path length. If you were looking at
this in a more applied context, you might also examine the cost of the links (e.g.,
the distance between people, and how much information can pass between them).
This question has been studied a few times, and the answers are less clear for
people in more interesting situations. Milgram ( 1967 ) performed the first experi-
ment. In this experiment he handed out a folder to be sent to someone the initiating
agent did not know. He recorded how many people the folder passed through
before it reached the target. The results were reported as between two and ten, with
five as the median. The study, while intriguing, is deeply flawed. Most of the
folders were not successfully returned, but we do not really know why. It could be
that the world is large, or that the subjects were not motivated or the task was too
hard. The minimum was not six, but ten, and it was a distribution. Numerous
attempts have been made to duplicate this work. Later work with the real world
(e.g., Travers and Milgram 1969 ) and with email (e.g., Dodds et al. 2003 ) has had
the same problems, that of not having every package delivered (sometimes around
1%). On the other hand, work with closed worlds—for example, how well sci-
entific authors are connected—does not find a minimum, because there are lots of
unconnected nodes that only publish one paper. The averages, however, seem to
suggest that those that are connected are not so far apart.
What does this mean for system design? It suggests that providing referrals can
be worthwhile but not guaranteed. It suggests that most—but probably not all—
people are well connected, that pairs of people who are long strings of connections
apart are somewhat rare. It remains an interesting theory and empirical problem that
is difficult to study completely because of the difficulty in obtaining complete data.
The Dunbar number. Some people may only have a single connection (they
would have to have at least one connection to be part of a network), whilst others
may have lots of connections. The maximum number of connections, or the largest
degree that a node can have in a social network, is called the Dunbar number
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