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CHAPTER 10. MINING SOCIAL-NETWORK GRAPHS
the third edge exists is thus 9/16 = .563. This fraction is considerably greater
than the .368 expected value for that fraction. We conclude that Fig. 10.1 does
indeed exhibit the locality expected in a social network.
✷
10.1.3
Varieties of Social Networks
There are many examples of social networks other than “friends” networks.
Here, let us enumerate some of the other examples of networks that also exhibit
locality of relationships.
Telephone Networks
Here the nodes represent phone numbers, which are really individuals. There
is an edge between two nodes if a call has been placed between those phones
in some ﬁxed period of time, such as last month, or “ever.” The edges could
be weighted by the number of calls made between these phones during the
period. Communities in a telephone network will form from groups of people
that communicate frequently: groups of friends, members of a club, or people
working at the same company, for example.
Email Networks
The nodes represent email addresses, which are again individuals.
An edge
represents the fact that there was at least one email in at least one direction
between the two addresses. Alternatively, we may only place an edge if there
were emails in both directions. In that way, we avoid viewing spammers as
“friends” with all their victims. Another approach is to label edges as weak or
strong. Strong edges represent communication in both directions, while weak
edges indicate that the communication was in one direction only. The com-
munities seen in email networks come from the same sorts of groupings we
mentioned in connection with telephone networks. A similar sort of network
involves people who text other people through their cell phones.
Collaboration Networks
Nodes represent individuals who have published research papers. There is an
edge between two individuals who published one or more papers jointly. Option-
ally, we can label edges by the number of joint publications. The communities
in this network are authors working on a particular topic.
An alternative view of the same data is as a graph in which the nodes are
papers. Two papers are connected by an edge if they have at least one author
in common. Now, we form communities that are collections of papers on the
same topic.
There are several other kinds of data that form two networks in a similar
way. For example, we can look at the people who edit Wikipedia articles and
the articles that they edit. Two editors are connected if they have edited an
