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sharing communities, for e.g. improving online
advertising campaigns (Richardson & Domingos,
2002), understanding viral marketing dynamics
(Leskovec et al., 2007) and identifying experts
(Zhang et al., 2007). Therefore, we introduce here
two measures in order to quantify the social influ-
ence on the content rating process. We name these
two measures, the u ser Social Susceptibility (SS)
I u , and the story Social Influence Gain (SIG) I r .
Definition 4 (Social Susceptibility - SS): The
social susceptibility of a given user u denoted
by I u quantifies the extent to which his/her vot-
ing behavior (as expressed by his voting set D u )
follows the behavior of his/her friends' voting
behavior (denoted by D u ´ ).
Here, we adopt the latter definition since it is di-
rectly comparable with the SS of a user, i.e. it can
be derived by removing the temporal constraint
from Equation 4. Note that SC may be attributed
to a combination of the following: (a) an inher-
ent tendency of friends to have similar interests
(homophily), (b) some external factor causing two
users to vote in favor of the same story (confound-
ing) and (c) the possibility for users to see through
the Digg interface which stories their friends have
already dugg (influence). By imposing temporal
constraints in Equations 4 and 5, we attempt to
isolate the effect of (a) and (b) in order to use SS
and SIG as measures of social influence rather
than measures of generic SC.
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cASe Study: SocIAl
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Since the case study for the discussion of the
chapter is based on data collected from Digg, a
short introduction on the specifics of the appli-
cation will precede the presentation of the data
analysis in order to facilitate the interpretation of
the derived results. The basic rationale of Digg
is the discovery of interesting web resources (or
stories as they are commonly called in Digg-speak)
by means of empowering simple users to submit
and then collectively decide upon the significance
(or interesting-ness) of the submitted web items
(mostly news items, images and videos). In other
words, Digg can be considered as an example
of a Social Media application. When a story is
submitted, it appears in the Upcoming section of
the site, where stories are displayed in reverse
chronological order. Users may vote on a story
by “Digging” it. Digging a story a story saves it
to a user's history (obviously a given user may
Digg a particular story only once). There is also
the possibility to “bury” a story, if one considers
it to be spam or inappropriate material.
When a story collects enough votes, it is pro-
moted to the Popular section, which is also the
(4)
Definition 5 (Social Influence Gain - SIG):
The social influence gain for a given story r
denoted by I r is a measure of the extent to which
r has benefited from the social network of the
story submitter.
'
= |
H
H
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I
r
, where
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(5)
and u 0 is the submitter of the story as defined in
Definition 3.
SS and SIG are similar in nature to the concept
of Social Correlation as discussed in (Anagnos-
topoulos et al., 2008). Social Correlation (SC)
within an SBS can be defined either for two users,
u 1 , u 2 as the Jaccard coefficient of the sets R u1 and
R u2 (cf. Definition 2) or for a single user u as the
proportion of his/her stories that are common with
the stories of the users of his/her social network.
 
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