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of Figure 5. Together with the distributions we
present the areas of confidence for their values;
more specifically, around each instance
n(t)
, we
draw the interval [
n(t)-σ
n
/3
,
n(t)+σ
n
/3
]. In 6(a),
the time series of the number of Diggs
n(t)
is
normalized with respect to the total number of
Diggs throughout the whole lifetime of each story.
In that way, it is possible to directly compare
the local temporal structures of popular stories
to the ones of the non-popular stories. In Figure
5(b), we present the absolute number of Diggs
per hour in order to provide a complete picture
of the comparison between the popular and the
non-popular stories.
Figure 5 clearly illustrates the fact that while
the non-popular stories gather the majority of
their Diggs during the very first moments of
their lifetime (first two bins in the histogram),
the popular ones are characterized by two growth
stages: (a) a first growth stage which is similar to
the full lifetime of the non-popular stories, i.e. it
is characterized by a monotonically decreasing
trend, (b) a second growth stage, which takes place
once a story is moved to the 'Popular' section of
the site and is characterized by a steep increase in
the number of votes that a story receives.
The intensity of popularity growth for the sto-
ries that become members of
R
P
can be attributed
to the high exposure that these stories get for a
few minutes after they are moved to the 'Popu-
lar' section (which happens to be the front page
of Digg). Also, one should note that big search
engines regularly index and rank favorably the
most popular stories of Digg (and stories coming
from other SBS and social media applications) and
thus they act as a secondary source of exposure
for these stories, which contributes to sustain their
popularity growth for some time.
After analyzing the temporal evolution of
story popularity, we apply a similar analysis on
the user Digging behavior. For such a study, we
investigate the structure of the time series that are
formed from counting the number of Diggs given
by users to stories that fall within the interval
[t-Δt,
D
=
max| ()
S xPx
-
()|
xx
(7)
min
Apparently, the plain power-law model is not
sufficient for accurately fitting all of the observed
distributions. For instance, the shape of the distri-
bution of Diggs per user in Figure 3(c) indicates
that a truncated log-normal distribution would be
a better fit for the observed variable. Further, by
inspection of the number of friends per user, a few
conspicuous outliers can be identified that deviate
significantly from the fitted power-law.
temporal Analysis of
content consumption
The temporal study of story popularity curves and
user activity of Digg was carried out by means
of the temporal representation and aggregation
framework presented in the previous section.
Based on that, a first noteworthy observation
about the popularity of submitted stories in Digg
is that they typically evolve in two ways: (a)
they reach a plateau of popularity while in the
'Upcoming' section of the site and remain there
until they are completely removed in case they
do not receive any Diggs for a long time, (b) they
attain the 'Popular' status after some time and
they are moved to the 'Popular' section, where
they undergo a second phase of popularity growth
at a much higher intensity. Figure 4 depicts the
cumulative number of Diggs,
N(t)
, collected by
a sample popular and a sample non-popular story
during their lifetime. For convenience, we denote
the set of unpopular stories as
R
U
and the set of
popular stories as
R
P
7
.
After establishing by inspection the difference
of temporal evolution between popular and non-
popular stories, we then proceed with comparing
the distributions of their Digg arrival times. To this
end, the time series,
n(t)
, of 5,468 non-popular and
852 popular stories, which were normalized by
means of the transformation of Equation 5, were
aggregated
8
. This resulted in the distributions
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