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Understanding co-evolution of social and content
networks on Twitter
Philipp Singer
Knowledge Management
Institute
Graz University of Technology
Graz, Austria
philipp.singer@tugraz.at
Claudia Wagner
DIGITAL Intelligent Information
Systems
JOANNEUM RESEARCH
Graz, Austria
claudia.wagner@joanneum.at
Markus Strohmaier
Knowledge Management
Institute and Know-Center
Graz University of Technology
Graz, Austria
markus.strohmaier@tugraz.at
ABSTRACT
Social media has become an integral part of today’s web and
allows users to share content and socialize. Understanding
the factors that influence how users evolve over time - for ex-
ample how their social network and their contents co-evolve -
is an issue of both theoretical and practical relevance. This
paper sets out to study the temporal co-evolution of con-
tent and social networks on Twitter and bi-directional in-
fluences between them by using multilevel time series re-
gression models. Our findings suggest that on Twitter so-
cial networks have a strong influence on content networks
over time, and that social network properties, such as users’
number of followers, strongly influence how active and in-
formative users are. While our investigations are limited to
one small dataset obtained from Twitter, our analysis opens
up a path towards more systematic studies of network co-
evolution on platforms such as Twitter or Facebook. Our
results are relevant for researchers and social media hosts
interested in understanding how content-related and social
activities of social media users evolve over time and which
factors impact their co-evolution.
Categories and Subject Descriptors
E.1 [Data Structures]: Graphs and networks;
J.4 [Computer Applications]: Social and behavioral sci-
ences—Sociology
General Terms
Experimentation, Human Factors, Measurement
Keywords
Microblog, Twitter, Influence Patterns, Semantic Analysis,
Time Series
1. INTRODUCTION
Social media applications such as blogs, message boards or
microblogs allow users to share content and socialize. Host-
ing such social media applications can however be costly,
and social media hosts need to ensure that their users re-
main active and their platform remains popular. Monitor-
ing and analyzing behavior of social media users and their
social and content co-evolution over time can provide valu-
able information on the factors which impact the activity
and popularity of such social media applications. Activity
and popularity are often measured by the growth of content
produced by users and/or the growth of its social network.
In recent work we have analyzed how the tagging behav-
ior of users influences the emergence of global tag semantics
[3]. However, as a research community we know little about
the factors that impact the activity and popularity of social
media applications and we know even less about how users’
content-related activities (e.g., their tweeting, retweeting or
hashtagging behavior) influence their social activities (i.e.,
their following behavior) and vice versa.
This paper sets out to explore factors that impact the co-
evolution of users’ content-related and social activities based
on a dataset consisting of randomly chosen users taken from
Twitter’s public timeline by using a multilevel time series
regression model. Unlike previous research, we focus on
measuring dynamic bi-directional influence between these
networks in order to identify which content-related factors
impact the evolution of social networks and vice versa. This
analysis enables us to tackle questions such as ”Does growth
of a user’s followers increase the number of links or hashtags
they use per tweet?” or ”Does an increase in users’ popular-
ity imply that their tweets will be retweeted more often on
average?”.
Our results reveal interesting insights into influence patterns
in content networks, social networks and between them. Our
observations and implications are relevant for researchers
interested in social network analysis, text mining and be-
havioral user studies, as well as for social media hosts who
need to understand the factors that influence the evolution
of users’ content-related and social activities on their plat-
forms.
2. METHODOLOGY
Since we aim to gain insights into the temporal evolution
of content networks and social networks, we apply time se-
ries modeling [2] based on the work by Wang and Groth [6]
who provide a framework to measure the bi-directional influ-
ence between social and content network properties. In this
work we apply an autoregressive model in order to model
our time series data. An autoregressive model is a model
that goes back p time units in the regression and has the
ability to make predictions. This model can be defined as
AR(p), where the parameter p determines the order of the
model. An autoregressive model aims to estimate an obser-
vation as a weighted sum of previous observations, which is
the number of the parameter p. In this work we apply a
simple model, which calculates each variable independently
and further only includes values from the last time unit.
The calculated coefficients of the model can determine the
influences between variables over time.
In regression analysis variables often stem from different lev-
els. So called multilevel regression models are an appropriate
way to model such data. Hence, the measurement occasion
is the basic unit which is nested under an individual, the
cluster unit. In our dataset we have such a hierarchical
nested structure. For each day different properties are mea-
sured repeatedly, but all of these values belong to different
individuals in our study. If we would apply a simple autore-
gressive model to our data we would ignore the difference
between each user and would just calculate the so-called
fixed effects, because we can not assume that all cluster-
specific influences are included as covariates in the analysis
[4]. The advantage of such multilevel regression models is
now that they add random effects to the fixed effects to also
consider variations among our individuals. Since we mea-
sure different properties repeatedly for different days and
different individuals in our study, our dataset has a hierar-
chical nested structure. Therefore, we utilize a multilevel
autoregressive regression model which is defined as follows:
x
(t)
i,p
= a
T
i
x
(t−1)
p
+
(t)
i
+ b
T
i,p
x
(t−1)
p
+
(t)
i,p
(1)
In this equation x
(t)
p
= (x
(t)
i,p
, ..., x
(t)
m,p
)
T
represents a vector,
which contains the variables for an individual p at time t.
Furthermore, a
i
= (a
i,1
, ..., a
im
)
T
represents the fixed effect
coefficients and b
i
= (b
i,1
, ..., b
im
)
T
represents the random
effect coefficients. It is assumed that
(t)
i
and
(t)
i,p
is the noise
with Gaussian distribution for the fixed and random effects
respectively. It has zero mean and variance σ
2
. To compare
the fixed effects to each other, the variables in the random
effect regression equations need to be linearly transformed to
represent standardized values. How this is done and how the
model is finally applied to our data is described in section 4.
3. DATASET
We chose Twitter as a platform for studying the co-evolution
of communication content and social networks, since it is
a popular micro-blogging service. We explore one random
dataset in this work, which was crawled within a time period
of 30 days. This random dataset consists of random users
from the public timeline who do not have anything special
in common.
To generate the random dataset, we randomly chose 1500
users from the public Twitter timeline who we used as seed
users. We used the public timeline method from the Twit-
ter API to sample users rather than using random user IDs
since the timeline method is biased towards active Twitter
users. To ensure that our random sample of seed users con-
sists of active, English-speaking Twitter users, we further
only kept users who mainly tweet in English, have at least
80 followers, 40 followees and 200 tweets. We also had to re-
move users from our dataset who deleted or protected their
account during the 30 days of crawling. Hence, we ended up
having 1.188 seed users for whom we were able to crawl their
social network (i.e., their followers and followees) and their
tweets and retweets. To identify retweets we used the flag
provided by the official Twitter API and to extract URLs
we used a regular expression. During a 30 day time period
(from 15.03.2011 to 14.04.2011) we polled the data daily at
about the same time.
4. EXPERIMENTAL SETUP
The goal of our experiments is to study the co-evolution of
social and content networks of Twitter users and influence
patterns between them. In order to achieve this we firstly
created a social and content network for each specific time
point.
Social network: The social network is a one-mode directed
network, where each vertex represents a user and the edges
between these vertices represent the directed follow-relations
between two users at a certain point in time. The con-
structed social network of seed users only reflects a sub-part
of a greater network. Therefore it makes no sense to cal-
culate and analyze specific network properties such as be-
tweenness centrality or clustering coefficient, because these
properties depend on the whole network and we only have
data available for a certain sub-network.
Content network: The content network at each point in
time is a two-mode network, which connects users and tweets
via authoring-relations. From these user-tweet networks one
can extract specific tweet features, such as hashtags, links or
retweet information, and build, for example, a user-hashtag
network. It would also be possible to create further types of
content networks, such as hashtag co-occurrence networks
(see [5] for further types), but we leave the investigation of
such network types open for future research.
Overall, the social networks capture the social following re-
lations between users, whereas our content networks account
the tweets users publish. Finally, we can connect both net-
works via their user vertexes, since we know which user in
the social network corresponds to which user in the content
network and vice versa.
A further step towards our final results is the normaliza-
tion of our available data. This is done by subtracting the
time-overall mean and dividing the result by the time-overall
standard deviation. The fixed effects can now be analyzed
as the effect of one standard deviation of change in the in-
dependent variable on the number of standard deviations
change in the dependent variable [6].
Based on the prepared data, the final model described in
section 2 can be applied to identify potential influences be-
tween social and content network properties over time. Ta-
Influence Network
Content Network
Social Network
RetweetedRatio 0.26
LinkRatio 0.25
RetweetRatio
-0.02
HashtagRatio
0.02
0.02
0.20
0.03 0.03
0.14
#Tweets 0.35
#Followees
-0.09
0.36
0.31
-0.23
1.00 #Followers
0.95
1.56 1.93
1.00
Figure 1: Influence network between the content and social network of a randomly chosen set of Twitter
users. An arrow between two properties indicates that the value of one property at time t has a positive
or negative effect on the value of the other property at time t + 1. Red dashed arrows represent negative
effects and blue solid arrows represent positive effects. The thickness of the lines indicates the weight of the
influence relations. Only statistically significant influences are illustrated.
ble 1 describes each social and content network property
used throughout our experiment. The properties are calcu-
lated for a corresponding social or content network at each
time point t of the random Twitter dataset. The depen-
dent variable of the model is always a property at time t
and the independent variable are all properties at time t − 1
including the dependent variable at that time. Including
the dependent variable in that step allows us to detect if
a variable’s previous value influences it’s future value. Fi-
nally, the resulting statistical significant coefficients show a
relationship between an independent variable at time t − 1
and a dependent variable at time t. Positive coefficients in-
dicate that a high value of a property leads to an increase
of another property, while negative coefficients indicate that
a high value of a property leads to an decrease of another
property. To reveal positive and negative influence relations
between properties within and across different networks, we
visualize them as graphical influence network.
5. RESULTS
Our results reveal interesting influence patterns between so-
cial networks and content networks. The influence network
in figure 1 shows the correlations detected in the multilevel
regression analysis via arrows that point out influences be-
tween a property at time t and another property at time
t + 1.
The influence network reveals significant influences of so-
cial properties on content network properties. The strongest
positive effects can be observed between the number of fol-
lowers of a user and the content network properties - i.e.,
users’ number of followers positively influences their link ra-
tio, their retweeted ratio and their number of tweets. This
indicates that users start providing more tweets and also
Table 1: Social and content network properties
Network
type
Property Description
Social #Followers The number of followers a user v has on
a specific time point t.
Social #Followees The number of followees a user v has on
a specific time point t.
Content #Tweets The number of tweets a user v has au-
thored on a specific time point t.
Content Hashtag
ratio
The number of hashtags used by a user
v on a specific time point t, normalized
by the number of daily tweets authored
by him/her.
Content Retweet
ratio
The number of retweets (originally au-
thored by other users) by a user v on a
specific time point t, normalized by the
number of tweets he/she published that
day.
Content Retweeted
ratio
The number of tweets produced by a user
v on a specific time point t that were
retweeted by other users, normalized by
the number of tweets user v published
that day.
more links in their tweets if their number of followers in-
creases. Not surprisingly, users’ tweets are also more likely
to get retweeted if their number of followers increases, be-
cause more users are potentially reading their tweets.
Further, figure 1 shows that the number of followees of the
social network has positive and negative influences on the
content network in our random dataset. While the positive
effects point to the link and hashtag ratio, the negative ef-
fects point to the number of tweets and the retweeted ratio.
This suggests that users who start following other users also
start using more hashtags and links. One possible expla-
nation for this is that users get influenced by the links and
hashtags used by the users they follow and might therefore
use them more often in their own tweets. The negative ef-
fect of the number of followees on the number of tweets and
the retweeted ratio suggests that users who start following
many other users start behaving more like passive readers
rather than active content providers.
Another observation of our experiment is that all properties
influence themselves positively, which indicates that users
who are active one day, tend to be even more active the
next day. This indicates for example, that users who attract
new followers one day tend to attract more new followers
the day after.
6. CONCLUSIONS AND FUTURE WORK
The main contributions of this paper are the following: (i)
We applied multilevel time series regression models to one
selected Twitter dataset consisting of social and content net-
work data and (ii) we explored influence patterns between
social and content networks on Twitter. In our experiments
we studied how the properties of social and content networks
co-evolve over time. We showed that the adopted approach
allows answering interesting questions about how users’ be-
havior on Twitter evolves over time and the factors that
impact this evolution. While our results are limited to the
dataset used, our work illuminates a path towards study-
ing complex dynamics of network evolution on systems such
as Twitter. Our analyses may also facilitate social media
hosts to promote certain features of the platform and steer
users and their behavior. For example, one can see from
our analysis that usage of content features, such as hashtags
and links, is highly influenced by social network properties
such as the number of followers of a user. Therefore, social
media hosts could try to encourage users to use more con-
tent features by introducing new measures such as a friend
recommender techniques which might impact the social net-
work of users. However, further work is warranted to study
these ideas.
Overall, our findings on one small Twitter dataset suggest
that there are manifold sources of influence between social
and content network properties. Our results indicate that
users’ behavior and the co-evolution of content and social
networks on Twitter is driven by social factors rather than
content factors. Previous research by Anagnostopoulos et
al. [1] showed that content on Flickr is not strongly in-
fluenced by social factors. This may suggest that different
social media applications may be driven by different factors.
The experimental setup used in our work can be applied
to different datasets to study these questions in the future.
Nevertheless, further work is required to confirm or refute
this observations on other, larger datasets.
Our experiments suggest that the number of followers pow-
erfully influences properties of the content network. One
interpreation for that is that the number of followers is a
very important motivation for Twitter users to add more
content and use more content features like hashtags, URLs
or retweets. However, the number of users a user is follow-
ing can also have a negative influence on content network
properties as one can see from figure 1. Our results suggests
that an increase of a user’s followees (i.e., the number of
users he/she follows) implies that the user starts tweeting
less and that his/her tweets get less frequently retweeted.
Further, our findings show that all properties influence them-
selves positively. This does not mean that the values of all
properties always increase over time, but that they tend to
increase depending on how much they increased the day be-
fore. For example, a Twitter user who started posting more
links at day t, is likely to post even more links at day t + 1
or a user who gain new followers at day t is likely to gain
even more new followers at day t + 1.
To summarize, our work highlights the existence of interest-
ing influence relationships between content and social net-
works on Twitter, and shows that multilevel time series re-
gression analysis can be used to reveal such relationships and
to study how they evolve over time. Based on the techniques
developed by Wang and Groth [6], our work investigated in-
fluence patterns in a new domain, i.e. on microblogging plat-
forms like Twitter. Our results are relevant for researchers
interested in social network analysis, text mining and be-
havioral user studies, as well as for community hosts who
need to understand the factors that influence the evolution
of their users in terms of their content-related and social
behavior.
Acknowledgments
This work is in part funded by the FWF Austrian Science
Fund Grant I677 and the Know-Center Graz. Claudia Wag-
ner is a recipient of a DOC-fForte fellowship of the Austrian
Academy of Science.
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