SOCNET 2018, February 28, 201845

Preferential Attachment in Social MediaThe Case of Nico Nico Douga
Johannes Putzke1 and Hideaki Takeda2
1

University of Bamberg,
An der Weberei 5, 96047 Bamberg, Germany
2
National Institute of Informatics (NII)
2-1-2, Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

Abstract. In the examination of evolving complex networks, the analysis
of preferential attachment is a core research problem. However, the results of studies that examine whether preferential attachment operates
in social media networks are conﬂicting. On the one hand, preferential
attachment generally has been found to be a stable predictor of network
evolution. On the other hand, IS researchers question the applicability of the preferential attachment hypothesis to social media networks.
This study shows that preferential attachment also operates on Nico
Nico Douga, a Japanese video sharing service similar to Youtube withmore than 20 million registered users. However, this study also reveals
that the attachment kernel diﬀers substantially from the classically assumed log-linear form, when estimating the kernel with nonparametricmaximum likelihood estimation (PAFit).
Key words: PAFit, preferential attachment, social media, social network

analysis

Introduction
Social media radically have changed the way in which we create and consume content. During content creation and consumption we are embedded in networks ofpeers that leave their digital traces on the social media platforms that we use. Consequently, a number of recent papers applies methods from network science forthe examination of social media, e.g. [1]. In this context, authors particularly tried46

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to answer the research question what might be a good model to describe the evolution of a network. As a general network formation model, preferential attachment(PA) [2] has been found to be a stable predictor for network evolution. PA meansthat newly arriving nodes in a network connect with a higher probability to those
nodes in the network that already have a large number of connections. However,since recent studies by information systems (IS) scholars [1][3] could not ﬁnd evidence for PA in social media networks, these scholars question the applicability of
the PA hypothesis to networks in social media. On the other hand, a recent study
about friendship networks on the social media website Flickr [4] provides evidence
for PA in social media networks, but not in the classically assumed log-linear formof the attachment kernel. Therefore, in this paper we try to shed further light on thequestion whether PA operates in social media networks. Particularly, we intend to
examine whether [4]’s ﬁndings can be replicated on a data set from the social media website Nico Nico Douga (NND). NND is a Japanese video sharing platform
similar to Youtube. As of 2014, it has more than 20 million registered users [5].
However, NND has a unique feature that diﬀerentiates it from Youtube. In NND,
users can add time-stamped comments to the videos. These comments are thenoverlaid to the original video when playing back the video. This commenting feature made NND famous for a new form of content co-creation. In this form ofcontent co-creation, song writers and (3D) illustrates collaborate and create music
videos. In doing so, they comment on their videos and (re-) use some content (e.g.
music or graphics) from each other. When creating content and using the content of other videos, the creators frequently attribute credits to the videos which
they used. In such a way a network of co-creation emerges. We analyze the PA
hypothesis for this evolving co-creation network.
The remainder of this paper will be structured as follows. The next section, Background, will be structured into two sub-sections. In the ﬁrst sub-section, we review the related literature about the PA hypothesis. In the second sub-section, we
present [4]’s nonparametric maximum likelihood (ML)-based preferential attachment kernel estimation method (PAFit) as well as its application to a Flickr dataset.
In the next section, Replication I, we describe the NND data set used for replicating
the results of [4]’s study, the procedures used in the replication, as well as the comparative results of the application of PAFit to our data set (see also [6]). Since we
could replicate [4]’s results with the NND data set, we performed another replica-SOCNET 2018, February 28, 201847

tion with a publicly available social media data from the Website Digg.3 This replication will be presented in the section “Replication II”. Finally, the paper closes
with a short Discussion section.

Background. The Preferential Attachment Hypothesis
The “preferential attachment hypothesis” has been examined in the literature under various names such as the “Yule distribution/process” [7], the “Mathew eﬀect”[8], or “cumulative advantage” [9].4 It states that subjects with an attribute X will
acquire new units of this attribute X according to how many units of this attributethey already have. In network science, “preferential attachment is generally understood as a mechanism where newly arriving nodes have a tendency to connect with already-well connected nodes” [12]. Most researchers attribute the name“preferential attachment hypothesis” to [2] who published a highly inﬂuential paper in Science about the subject.5 Considering the vast amount of papers on PA,
it would not be meaningful to provide a complete (interdisciplinary) literature review on this subject at this place.6 Rather, an appropriate literature review focusses
on the groundbreaking works about PA (e.g., [13,14]), as well as on the works of
IS researchers who conducted network studies and pointed out to the (missing)
PA process in the context of social media. Concerning the groundbreaking works
about PA, the reader is referred to the literature reviews in [15] and [16], as wellas the corresponding sections in the work by [4]. Concerning the works by IS researchers, there were some interesting ﬁndings concerning PA in social media.
For example, [3] could not ﬁnd evidence for the PA hypothesis examining datafrom 28 online communities. Also [1] do not ﬁnd evidence for PA examining enterprise social media networks such as an online social networking platform. On
http://digg.com/, accessed on 02/28/2017.
For the history of the PA hypothesis see also [10] and [11]. The interested reader isalso referred to a lecture by Aaron Clauset (available at http://tuvalu.santafe.
edu/~aaronc/courses/5352/fall2013/csci5352_2013_L13.pdf, accessed on
04/12/2017) in which Clauset explains the PA hypothesis and its history in detail.
5
The paper has been cited more than 25,000 times as of a google scholar search on
04/17/2017.
6
For example, a google scholar search for the term “preferential attachment” provided
more than 24,000 search results as on 04/17/2017.

3

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the other hand, PA is supposed to be a robust predictor of tie formation [1], andother IS researchers state that, for example, fundraising over social media is a PA
process [17]. In the light of these contradicting results, it is evident that we need aclearer understanding about the “conditions under which preferential attachment
operates (or not) in diﬀerent network settings”. Therefore, [1] call exactly for thistype of research. In order to answer [1]’s call, a robust method for estimating PA in
diﬀerent network settings is needed. Such a method has been recently proposedby [4]. However, this method has never been applied in IS research. Therefore, inthe following sub-section we highlight [4]’s method, as well as its application by[4] to a Flickr social network dataset [18].
. Nonparametric Maximum Likelihood-Based Preferential Attachment Kernel
Estimation and its Application to Flickr
Following [4], we denote an observable seed network at a time-step �0 = 0 with
�0 . This network grows from each period � = 0, 1, …, � with �(�) nodes and �(�)edges. At discrete points in time � = 0, 1, …, � we can observe these static network
conﬁgurations �� . In each time-step �, the probability that an existing node � within-degree � acquires a new edge is given by� �(� acquires a new edge) ∝ �� .

(1)

�� is the value of the attachment kernel at degree �. A number of authors proposed estimation methods for the attachment kernel. A good overview of thesemethods can be found in Table 1 in [4].7 However, most of these methods assume a log-linear form �� = �� of the attachment kernel. Notable exceptions
are the works by [13] and [14] who base their estimation on histograms, and arethus nonparametric. However, also these two methods have their shortcomings.
In contrast, [4] derive the ML estimator as8��� =∑�=1 �� (�)

�

∑�=1

�(�)�� (�)∑�� (�)��
�=0 �(2)for � = 1, …, �. The solution to this equation can be found using the MinorizeMaximization (MM) algorithm (e.g., [19]) that is beyond the scope of this paper.
7
8

doi:10.1371/journal.pone.0137796.t001, accessed on 3/31/2017.
For the details of derivations and proofs of the following paragraph see [4].

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The interested reader is referred to the aforementioned literature. [4] apply their
method to a publicly available Flickr social network dataset [18].9 This dataset consists of 2,302,925 users and their 33,140,017 directed friendship relationships thatgrow over a period of 133 days. After the period � = 0, 815,867 new nodes and16,105,211 new edges arrive in the data set. As convergence criterion for the MM
algorithm, [4] use a value of � = 10−7 . Figure 1 [4] illustrates the results of theestimation of the attachment kernel. The plot is on a log-log scale, and a solid line
illustrates �� = � as a visual guide. Although the results clearly indicate PA, theyalso indicate a clear signal of deviation from the log-linear model �� = �� [4].

Fig. 1: Estimation of the attachment kernel in the Flickr social network dataset(doi:10.1371/journal.pone.0137796.g003)

Replication I. Data Set: Nico Nico Douga
We replicated [4]’s study using a data set of NND that was provided by [5], and thatis partially available on ﬁgshare10 . The data set contains the metadata of all videos
uploaded on NND between January 2007 and December 2012 (i.e. the author, keywords, author’s comment, number of views and the timestamp of the upload). In
Available at http://konect.uni-koblenz.de/networks/flickr-growth, accessed
02/28/2017.
10
Available at https://dx.doi.org/10.6084/m9.figshare.2055597, accessed
02/28/2017.
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total, we extracted 2,622,495 VideoIDs from the data set that had at least one keyword associated to them, together with their timestamps. Out of these 2,6 million
videos, 1,427,715 videos could be assigned to an author ID (see [5]). Our following
analyses are based on these 1.4 million videos.
. Methods
For the estimation of the PAFit model, we focused on the author co-creation network, i.e. we assumed a directed link from author A to author B, if an author A
cited a video that had been created by author B. In this way, we obtained 4,773,163
directed edges. After excluding self-citations, 3,014,423 edges remained in the data
set. When estimating the model in R v. 3.2.2 with the package PAFit v. 0.9.3 on thewhole data set, we obtained an error due to memory problems. Therefore, we decided to split the data set into two (random) parts. The ﬁrst part contains 2,016,458
random edges, the second part contains the remaining 997,965 edges. The size ofthe ﬁrst part is the maximum number of edges for which the estimation worked
on our system. The ﬁrst part of the data set will be used for model estimation,and the second part of the data set will be used for cross-validation. The ﬁnal data
set consists of 124,996 authors and their relationships that grow over a period of
1,449 days. In the ﬁrst part of the data set, after the period � = 0 115,134 newnodes, and 1,635,827 new edges arrived. The node with the highest number ofedges has a degree centrality of 38,234. In the second part of the data set, after
period � = 0 115,134 new nodes, and 808,740 new edges arrive. The node withthe highest number of edges has a degree centrality of 19,037. Like [4] we use avalue of � = 10−7 as convergence criterion for the MM algorithm. Furthermore,
we use logarithmic binning (with 200 bins) in order to stabilize the estimation of
the attachment kernel.
. Results
Figure 2 (a/b) illustrates the results of the estimation of the attachment kernel.
Again, the plots are on a log-log scale, and solid lines illustrate �� = �.
The estimated attachment exponents of the log-linear model �� = �� are (1)� = 0.8819457 for the ﬁrst part of the data set, and (2) � = 0.8841727 for thesecond part of the data set. In summary, these results are very stable, and provide
strong empirical evidence for preferential attachment in the Nico Nico Douga co-

SOCNET 2018, February 28, 201851

Fig. 2: (a/b).Estimation of the attachment kernel in the NND data set (ﬁrst part,second part)
creation network. Nevertheless, like Pham et al. [4] we observe a deviance fromthe log-linear functional form of the attachment kernel, particularly in the highdegree region.

Replication II
Since we could replicate [4]’s results with the NND data set, we performed another replication with a publicly available social media data. This data set comprises user interactions on the social media website Digg between 10/28/2008 and11/12/2008.11 In the data set, each node reﬂects a user in the network, and an edge
between user A and user B reﬂects that user A replied to user B. The data set consists of 30,398 nodes, and 87,627 edges between them. Concerning the evolution of
the network, there was only one edge with a timestamp 10/28/2008 in the dataset.
Therefore, we assumed that the observable seed network at a time-step �0 = 0
comprises all edges with a time-stamp ≤ 10/29/2008. During the evolution of the
network, 30,382 new nodes and 59,655 new edges arrived. Since the maximum
degree of the nodes was rather low (243), we did not apply logarithmic binning.
Figure 3 displays the estimation results. The estimated attachment exponent
has a value of � = 0.3958123. Again, the results indicate PA, but also not in loglinear form. The low value of the attachment exponent � is an interesting ﬁnding,particularly since the social news website Digg is used for professional as well as
for private use.
11

Available at http://konect.uni-koblenz.de/networks/munmun_digg_reply, accessed 02/28/2017.

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Fig. 3: Estimation of the attachment kernel in the Digg data set

Discussion
In this paper, we showed that the evolution of the co-creation network on NND
is driven by PA. However, nonparametric ML-based estimation of the PA kernel
revealed that the process does not follow the classically assumed log-linear form.
Hence, this study makes at least the following contributions to the IS literature:
First, we introduced a new method for attachment kernel estimation, PAFit [4],from physics to the IS literature. This is important, as our results show that the
predominant praxis to estimate the attachment kernel with parametric methods
falls short. Second, IS researchers argue that PA might be a structural feature that
operates in a variety of physical and technical networks [20], but question the applicability of the PA hypothesis for social networks in social media (e.g. [1,3]). This
study showed that PA also operates in social media networks such as the NND
co-creation network. This is an interesting ﬁnding as it substantiates [1]’s call for
research that we should ﬁgure out the conditions under which PA operates insocial media. The proposed method, PAFit can help us to fulﬁl this aim. Using
PAFit, we also made an interesting second ﬁnding. Although we could observe
some deviance from the log-linear model in the NND data set, the deviance waseven more pronounced in the Digg data set (see Figure 3). Despite the large deviance, however, there was a strong evidence for PA. Nevertheless, we suggest that
future research should examine the functional forms of the attachment kernel for
diﬀerent social media data sets. In an exploratory study, future research should
particularly ﬁgure out the conditions when the PA hypothesis holds in social media. For example, based on the results of the NND study and the Flickr study [4] one
might speculate that the PA hypothesis holds in social media settings that focus

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on the creation of artistic goods (such as photos and videos), which people mainly
use during their free time. On the other hand, based on the analyses of technology
related discussion forums [3] and enterprise social media platforms [1] one might
speculate that the PA hypothesis does not hold in social media settings that focus
on increasing productivity (in enterprises). However, these conjectures still haveto be substantiated by examining more social media data sets. We hope that thisstudy will lie the basis for more work into this direction.
Acknowledgments. This work was supported by a fellowship within the FITweltweit
programme of the German Academic Exchange Service (DAAD). The authors
thank Remy Cazabet for the provision of the Nico Nico Douga data set.

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