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Real-World Popularity Estimation from Community
Structure of Followers on SNS
Shuhei Kobayashi

Keishi Tajima

Kyoto University
Kyoto, Japanskobayashi@dl.soc.i.kyoto-u.ac.jp

Kyoto University
Kyoto, Japantajima@i.kyoto-u.ac.jp

Abstract—In this paper, we propose methods of estimating thereal-world popularity of users of online social network services(SNSs). Because their followers on an SNS are biased samplingfrom their real-world fans, we cannot estimate their real-world
popularity simply by the number of their online followers. Our
methods are based on the following hypothesis: SNS users withfollowers more distributed over the SNS graph are likely to havemore real-world popularity. Because the entire social graph isoften unavailable, we design four methods of measuring how
much followers are distributed by using only the local structureof the neighbors of the followers. Three of them uses variations of
the clustering coefficient of node, and one of them uses a metric
we newly designed. Through the development and evaluation of
our methods, we validate the hypothesis above.
Index Terms—social network, Twitter, Instagram, clustering
coefficient

I. I NTRODUCTION
On today’s online social network services (SNSs), such as
Twitter and Instagram, a wide range of people, from superfamous celebrities to nameless ordinary people, can obtain
popularity by posting messages on some topics. The numberof followers is the most widely used metric for measuring
the popularity of such SNS users. The number of followers
generally works well as a metric of popularity, but there areseveral factors that can make it inaccurate. For example, theexistence of bought fake followers is a well known problem.
For this problem, there have been studies on the detectionof such fake accounts without real persons behind them. The
definition of the popularity also affect the accuracy because
we may not define popularity simply by the number of fans.
However, even when we do not have fake users and we
define the popularity by the number of fans, the number offollowers is not still a perfect metric of popularity. It is because
the set of followers of some user’s SNS account is a sampled
set of the fans of the user, and the sampling process caninvolve various kinds of bias. Sometimes most fans of an user
explicitly follow the user’s account, and sometimes there aremany fans of a user who do not explicitly follow the user’s
account. This discrepancy becomes especially evident when
we use the number of followers to estimate a user’s popularity
in the real-world, not the online popularity of the account.
One of the factors that make this discrepancy is the explicit
request of the “follow” actions from the account user. That is,sometimes SNS users explicitly ask people within the closeu1

u2

Fig. 1. Example of users with the same number of followers but with different
community structure of the followers. Both u1 and u2 have three followers.
Followers of u1 are densely connected, which means u1 is followed only
by people in one community, while followers of u2 are unrelated with eachother, which means u2 may have popularity in wider range of people.

community, e.g., their personal friends, to follow their account.
Sometimes people within the same community as an SNS user
voluntarily do it even if the SNS user does not ask it. In suchcases, these accounts will have a larger number of followers
than users who have similar degree of popularity but do not
explicitly request it.
The example above is an extreme case, but in general,
if two SNS accounts u1 and u2 have the same number offollowers, and the followers of u1 are densely connected witheach other while the followers of u2 are distributed over thesocial graph without dense connection, we expect that u1 has
many followers densely sampled from the close communityof u1 , and the user u2 actually has more fans. Because thefollowers of u2 are distributed over the graph, u2 has a greater
chance of having many latent fans within the neighbors of
those followers. Figure 1 illustrates this example. Both u1
and u2 have three followers. Followers of u1 are densely
connected, which means u1 is followed only by people ina local community, while followers of u2 are unrelated witheach other, which means u2 has more global popularity.
Following this observation, in this paper, we propose andcompare several methods of estimating the real-world popularity of SNS users based not only on the number of theirfollowers but also on their community structure, i.e., thestructure formed by the follow edges from/to the followers.
Because our methods use that information, our methods
need to collect the following data for estimating the popularityof a given target user:• the list of followers of the given target user,• the list of the followers of each follower, and• the list of the followees (friends) of each follower.

By collecting these three types of data, we construct a subgraph of the SNS’s social graph induced by these users. We
call this graph the follower-neighbor graph of the target user.
One advantage of this approach is that we do not need
the information on the entire social graph of the SNS. There
have been many studies proposing methods for estimatingsome properties of nodes in a large graph, and they can beclassified into two types: those that require the entire graphand those that require only the local structure in the neighborof the node in question. Many (not all) SNSs allow us toretrieve local graph structure of some nodes, but today’s mostSNSs restrict large scale crawling of their social graphs. For
example, Twitter is selling their tweet information, but do notsell their social graph data. Instagram allows us to browse thelist of followers of a given user, but they forbid scraping of
the follower lists. As a result, the entire social graph is notavailable for most of us. Therefore, methods that only require
the local structure of a node in question are advantageous.
For each follower, the following types of information canbe obtained only from the follower-neighbor graph without
requiring the entire graph:• how many followers each follower has,
• how many followees (friends) each follower has, and• which pairs of the followers are connected and whichpairs are not.
our methods first calculates the score of each follower of thetarget user by using these three types of information. We thensum up the scores of all the followers to estimate the popularityof the target user.
For calculating the score of each follower, we propose
four methods. Three of them uses the clustering coefficientand its variations. The clustering coefficient is a widely usedmetric for measuring the edge density within the neighbor ofa node in a graph. If the clustering coefficient of a node islarge, the node is mainly connected to a small number of
specific communities, and if the clustering coefficient of anode is small, the node is connected to wider communities
distributed over the graph. We expect that a user with followers
with smaller clustering coefficients have greater real-world
popularity. Therefore, we give higher scores to the followers
with smaller clustering coefficients.
The fourth methods define the score of the followers more
directly following our hypothesis. For each follower, we
hypothesize that the larger the number of followers (i.e., 2hop followers of the target user) is, the greater the follower’s
influence is, and the larger the number of followees (friends)
is, the wider the range of the communities the follower isconnected to, and also the smaller the likelihood that thefollower is a personal friend of the target user. In summary,the larger the number of followers and followees of a follower
is, the greater the value of the follower.
We conducted experiments for evaluating and comparing
our proposed methods and a simple baseline method that onlyuses the number of followers as the metric of the popularity.
For the evaluation, we need a dataset with the ground truth of
the real-world popularity. To collect such dataset, we focusedon Ms/Mr university competitions. We chose 9 universities thathave competitions where the winner and the runners-up arechosen not solely by the judges of the competition but based on
the public popularity votes (either online, offline on the contest
day, or both). All the contestants of those competitions havetheir Twitter accounts. We collected follower-neighbor graphsof the contestants’ Twitter accounts, estimated their popularity
by our methods and by the baseline method, and evaluate theiraccuracy based on the results of the competitions.
Through the development and evaluation of these methods,
we validate the following two hypothesis:•

SNS users with followers more distributed over the SNS
graph are likely to have more real-world popularity, andtherefore, we can improve the accuracy of the popularity
estimation by using the information on the community
structure of the followers compared with the simple
method solely based on the number of followers.

The remainder of this paper is organized as follows:
Section II describes related research, Section III details the
proposed method, Section IV describes experimental details,
and Section V concludes the paper.
II. R ELATED W ORK
In this section, we first survey the research on the estimationand prediction of the popularity of SNS users. We also explain
existing metrics on the edge density in the neighbors of a node
in a graph. The most well-known method of measuring it is
the clustering coefficient [1]. We briefly survey research on
the extensions of the clustering coefficient. We also explain astudy that use the clustering coefficient in a problem related
to our problem.
A. SNS user popularity prediction
Although there have been a large number of studies on theprediction of the popularity of online contents, such as tweets,
images on Flickr, and videos on YouTube, there have been only
a few research on the prediction or estimation of the popularity
of SNS users because most studies define the popularity ofusers by the number of followers or by the popularity of theirposts in the past, not by their real-world popularity.
Imamori and Tajima [2] proposed a method of predicting the
popularity that a new Twitter user will have in future. Osawa
and Matsuo [3] proposed a method of predicting the popularitythat some real-world entity, e.g., a person, will have if it createsan SNS account. On the other hand, our purpose is the oppositeof the latter one: estimation of the real-world popularity of anentity from the information of its SNS account.
There have been more research on the estimation of theinfluential power of SNS users [4]–[7]. However, Romero etal. [5] has shown that popularity and influence power do notcoincide. In addition, these studies estimate the SNS users’
influential power on SNS, not the estimation of offline realworld popularity from the online information.

B. Clustering coefficients for weighted graphs
Suppose we have an undirected unweighted graph G(V, E)
where V is the set of nodes and E is the set of edges. The
clustering coefficient of a node vi ∈ V , denoted by C(vi ),indicates the degree to which its neighbors are connected toeach other, and is defined as below:
C(vi ) =2|{{vj , vk } ∈ E | {vi , vj } ∈ E, {vi , vk } ∈ E}|
ki (ki − 1)

where ki is the degree of vi . That is, C(vi ) finds the pair ofvi ’s neighbors forming a triangle with vi , and calculate theratio of the number of existing triangles to the number of all
possible pairs.
Various extensions of clustering coefficients have been
proposed, some of which are summarized by Saramäki et al.
in [8]. In the following, we explain some of the extensions
including those we use in our methods.
There are many applications where we need to model
networks as weighted graphs. In weighted graphs, a weight
representing the strength of the connection is assigned to eachedge. When we analyze such data, we sometimes want totake into account the weights in the calculation of clustering
coefficient. Barrat et al. [9] proposed clustering coefficients forweighted graphs. They define the weight of a triangle by thesum of the weights of the two edges adjacent to the node inquestion. On the other hand, the method proposed by Onnela
et al. [10] defined clustering coefficients for weighted graphs
by the formula below:
X
1
C̃(vi ) =(ŵij ŵik ŵjk )1/3
ki (ki − 1)j,kIn the formula, ŵij is the normalized weight defined byŵij = wij / maxx,y (wxy ) where wij is the weight of the edge
connecting vi and vj . Because they use the geometric meanof the weights of edges in a triangle, if there is an edge witha small weight in a triangle, its contribution to the clustering
coefficient is very small. The C̃(vi ) is 1 if all adjacent nodes ofvi are connected and the weights of the edges in the triangles
equal to maxx,y (wxy ), the maximum weight in the graph.
Fagiolo [11] has proposed clustering coefficients for directed graphs. For unweighted directed graphs, their clustering coefficients are defined by the ratio of existing directed
triangles to the total number of all possible directed triangles.
In other words, they distinguish triangles consisting of thesame nodes but consisting of edges in different directions.
For weighted directed graphs, they extended the clustering
coefficient for weighted graphs by Onnela et al. [10] in thesame manner by distinguishing the triangles with different
edge directions. In this study, we use their definition ofclustering coefficients for weighted directed graphs.
C. Use of clustering coefficient in a related problem
Berahmand et al. [12] used clustering coefficient and thesecond-level clustering coefficient for estimating the influential
power of a node in a graph by using only semi-local information, i.e., without global graph data. However, their aim isto estimate influential power, not popularity, and the usage ofthe clustering coefficient is completely different from ours.
III. P ROPOSED M ETHOD
In this section, we describe our methods of estimating thereal-world popularity of SNS users. As explained in Section I,
our method estimate it based on whether the user in question
has the followers from wider communities and is expected tohave global popularity, or it has followers only from a small
local community, and seems to only have local popularity.
Our methods first calculates a score of each follower of
the target user, which represents how much the follower isglobally connected to wider communities. We then sum up
the scores of all the followers, and use the result as the metricfor estimating the real-world popularity of the target user.
We first explain three methods that assign scores to thefollowers based on their clustering coefficients. When many
followers are connected to each other, it is highly likelythat they form a group, and the target user has followers
mainly from a small local communities. On the contrary, if
the followers are not densely connected with each other, they
are less likely to form a group and expected to be connected
to wider communities. Therefore, if the clustering coefficientof the followers are large, we expect that the real-world
popularity of the user is relatively low compared with otherusers with the similar number of followers. If the clustering
coefficient of the followers are small, we expect the opposite.
Because a clustering coefficient takes its maximum value
1 when the node is embedded in a dense local community,
we subtract the clustering coefficient from 1, and the resulting
value is used as the score of the node.
A. Scores based on undirected clustering coefficient
Our simplest method based on the clustering coefficientuses the most classic clustering coefficient for unweighted
undirected graphs explained in Section II. It is well known
that the clustering coefficients of nodes in social graphs arehigh [1]. It is one of the most important characteristic of social
networks, and has also been observed in SNSs [13].
Even though the clustering coefficients of nodes in social
graphs are generally high, there is still a large variation among
the nodes. We use it to estimate the expected contribution ofeach follower to the popularity of the target user.
B. Scores based on directed clustering coefficient
We also compare a method that calculates the scores ofnodes based on the clustering coefficient for directed graphs.
We follow the definition by Fagiolo [11].
As explained in Section II, it is defined by the ratio of theexisting directed triangles to the all possible directed triangles.
By using it, we can take into account more information
available in the social graph, which is a directed graph. The
value of a directed clustering coefficient becomes larger whenrelated nodes are connected reciprocally than when they areconnected only by one-way edges. Therefore, we can givehigher coefficients (and therefore, lower scores) when related
nodes are more strongly connected.

u

u1

u2

4
c1
c2
c3
Fig. 2. Weights of edges between followers of the target user u. Two filled
circles are followers of u. u is always their common neighbor, and in thisexample, they have three other common neighbors, c1 , c2 , c3 . Therefore, they
have four common neighbors in total, and the weight of the edge between
them is defined to be 4. Note that the weight is always larger than 1 because
the target user is always a common neighbor for its followers.

C. Scores based on weighted undirected clustering coefficient
The discussion above suggests that the strength of the connection among related nodes are useful information. Therefore,
we next consider a method that use the clustering coefficientfor weighted undirected graphs.
There are several ways to define the strength of the connection between two nodes by only using the graph structure,
but the most popular one is the common neighbor method.
We adopt it in our method. The strength of the connection
between two followers is considered stronger when they havemore followers/followees in common.
Figure 2 illustrates the idea by using an example. In thisexample, two filled circles are the followers of the target user
u. Because we only consider followers of the target user,
they always have at least one common neighbor, which is thetarget user. In this example, the two followers also have threeother common neighbors c1 , c2 , c3 . Therefore, they have fourcommon neighbors in total, and we define the weight of theedge between the two followers to be 4.
On the other hand, if there is not an edge between two
followers, the strength of their connection is 0 even if they
have many common neighbors. In summary, the weight of theedge between two followers v1 and v2 , denoted by wij , isdefined as follows:(
the number of common neighbors if edge exists
wij =0
otherwise
When we calculate clustering coefficients of followers, we
also need the weights of edges connecting the followers andthe target user. We set it to be the average of the weights ofthe edges between the followers.
We then calculate the clustering coefficients of the followers
by using these edge weights. When calculating them, weonly include the target user and its followers in the graph,and exclude all other nodes from the graph. Therefore, themeaning of the clustering coefficient in this method is different
from the meaning of the clustering coefficient in the two
previous methods. In this method, clustering coefficients ofthe followers are calculated only based on their connection
with the target user and with each other.
The difference is depicted in Figure 3. Each of the two
subgraphs represents our follower-neighbor graph. The nodes

Fig. 3. Subgraphs used for the calculation of clustering coefficients. Twographs are the follower-neighbor graphs of target users u1 and u2 . Filled
circles represent the direct followers of the target users, and nodes at thebottom of each graph are followers/followees of the direct followers. The
graph on the left depicts the subgraph used in the calculation in the first andsecond methods that use the classic clustering coefficient and the directedclustering coefficient. In those methods, we use the entire follower-neighbor
graphs. The graph on the right depicts the subgraph used in the calculationin the third method that uses the weighted undirected clustering coefficient.
In that method, we use subgraphs within the circle which only includes thetarget user and its direct followers.

u1 and u2 at the top of each graph are target nodes, filled
circles represent the direct followers, and nodes at the bottomof each graph are followers/followees of the direct followers.
The graph on the left depicts the subgraph used in thecalculation in the first and second methods that use the classicclustering coefficient and the directed clustering coefficient.
In those methods, we use the entire follower-neighbor graphs.
The graph on the right depicts the subgraph used in thecalculation in the third method that uses the weighted directedclustering coefficient. In that method, we use subgraphs within
the circle which only includes the target user and its direct
followers.
The clustering coefficients of nodes in the produced graphs
are calculated following the definition for weighted undirected
graphs by Onnela et al [10], explained in Section II.
D. Scores based on the number of edges between followers
and the number of 2-hop followers/followees
The previous three methods use variations of the clustering
coefficient. Our fourth method tries to define the metricdirectly following our hypothesis.
For a given follower, the more followers (i.e., 2-hop followers of the target user) it has, the more influential it is, and themore followees it has, the less likely it is a personal friends ofthe target user. In addition, the greater the number of followers
and followees are, the wider the community the follower isconnected to. Therefore, our hypotheses is that followers withthe larger number of followers and followees are expected tomore contribute to the popularity of the target user.
In addition, even if the followers of the target user have
many followers and followees, if the followers are also closely
connected to each other, the communities to which the followers are connected are likely to be limited, and it is a negative
factor in the estimation of the popularity of the target user.
Figure4 illustrates the idea. The red nodes are the direct
followers of the target node u, and the blue nodes are thefollowers/followees of the direct followers. We hypothesizethat the larger the number of blue nodes is, the greater theuand the average number of adjacent blue nodes of the otheropen followers.
IV. E XPERIMENTS

Fig. 4. The overview of our fourth method. The red nodes are the direct
followers of the target node u, and the blue nodes are the followers/followeesof the direct followers. We hypothesize that the larger the number of blue
nodes is, the greater the popularity of u is, and the smaller the number ofedges between red nodes is, the greater the popularity of u is. To represent
the latter, for each follower (a red node), we count the number of connected
red nodes.

popularity of u is, and the smaller the number of edges
between red nodes is, the greater the popularity of u is.
Following these observations, we define the score of eachfollower in our fourth method by the formula below:
score =

log2 (# of non-red nodes adjacent to red nodes + 2)
log2 (# of red nodes adjacent to red nodes + 2)

By taking the inverse of the logarithm of the number of
red nodes adjacent to red nodes, the more adjacent red nodes
the follower has, the smaller the score of the follower is. In
addition, by the logarithm of the number of non-red nodes
adjacent to red nodes (i.e., blue nodes), the more blue nodes
the follower has, the larger the score of the follower is.
The reason for taking the logarithm is the number ofadjacent nodes usually follow power law distribution. We
add 2 to the number of adjacent nodes to prevent the scoresfrom diverging or taking negative values when the number ofadjacent nodes is 0 or 1.
E. Final Score of the target user
Given the score of each follower, we sum up their scoresand the result is used as the score of the target user. Because
we sum up the score of the followers, generally speaking, themore follower the target user has, the higher the score of thetarget user is. However, the followers are not count equally.
They are given scores, which are used as their weight.
In the first three methods that use clustering coefficients,
the score is defined to be 1− coefficient, as explained before.
Therefore, the score takes the value between 0 and 1, and thescore is bigger when the clustering coefficient is small.
A clustering coefficients cannot be defined for locked accounts because we cannot obtain the list of their followers andthe list of their followees. When a direct follower of the target
node is locked, we assign the average score value of the open
(i.e., not locked) direct followers of the target node.
A clustering coefficient of a follower cannot be definedalso when the follower only has one adjacent node. Note thatthey always have at least one adjacent node because they arefollowers of the target node. For such followers, we also use
the average score of the other follower nodes. However, afollower with only one adjacent node is very rare.
Similarly, in the fourth method, if a follower is a locked
account, we use the average number of adjacent red nodes

In this section, we describe the details of the experiment we
conducted, and discuss the result.
We conducted experiments by using the data on Ms/Mr
competitions of the following nine universities in Japan: Komazawa University, Gakushuin University, Ryukoku University, Chuo University, Seikei University, University of Tokyo,
Kwansei Gakuin University, Doshisha University, and Kansai
University.
In the experiment, we collected information on the Twitter
accounts of the female contestants of the competitions of
those universities. Data were retrieved on the day of thecompetition or the day before that for most universities. For
some universities, data were retrieved several days after thecompetition, but the number of followers did not change
significantly during those several days. Therefore, we believethat this does not largely affect the result of the experiment.
We then construct the follower-neighbor graph for eachcontestant, estimate the popularity of each contestant by using
our method, and predict the winner and the runners-up of eachcompetition. We then compare the result of our prediction andthe result of the competitions, which are determined based on
the public popularity.
We also compare the accuracy of our methods with theaccuracy of a simple baseline method. The baseline method
predicts the winner and the runners-up simply based on thenumber of followers of the Twitter accounts of the contestants.
A. Evaluation metrics
We evaluate the accuracy of our methods and the baseline
method by using the following metrics::
1) combination: accuracy where the prediction is regarded
as correct if the winner and the runner-up of the competition are the top-two contestants in the prediction,2) ordered: accuracy where the prediction is regarded ascorrect if the winner is the top contestant in the prediction, and the runner-up is the second best contestant in
the prediction,3) winner only: accuracy where the prediction is regarded
as correct if the winner is the top contestant in theprediction, and
4) separate: accuracy where the prediction of the winners and the prediction of the runner-up are counted
separately. For example, if a method correctly predicted the winners of 3 competitions and the runnersup of 4 competitions, the accuracy of the method is(3 + 4)/(9 + 9) = 7/18.
B. Results
Tables I through IX show the results of the prediction by thebaseline method, which simply uses the number of followers
on Twitter, and our four prediction method, denoted by s1 to
s4, for nine competitions. Each score is rounded down to theTABLE I
KOMAZAWA
No1
No3
No5
No7

# followers
1900
3126
1371
1320

s1
1687
2826
1235
1129

s2
1707
2835
1241
1158

TABLE VII
K WANSEI G AKUIN
s3
1892
3115
1359
1309

s4
3713
5872
2563
2750

result
2nd
1st

TABLE IIG AKUSHUIN
No1
No2
No3
No4
No5

# followers
2489
2577
2836
2694
3212

s1
2149
2385
2536
2374
2931

s2
2167
2389
2548
2393
2943

s3
2475
2568
2827
2685
3210

s4
4607
5223
4929
5211
6373

No1
No2
No3
No4
No5
No6

s1
1546
2341
1016
1582
1052
778

s2
1549
2344
1018
1589
1058
790

1st

s3
1670
2515
1108
1754
1157
889

s4
2732
4004
1642
3234
2110
2048

result

s3
1776
1788
2801
1700
1551

s4
3729
3763
7244
4134
2916

result

s3
2914
2398
3395
919
1300

s4
5422
4403
5549
1837
2709

result

s3
2930
4597
2085
3128
2266

s4
5863
8754
3607
9398
4454

result

1st
2nd

No1
No2
No3
No4
No5

s1
1444
1393
2331
1433
1306

s2
1508
1477
2403
1481
1337

1st
2nd

s1
3430
3380
716
3616
1712
3354

s2
3446
3388
746
3632
1725
3363

s3
3845
3713
849
4000
1926
3647

s4
6511
7060
2000
6748
3752
6315

result

s3
4979
1299
3769
2387
2458

s4
12170
2596
7601
4618
4521

result
1st

s3
2907
2353
3689
2372
1854
1651

s4
5674
3985
7345
4670
3513
2867

result
1st

1st
2nd

TABLE VIII
D OSHISHA

2nd

TABLE IV
C HUO
# followers
1785
1797
2813
1720
1563

# followers
3856
3721
869
4010
1939
3660

resultTABLE IIIRYUKOKU# followers
1680
2520
1114
1767
1165
898

No1
No2
No3
No4
No5
No6

No1
No2
No3
No5
No6

# followers
4994
1310
3785
2400
2471

s1
4014
1093
3004
2015
2184

s2
4159
1118
3089
2047
2202

2nd

TABLE IXK ANSAI
No1
No2
No3
No4
No5
No6

# followers
2919
2366
3694
2378
1865
1662

s1
2487
2170
3420
2147
1671
1517

s2
2511
2176
3432
2160
1683
1523

2nd

TABLE X
S UMMARY# followers
s1
s2
s3
s4

combination
3/9
3/9
3/9
3/9
5/9

ordered
1/9
1/9
1/9
1/9
4/9

winner only
6/9
6/9
6/9
6/9
6/9

separate
7/18
7/18
7/18
7/18
10/18

TABLE VS EIKEI
No1
No2
No3
No4
No5

# followers
2921
2416
3411
938
1310

s1
2662
2159
2969
810
1067

s2
2672
2165
2985
817
1089

2nd
1st

TABLE VI
T OKYO
No1
No2
No3
No4
No5

# followers
2941
4611
2096
3201
2275

s1
2566
3536
1658
2865
2050

s2
2598
3650
1687
2922
2058

2nd
1st

nearest integer number. The column labeled “result” shows thetrue results of the competitions. Each row corresponds to one
contestant, and it shows the number of followers and the score
given by our four methods. Yellow cells are the top contestantin each prediction or in the true result, and blue cells are thesecond best contestant in each prediction or in the true result.
Table I shows that all the baseline and the proposed methods
correctly predicted the winner and the runner-up for thecompetition of Komazawa University. For the competitionof Gakushuin University (Table II), only our fourth method
correctly predicted both the winner and runner-up, and all

the other methods correctly predicted the winner, but wrongly
predicted the contestant No 3 as the runner-up while the true
runner-up was the contestant No 2.
Table X summarizes the total accuracy of the baseline
method and each of the proposed methods over the ninecompetitions. It shows that all the methods are tie for winneronly accuracy, but our fourth method was the best for all theother three accuracy metrics we defined before. This result
validates our two hypotheses that was explained before andshown again below:• SNS users with followers more distributed over the SNS
graph are likely to have more real-world popularity, andtherefore, we can improve the accuracy of the popularity
estimation by using the information on the community
structure of the followers compared with the simple
method solely based on the number of followers.
On the other hand, the accuracy of the other three proposed
methods that use variations of the clustering coefficient were
exactly the same as the accuracy of the baseline method. In
more detail, the prediction by our third method, which uses theweighted directed clustering coefficient, was exactly the sameas the prediction by the baseline method, and the prediction
by the other two methods, s2 and s3, are also the same as theprediction of the baseline method except for the prediction

TABLE XI
KOMAZAWA :T WITTER +I NSTAGRAM
No1
No3
No5
No7

Twi
1900
3126
1371
1320

Ins
3385
4882
2154
5172

sum
5285
8008
3525
6492

s1
2446
3941
1725
2246

s2
2475
3953
1734
2303

s3
2743
4343
1897
2604

TABLE XVIIK WANSEI :T WITTER +I NSTAGRAM
s4
5382
8186
3579
5471

result
2nd
1st

TABLE XIIG AKUSHUIN :T WITTER +I NSTAGRAM
No1
No2
No3
No4
No5

Twi
2489
2577
2836
2694
3212

Ins
3354
4920
2283
3885
3912

sum
5843
7497
5119
6579
7124

s1
2880
3534
3051
3238
3832

s2
2903
3540
3065
3265
3848

s3
3317
3806
3402
3662
4197

s4
6174
7740
5931
7108
8333

No1
No2
No3
No4
No5
No6

Ins
1612
2585
1740
3614
1781
1881

sum
3292
5105
2854
5381
2946
2778

s1
1921
2947
1417
2399
1458
1190

s2
1924
2951
1419
2410
1466
1208

s3
2074
3166
1545
2659
1604
1360

s4
3394
5041
2290
4904
2924
3130

No1
No2
No3
No4
No5

Ins
6677
2500
14625
1832
6092

sum
8462
4297
17438
3552
7655

s1
2808
1882
5390
1818
2592

s2
2932
1996
5558
1879
2653

s3
3452
2415
6477
2157
3077

s4
7249
5085
16749
5245
5784

1st

Twi
2921
2416
3411
938
1310

Ins
2208
3144
5172
948
1816

sum
5129
5560
8583
1886
3126

s1
3171
2868
4105
1017
1440

s2
3182
2876
4128
1025
1470

s3
3470
3186
4694
1153
1755

1st
2nd

result

1st
2nd

s4
6456
5849
7672
2306
3657

result

s4
6588
11779
4471
11717
4875

result

2nd
1st

TABLE XVIT OKYO :T WITTER +I NSTAGRAM
No1
No2
No3
No4
No5

Twi
2941
4611
2096
3201
2275

Ins
1440
6315
1989
3130
852

sum
4381
10926
4085
6331
3127

s1
2883
4758
2055
3573
2244

s2
2919
4912
2091
3644
2252

s3
3292
6186
2585
3900
2481

Twi
4994
1310
3785
2400
2471

No1
No2
No3
No5
No6

2nd
1st

for the competition of Chuo University. These results showthat variations of the clustering coefficient is not large enoughto produce the prediction which is different from the simple
prediction by the number of followers.
C. Additional Use of Instagram Information
All the contestants involved in the previous experimentalso have Instagram account. Therefore, we could apply our
methods also to their Instagram accounts for predicting thecompetition results. However, Instagram does not provide API
for accessing the social graph information, and also forbid thescraping of the information. Therefore, we could not retrieve

sum
10793
9245
2628
13513
4410
12996

Ins
22417
3513
11580
12889
5832

s1
4988
4647
1082
5779
2263
5513

s2
5010
4657
1127
5805
2280
5529

s3
5591
5104
1283
6392
2545
5995

s4
9467
9705
3022
10785
4959
10381

result

s4
25957
4353
13470
10879
7215

result
1st

1st
2nd

sum
27411
4823
15365
15289
8303

s1
8561
1833
5325
4747
3485

s2
8871
1876
5474
4821
3514

s3
10620
2178
6679
5623
3923

2nd

TABLE XIXK ANSAI :T WITTER +I NSTAGRAM

resultTABLE XVS EIKEI :T WITTER +I NSTAGRAM
No1
No2
No3
No4
No5

Ins
6937
5524
1759
9503
2471
9336

TABLE XVIII
D OSHISHA :T WITTER +I NSTAGRAM

2nd

TABLE XIVC HUO :T WITTER +I NSTAGRAM
Twi
1785
1797
2813
1720
1563

Twi
3856
3721
869
4010
1939
3660

resultTABLE XIIIRYUKOKU :T WITTER +I NSTAGRAM
Twi
1680
2520
1114
1767
1165
898

No1
No2
No3
No4
No5
No6

No1
No2
No3
No4
No5
No6

Twi
2919
2366
3694
2378
1865
1662

Ins
4541
2207
3182
3481
2911
1902

sum
7460
4573
6876
5859
4776
3564

s1
3464
2681
4164
2940
2329
1955

s2
3497
2688
4178
2959
2347
1963

s3
4049
2907
4491
3249
2584
2128

s4
7902
4923
8942
6395
4898
3696

result
1st
2nd

TABLE XXVALUATION :T WITTER +I NSTAGRAM
twitter only
Instagram only
sum
s1
s2
s3
s4

combination
3/9
5/9
5/9
5/9
5/9
5/9
4/9

ordered
1/9
3/9
3/9
3/9
3/9
3/9
2/9

winner only
6/9
6/9
7/9
6/9
6/9
6/9
6/9

separate
7/18
9/18
10/18
9/18
9/18
9/18
8/18

the follower-neighbor graph of their Instagram accounts. All
we can easily obtain for their Instagram accounts is theinformation on the number of followers.
Instead of applying our methods to their Instagram accounts,
we developed a method of integrating the information on
the number of followers of their Instagram accounts into
our prediction. Assuming that the structure of the followerneighbor graphs of their Twitter accounts and that of their
Instagram accounts are similar to some extent, we estimate
the score of their Instagram account by the formula below:# Instagram followers 0.106·# Twitter followers
0.42
The Insta-score is the score of the user’s Instagram account,
Twitter-score is the score of the user’s Twitter account estimated by one of our methods, # Instagram followers means
the number of followers of the user’s Instagram account, and# Twitter followers means the number of followers of theuser’s Twitter account. This formula convert the score of theuser’s Twitter account into the score of the user’s Instagram
account by first rescaling the Twitter score up to the size of
the Instagram follower count by using the ratio of the numberof Twitter followers and the number of Instagram followers,
Insta-score = Twitter-score ·and also by normalizing the result by multiplying 0.106/0.42
which is the ratio of the clustering coefficient of Twitter social
graph and Instagram social graph. The value 0.106 is theclustering coefficient of Twitter graph reported by Java et al.
[14], and 0.42 is the clustering coefficient of Instagram social
graph reported by Manikonda et al. [15].
We then sum up the score of the user’s Twitter accountand the score of the user’s Instagram account estimated by
the formula above to produce the final score, which integrates
information from the Twitter and from the Instagram.
The results of the experiment are shown in Tables XI
through XX. In each table, the columns Twi and Ins show
the number of Twitter followers and Instagram followers of
the user, respectively. The column Total shows the sum ofthem. These columns corresponds to three baseline methodthat simply uses these values to predict the winners and therunners-up. The column s1 to s4 shows the prediction basedon the sum of the Twitter score by one of our four methods
and the Instagram score estimated by our conversion method.
Table XX summarizes the accuracy of the three baseline
methods and our four methods. It shows that the simple
baseline method that uses the total number of Twitter followers
and Instagram followers is the best (including tie) in all thefour accuracy metrics. The baseline method that only uses
the number of Instagram followers, and our three methods
that use variations of the clustering coefficient are tie in two
metrics, but inferior to the simple method using the numberof Instagram followers in the other two metrics.
Our fourth method, which was the best in the previous
experiment, is inferior to the method by the number ofInstagram followers in all the four metrics. This result suggeststhat our method converting the number of Instagram followers
into the score by using the Twitter score, in other words, byusing the Twitter graph structure, does not work well. It may
imply the property of a Twitter account and an Instagram
account of the same user are sometimes very different.
Table XX also shows that the method by the number ofInstagram followers is better than the method by the numberof Twitter followers. It can also be a reason why the method
simply using the number of Instagram followers was better
than the method that converts it by using the Twitter score.
Nonetheless, when we only use Twitter information, ourmethod outperforms the method that simply use the numberof followers, as shown in the previous experiment. Therefore,
we expect that our method can outperform the simple methodthat uses the total number of Twitter followers and Instagram
followers if we can retrieve the Instagram social graph andapply our methods to it. Unfortunately, however, Instagram
does not allow it for now.
V. C ONCLUSION
In this study, we proposed a method for estimating the realworld popularity of SNS users, which is different from thesimple number of followers. Our methods take into account not
only the number of followers but also the community structure
within the neighbor of the followers. If a user is followed byfollowers from wider communities, we expect that the user has
more global popularity, and more popular in the real world
than a user with the similar number of followers only from asmaller local communities.
To validate this hypothesis, we conducted an experimentusing data from nine Ms/Mr university competitions. The
result shows that the prediction by one of our method achieves
higher accuracy than the baseline method that predict the
popularity simply by the number of Twitter followers. This
result support our hypothesis that a user with followers fromwider communities is more popular in the real world.
We also developed a method of integrating the informationof the number of Instagram followers into the score by our
methods. We convert the number of Instagram followers into
a score based on the score of the user’s Twitter accountand the ratio of the number of user’s Twitter followers andthe Instagram followers. However, this method was inferior
to a simple method that uses the total number of Twitterand Instagram followers. We expect that our methods canachieve higher accuracy if we can retrieve the social graphof Instagram and apply our methods to it.
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