User Influence and Follower Metrics in a Large Twitter Dataset

Jari Veijalainen

1,2

, Alexander Semenov

1,2

and Miika Reinikainen

University of Jyvaskyla, Department of Computer Science and Information Systems,

P.O.Box 35, FI-40014, Jyvaskyla, Finland

University ITMO, Kronverksky Pr. 49, Saint-Petersburg, Russia

Keywords: Twitter, Social Media Mining, Retweeting, Influence, Message Diffusion, Followers.

Abstract: Social media has become an important means to convey information. The microblogging service Twitter

with about 284 million users and currently over 500 million tweets per day is an example. The site stores all

the tweets once sent so that they can be retrieved later. The site has rather simple site ontology, i.e. the

concepts it implements; the users are represented by a profile. They can follow other users, and a received

tweet can be retweeted to all the followers of a user. In this paper we investigate diffusion of messages and

influence of users on other users, mainly based on the retweet cascade size and attenuation patterns inside

the cascade. We rely on a big data set collected after Boston marathon bombing on April 15, 2013. It

contains about 8 million tweets and retweets sent by over 4 million different users. It was collected through

the Twitter API that selects all the messages containing given keywords, including hashtags. We also

collected all 7-8 billion followers of the above users during 2014. The follower relation is also used in

influence estimations in some respects. The largest cascades originate from users with most followers and

the cascade dies out after two or three frequency peaks.

1 INTRODUCTION

There are hundreds of social media sites in the

world. The number of Facebook users has exceeded

one billion and there are other sites that have tens or

hundreds of millions of users. According to English

Wikipedia, the Chinese microblogging service Sina

Weibo (weibo.com) has currently over 500 million

users, Vkontakte (vk.com) ca. 270 million users, and

LiveJournal had in 2012 ca. 40 million accounts.

The latter two are mainly based in Russia and

controlled by Russian citizens and companies.

There are many more social media sites created

for different purposes, but in this paper we are

concentrating on Twitter, the microblogging service

originating from San Francisco, California. It has

currently 284 million users all over the world and

500 messages (tweets) are sent per day. 80 % of the

users are using mobile devices and 77 % of the users

are living outside the USA. The site supports over

35 different languages. (“About Twitter, Inc. |

About” 2014).

The core concepts Twitter implements in its site

ontology are simple. A human user has a profile (or

account) representing the real user on the site. It is

identified by a (locally) unique screen name of form

@<string>, chosen by the user while registering –

unless altered later. Internally, the site has a locally

unique numeric user_id. It is essentially an integer

for each user that does not change as long as the

account exists (in our data set the smallest user_id is

12, the largest one is 1364151169). A user can send

140 character long messages called tweets and also

send a tweet further to other users. This is called

retweet(ing) and retweets are indicated to the

recipents by “X retweeted” at the beginning of the

message in the user interface. A user can follow

other users. After that, the user can get the public

tweets or retweets sent by the user to be followed. A

user can select a setting on his or her profile that

allows the tweets to be protected. In this case he or

she can select the followers by issuing a separate

confirmation for each user wanting to follow him or

her. The search engine offered by the site to find

tweets and user profiles to be reviewd or to be

followed. In addtion to text, the users can include

digital photos, URIs or screen name into tweets. The

URIs usually refer to web sites that contain longer

articles or videos about the theme the user wants to

convey to others.

The site is location-aware. It means that the

user’s location can be included into the tweet if the

487

Veijalainen J., Semenov A. and Reinikainen M..

User Inﬂuence and Follower Metrics in a Large Twitter Dataset.

DOI: 10.5220/0005410004870497

In Proceedings of the 11th International Conference on Web Information Systems and Technologies (WEBIST-2015), pages 487-497

ISBN: 978-989-758-106-9

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

user has allowed it in the privacy settings. Location

is obtainable as part of the metadata of each

message through the Application Programming

Intefaces (API). A message retrieved through the

API contains further information, such as the actual

(re)tweeted text, retweet flag, the number of

followers, and friends, the user-id/screenname of the

user, time stamp of the tweet (in two formats), used

language, and further information. These can be

used while analysing the temporal and spatial user

behavior, contents transformations, and so on.

The site offers several APIs though which the

user-generated and stored contents, as well as the

followers of a user on the site can be retrieved –

unless the user has indicated in the privacy settings

his or her tweets to be protected. In this case neither

the (re)tweets nor the followers can be retrieved. We

will discuss in a more detail below the APIs we have

used in this study.

2 RELATED WORK

The social media related research has increased

rapidly during the last three to four years. Currently,

for instance Google scholar returns over 15000

articles that contain “social media” in their title,

keyword list, or abstract since 2005. The literature

concerning Twitter analysis is also already

substantial. Therefore, we only concentrate on

major papers that deal with influence analysis in

Twitter.

2.1 Twitter Influence Metrics in the

Literature

A general overview of influence measures in various

social networks can be found in (Sun and Tang

2011). Some approaches, like measuring the strength

of the ties based on the size of the intersection of

follower and followee sets of users might be

interesting in predicting the tweeting behaviour of

users. This requires, however, the collection of

those sets and their analysis. To the best of our

knowledge this has not been done for Twitter users

yet in larger scale. The influence measures have so

far been based mainly on collected tweet sets.

There are several ways to look at influence in

Twitter based on tweets. The first obvious fact is

that if a user never creates and sends a tweet or

retweets tweets he or she receives from other users,

such a user does not influence others in that Twitter

stream. Any reasonable influence measure

Inf(X,Stream)->R should attach a small value, even

zero, for such users X in the Stream. One must still

take into account that in most cases an influence

measure is calculated based on a finite stream of

messages, Stream, captured during a few days,

weeks or months. Which particular users are the

most influential ones during that period of time can

greatly vary and one cannot necessarily generalize

the results to the future or past tweet streams.

A property that a reasonable influence measure

Inf(X, Stream) should measure is “how many other

users received a tweet originally sent by user X in

Stream?”. Intuitively, the more users received the

tweet directly or retweeted, the more the user had

influence on others. It is evident that the more a user

has followers the more potential influence he or she

has. This is because any (re)tweet the user sends is

received and hopefully read by a large number of

people. Further, the more followers the user has the

larger absolute potential the tweet also has to

become retweeted, and so on. The maximum number

of people that potentially received the tweet, either

directly from the user who created it or retweeted by

followers, can be calculated directly from the tweets

in the stream, because the metadata in the message

obtained through the Twitter API contains the

number of followers of the user.

The cast size, i.e. the number users who received

a tweet as retweeted can be used as a separate

measure for the perceived importance of the original

tweet, and thus for the influence of the originating or

“seed” user.

Thus, a rudimentary influence measure for user

X in a particular Stream can be defined as follows

Infr(X,Stream) = p1*Mx*Fx+

+p2*RTm1+..+pmx*RTmMx, where

Mx = number of seed tweets sent by X,

Fx = number of followers of X

RTmi = Fmk1+Fmk2+Fmki is the combined number

of followers of those users Xmk1..Xmki who

retweeted message mi, 0< i < Mx+1, i.e. it is the

potential receiver set size of message mi with cast

size ki. Each 0<=pi<=1 is an adjustment coefficient

(see below) that tells which fraction of followers are

passive or addressed several times. Setting pi=1 for

all i, the overall measure sums up the potential

receiver set sizes for all seed tweets of user X.

The rudimentary measure above tries to answer

the question how many users got the tweet initiated

by X, but overestimates the influence of X in the

sense that the follower sets of different users are

usually overlapping. Thus, the set of different users

who received the tweet is in reality smaller, as some

users can receive the retweeted message several

times from different users they follow. Further, not

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all users even read the tweet (sender might be even

muted), not to speak about retweeting. Therefore, pi

<1 usually holds. The minimum value is obtained by

calculating the fraction of followers that retweeted a

tweet in the chain. An upper bound for a particular

pi is obtained by calculating

pi= |Fx U Fmk1 U Fmk2.. U Fmki|/RTmi, i.e.

removing the effect of common followers.

Calculating the coefficients pi requires collection

of followers of all those users who tweeted or

retweeted something in a Stream.

A further idea to measure the influence of a user

is to count the mentions of that user in other user’s

tweets or retweets. Intuitively, the more mentions

the user gathers in the data set, the more influence he

or she has in the community. This can also be

calculated directly from a Stream in one pass. The

above rudimentary measure can be enhanced by this

aspect in various ways. An obvious one is to add for

each such tweet issued by user Y, mY, a term RTmk

to the cast count of X, as if the mention was a

retweet of a seed tweet of X.

Tweets can contain URLs that refer to web

sources. One can also measure how many receivers

click the ULRs in the tweets. The click confirms that

the receiver reacted to the tweet and presumably

accessed the contents pointed by the URL. One can

also measure how the presence of URLs and

hashtags in tweets influence the retweeting activity.

This is measured by the cast size RTmi above and

correlations with it and the tweet content can be

established (see below)

A further idea is to measure the development of

the potential influence of certain user X over time.

Intuitively, if user X had a year ago 10 followers and

now 10000 followers, the potential influence of that

user is now intuitively at least 1000 times higher

than a year ago. Calculating the measure can be

based on the follower numbers at certain points of

time obtained from a suitably large tweet set

(spanning a year) or accessing the data through a

suitable Twitter API or both.

The above basic ideas have been applied in

various forms and combinations in the literature.

There are also further orthogonal ideas. We discuss

both of them below shortly. A study made about

four years ago (Bakshy et al. 2011) investigated the

cascade size in a data set of 1.6M Twitter users

contributing to 74 million diffusion events. One

finding was that it is not clear how to identify the

influencers that would most probably spread the

tweets further. The authors ponder extensively what

kind of marketing strategies could be developed

based on the Twitter users that mostly “influence”

other users. The authors use as the influence

measure the size of the cascade, that is, the number

of retweets of the original message, but do not take

into account the follower numbers of retweeters.

They also measure the depth of the cascade, that is,

how many users there are on the longest path where

the same (re)tweet was retweeted. The observed

maximum depth was 9. The current Twitter API 1.1

does not allow this measure to be computed.

Korean researchers (Kwon and Han 2013)

investigated in their article how content

dissemination from the web sites (see above URLs)

other than Twitter itself influences the cascade size

of the Tweets. They concentrated on tweets in

Korean language. The authors write: “Source

influence and peer-referrals have a positive impact

on cascade size in the content dissemination. In the

case of contents crossover the impact of source

influence decreases. However, the impact of peer-

referrals increases in external content

dissemination.

In (Suh et al. 2010) the authors wanted to

understand why certain tweets spread more widely

than others by investigating the features of tweets

that have a potential for retweetability. The study

draws on 74 million individual tweets. According to

the study, URL´s and hashtags amongst content

features, have strong correlation with retweetability.

Among the contextual features, the number of

followers and followees also affect retweetability.

The study (Galuba et al. 2010) examined the

information propagation laws in a 300 hour data set

containing 15 million tweets and 2.7 million users.

A propagation model was proposed to predict power

laws in user activity and predicting the hops of

cascades into sub cascades. An information

propagation model predicting which users are likely

to mention which URLs was also proposed. Findings

were that the user activity and the frequency of URL

mentions are distributed according to power-law.

Also so-called “power user’s” URLs were tweeted

more than others because those users had many

followers and the tweets they contributed tend to be

interesting and viral. The authors also write: “The

URL cascades were shallow with exponentially

falling off height. They are composed of sub

cascades whose both number and size follow power-

law distributions.”

Information diffusion has been studied in (Hui et

al. 2012) by using tweets from an actual crisis

events. The focus was to show how tweets spread

among the users on Twitter including observations

about the users involved and information cascades.

In (Cha et al. 2010) the authors compared three

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different measures of influence: indegree, retweets

and mentions. The authors collected data over a

period of 8 months and investigated the degree of

influence among the users over this time period from

different perspectives. It varied over time. Perhaps

the most interesting finding was that gaining

influence is not accidental, but requires targeted

effort from the users.

The study by (Romero et al. 2011) took into

account the passivity of the followers while

determining the influence; The authors state “Our

influence measure utilizes both the structural

properties of the network as well as the diffusion

behaviour among users. The influence of a user thus

depends not only on the size of the influenced

audience, but also on their passivity.” The authors

observe that their measure predicts well the URL

clicking activity of the users receiving the tweets.

Another set of model sexists for measuring user

influence. An algorithm called TwitterRank was

proposed in (Weng et al. 2010) for measuring the

user influence taking both topical similarity between

users and the link structure into account. The latter

measures the reciprocal follower relationship among

Twitter users. In the data set of the authors roughly

80 % of the users followed each other. This is

explained by homophily. The data set consisted of

about 1 million tweets gathered in 2009.

In (Yang and Leskovec 2010) a linear influence

model was proposed to measure information

diffusion and influence of nodes in Twitter. The data

set included 500 million tweets and a set of 170

million news media articles. One of the main

observations was that the users with the most

followers were not the most influential in terms of

tweet propagation.

2.2 Further Metrics of Relevance

A recent article (Bruns and Stieglitz 2013) discusses

methodical issues that are of relevance here, because

we have used a very similar approach while

collecting our data set, namely the keyword-based

API. Our aims in the research are also somewhat

similar as those of the authors, i.e. to investigate the

activity of various users in the data set over time and

their influence in the discussions. The messages in

our data set were collected using mostly hashtags

that tie together the messages in the overall stream,

although our keywords (Boston and bombing) did

not contain the #-sign. What the authors say about

the completeness of the data set is relevant also in

our case. We only collected one data set over a

period of time of ca. 5 days in April 2013, and not

many in parallel. Therefore, we cannot be fully sure

that the Twitter API returned all the matching

tweets. On the other hand, in our case this is not

very essential, because the data set is large and we

are interested in influence and diffusion.

The article above has many metrics we can use

directly in our research. User activity metrics tell

how active a particular user has been in generating

tweets and retweets during the observation period.

Visibility metrics measures the number of mentions,

replies and retweets received by a particular user.

Temporal metrics measure the distribution of user

activity over time, e.g. tweets, retweets etc. per

every minute/15 minutes/hour during the

observation period.

Another recent and relevant article is (da Cruz

and Menezes 2015) where the authors have

measured the influence of non-famous users. They

also introduced essentially the metrics discussed

above that takes into account the number of

followers of the user, the number of tweets created

by the user and the number of retweets those tweets

gained, i.e. the cascade size (see above).

Whereas the previous approaches primarily

measure the influence a user had in the past in a

dataset, the authors of (Cheng et al. 2014)

investigate to which extent it is possible to predict

the final cascade size and thus influence of certain

users. To develop and test their approach the authors

have used a complete photo-resharing data from

Facebook over a month. Their results seem

promising for this kind of contents and Facebook

platform, but to which extent they can be

generalized to tweets in Twitter and further

platforms and contents hosted by them remains to

be seen.

3 DATA COLLECTION AND

METHODS

The original data collection was started on April 15,

2013 about an hour after the news from the Boston

bombing was spread throughout the world. It

continued ca. 5 days. The data was collected using

the Twitter Rest API operational during the above

period of time that accepts keywords as parameters.

The keywords used were “Boston”, and “bombing”

No hash-tag sign # was used in keywords.

The data set is a set of ca. 8 million messages

stored into a PostgreSQL database originally in

JSON format. From these messages different users

were picked up and their screen name and user_id

stored into another database table, along with a

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running internal identifier, and number of friends.

There are ca. 4150000 different users in the data set.

In April 2014 we started a collection of the

follower relation, in order to investigate the

networking of the users and the spreading density of

the retweets among the followers. The collection

was idle during July-October 2014 and was

continued in November-December 2014. We have

used the Tweepy software package

(https://pypi.python.org/pypi/tweepy) as part of our

collection software.

The collector software is a Python program with

about 150 lines of code. It is designed to run in

parallel with itself and about 100 copies were in

operation simultaneously on a virtual cloud server.

The collection is fragile in the sense that the

collector processes can crash for various reasons.

The collector crashes cause the problem that there

might be partially collected follower data in the

result relation. In this case the collector must be

restarted and it recollects the followers once

collected already. This is unavoidable, because the

Twitter API does not offer recovery features. The

collector crash problem is aggravated by the fact that

if the user has e.g. 10 million followers, it takes at

least 33 hours to collect them. Evidently, the

probability of a crash of the collector is the higher

the longer it takes to collect the followers of one

user.

Another issue is that not all users get their

followers collected. There can be several reasons for

this, but the most common is that the user has set on

the flag protected (see above) on his or her account.

Thus, there is a substantial hole in the follower data,

as up to 15% of the users do not expose their

followers.

As mentioned above, the follower collection has

been made over a year after the original message

data set was collected. This means that most

probably the followers the users in the data set had

back in April-July 2013 are not the same as those in

April- December 2014. They also differ from the

follower numbers recorded to the metadata of the

tweets from April 2013. For instance Justin Bieber

had on April 15, 2013 about 38 million followers

and in December 2014 about 58 million.

4 THE MAIN RESULTS

In this section we report the main results of the

analysis. We first report some average numbers and

follower distributions. We then treat the answers to

the actual research questions.

4.1 Main Characteristics of the Data

Set

The average numbers of followers in a subset

consisting of randomly selected 1820000 users is ca.

2060 users. There are 14 users that have more than

10 million followers (see Table 1). Those with an

exact follower count were collected in December

2014 by our software. The others were collected in

the summer 2014, but because the follower number

was considerably smaller than the real one in

December, it was corrected manually to this paper

by visiting the Twitter profile of the users. We see

that one of entities with most followers is New York

times and the other one BBC World Breaking News.

SportsCenter is a business entity, TheEllenShow is a

TV show hosted by Ellen DeGeneres, and MTV is a

TV channel. The rest are individuals, like Selena

Gomez, a singer and actress. Mohamad bin Abdul

Rahman al-Arefe is a Saudi-Arabian imam, and Neil

Patrick Harris (ActuallyNPH) is another actor,

producer, director, and magician. Finally Justin

Bieber (justinbieber), a famous celebrity was also

included into our data set, along Alecia Beth Moore

(Pink), Alejandro Sanz (AlejandroSanz), Lil Wayne

(LilTunechi), Kimberly Kardashian West

(KimKardashian), and Alicia Keys (aliciakeys).

According to http://twitaholic.com/top100/followers

the person with most followers in Twitter was Katy

Perry with about 62 million followers in Dec. 2014

and the second was Justin Bieber with ca. 58 million

followers, just barely above president Obama. From

the profile of BBC Breaking News one sees that

after the exact collection of the followers a few days

earlier in December 2014 the follower count has

increased by about 100000 followers.

Table 1: The users with over 10 million followers.

Twitter_id #of followers Twitter_name

807095 14188280 nytimes

23375688 25000000 selenagomez

90420314 11800000 ActuallyNPH

219255067 10300000 MohamadAlarefe

5402612 12249051 BBCBreaking

27260086 58000000 justinbieber

35094637 20600000 aliciakeys

15846407 36800000 TheEllenShow

26257166 12350924 SportsCenter

25365536 27000000 KimKardashian

43152482 11885524 AlejandroSanz

116362700 20000000 LilTunechi

28706024 25000000 Pink

2367911 11695294 MTV

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As is to be expected in a social network, the

distribution of the number of followers is heavily

skewed also in our data set. Figure 1 shows that

many users only have one follower, and a really few

have more than thousand followers. The average

number of followers is ca. 2130, but the median is

around 280 in the collected data set (in 2014).

Overall ca. 62 % of the users in the data set have

more than 100 but less than 1000 followers and ca.

18 % has between 10 and 100 followers, that is, ca.

80 % have between 10 and 1000 followers and ca.

98 % of the users have between 0 and 10000

followers. Figure 1 shows the follower numbers.

4.2 Main Characteristics of the Tweet

Set

In total, dataset contains 8090803 tweets. Of these,

4347107 are retweets, and 3743696 are not.

Figure 1: The followers’ distribution.

Figure 2: Twitter message frequency, without retweets.

754548 original messages (ca. 9 %) were retweeted

at least once, thus about 37% were never retweeted,

see figure 4. The first collected message in our data

set was posted to Twitter at 2013-04-15 20:17:18

UTC. As some of the collected messages are

retweets of earlier messages, there are 20691

message having timestamp earlier than 2013-04-15

20:17:18 UTC. Minimal timestamp equals to 2009-

04-21 17:52:57 UTC. Figures 2 and 3 show

messages frequency.

Figure 3: Twitter messages frequency, including retweets.

Figure 4: Tweets and retweets.

The latest timestamp in the present collection equals

to 2013-04-19 11:04:29 UTC. In average, there were

91706 messages per hour. The number of tweets per

hour during April 15 in our data set was at most a

few ten before the bomb explosions. The number of

tweets exploded after that to over 10000 tweets per

hour after18:49 UTC. Table 2 shows the messages

with timestamps around 18:49. So, the first message

in our dataset, related to the bombing was posted at

18:52:56.

Table 3 shows the mostly retweeted tweets,

screen name of the user who sent the seed tweet, the

number of retweets and the number of followers of

the user. Although many of the users who sent these

10 tweets have a large number of followers, there is

no clear correlation between the number of followers

and retweets. For example, the 4

tweet is posted by

a user having 5783 followers, but it was retweeted

32349 times. 72539 of Justin Biebers followers

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retweeted the #PrayForBoston, yielding min pjb

=0.2 % for the passivity coefficient.

Table 2: Messages posted as the 1

bomb exploded.

time Text