social behavior patterns_short

5 mm

Inset: The displacement field demonstrates local heterogeneities in the flow.

A typical snapshot of an experiment: The white spots indicate the positions of the beads floating on surface waves.

[email protected]

http://fcxn.wordpress.com ! Month 6 General Meeting

http://xn.unamur.be

Fluctuations drive viral memes in online social media: Integrating criticality into network science

Ceyda Sanl, Vsevolod Salnikov, Lionel Tabourier, and Renaud Lambiotte

CompleXity Networks, naXys, University of Namur, Belgium.

To spread our posts throughout online social network such as Twitter: When do we need to post? How often should a #hashtag be posted? These questions emphasize the time features of our twitting activity. They would be controlled much more easily compared to the followings: What we post and how many number of followers we have.

To be mobile in dense granular media such as highly packed beads on surface waves: Do single beads move independently or form a group? Is the trajectory of each bead regular in time? The quantification of the bead dynamics shows that the beads perform heterogenous motion with a distinct time scale to characterize this heterogeneity.

restricted amount of attention restricted amount of space

Restricted amount of sources forces social and physical systems to present emergence of order.

hypothesis

Twitter users want to spread their messages and beads under driving want to be mobile. As a result, the twitter users collectively advertise and the beads form groups to move together. Both systems self-organize and create dynamic heterogeneity.

The origin of the fluctuations in dynamics would be the same origins:

Therefore, the interpretation of the dynamic heterogeneity of the beads in a critical limit would help to characterize viral memes (#hashtags) in twitter.

Refs: 1 C. Sanl et al. (arXiv - 2013). 2 L. Berthier (2011).

Refs: 1 H. Simon (1971). 2 L. Weng et al. (2012). 3 J. P. Gleeson et al. (2014).

0 12 24 36 48 60 72 840

10

20

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40

time (hours)

num

ber o

f tw

eets

/uni

t tim

e daily tweet cycles

propogations of #hashtags 0 10 20 30 40 50 60 70 80 90

0

5

10

15

20

25

4(l=

2R,

)

(s)

=0.652=0.725=0.741=0.749=0.753=0.755=0.760=0.761=0.762=0.766=0.770=0.771

(a)

4(l, )

h

4(l, )

mobility of beads

spatiotemporal granular flow

time

0.2

0.6

1

1.4

1.8

*

P(r

=2

R,t

)M

M

Twitter #hashtag analysis

single beads: groups:

perim

eter

quantifying dynamic heterogeneity:

time (s) 0 0.5 1 1.5 2

[Ref:2]

[Ref:2]

#nice: #pepsi:

observation: artificial representation:

0 10 20 30 40 50 60

time (hours) 0 1 2 3 4 5 6 7 8

time (hours)

analysis:

time (hours)

cum

ulat

ive

time (hours)

cum

ulat

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5 mm



[email protected]


http://xn.unamur.be








hypothesis






0 12 24 36 48 60 72 840

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40

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f tw

eets

/uni

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15

20

25

4(l=

2R,

)

(s)

=0.652=0.725=0.741=0.749=0.753=0.755=0.760=0.761=0.762=0.766=0.770=0.771

(a)

4(l, )

h

4(l, )

mobility of beads


time

0.2

0.6

1

1.4

1.8

*

P(r

=2

R,t

)M

M



perim

eter


time (s) 0 0.5 1 1.5 2

[Ref:2]

[Ref:2]

#nice: #pepsi:


0 10 20 30 40 50 60

time (hours) 0 1 2 3 4 5 6 7 8

time (hours)

analysis:

time (hours)

cum

ulat

ive

time (hours)

cum

ulat

ive

Social Dynamic Behavior Patterns

@CeydaSanli

CompleXity Networks

5 mm



[email protected]


http://xn.unamur.be








hypothesis






0 12 24 36 48 60 72 840

10

20

30

40

time (hours)

num

ber o

f tw

eets

/uni

t tim



0

5

10

15

20

25

4(l=

2R,

)

(s)

=0.652=0.725=0.741=0.749=0.753=0.755=0.760=0.761=0.762=0.766=0.770=0.771

(a)

4(l, )

h

4(l, )

mobility of beads


time

0.2

0.6

1

1.4

1.8

*

P(r

=2R

,t)

MM



perim

eter


time (s) 0 0.5 1 1.5 2

[Ref:2]

[Ref:2]

#nice: #pepsi:


0 10 20 30 40 50 60

time (hours) 0 1 2 3 4 5 6 7 8

time (hours)

analysis:

time (hours)

cum

ulat

ive

time (hours)

cum

ulat

ive

August 31, 2015, Meeting.

Research Questions

Social Dynamic Behavior Patterns 1C. Sanli, CompleXity Networks, UNamur

data science behavior

science

nonequilibrium physics

? online social media computational

social science

complex networks

complex systems

(bursts)

(dynamic heterogeneity)

Research Interests

C. Sanli, CompleXity Networks, UNamur

hashtag diffusion in Twitter

communication patterns of online users

timeSocial Dynamic Behavior Patterns 2

circadian human behavior (internal)

elections, discoveries, etc. (external)

complex decision-making

RT + @ RE

WHO WHOM

aU : activity of users

RT

@

RE

RT + @ RE

pU : popularity of users

RT

@

RE

KPI

Discrete Digital to Continuous Behavior


Not everything is connected (structure), no homogeneity in time (temporal) = complexity

What do we measure from the data? = challenge

Social Dynamic Behavior Patterns 3

{hash":["OptimizRBudapest"],"source":"stream","user_alias":"ateknea","corpus":["en"],"text":"See you all in August 26-27, 2015! #OptimizRBudapest @CeydaSanli,"_id":"010101010","date":1440499664,"at":[{"type":"","alias":"CeydaSanli"}], "user_id":"101010101"}


Two Examples from My Research: Local Variation of

Hashtag Spike Trains and Popularity in Twitter

Temporal Patterns of Online Communication in Spreading a Scientific Rumor: How Often, Who Interacts with Whom?

C. Sanl and R. Lambiotte, PLoS ONE 10(7): e0131704 (2015).

C. Sanl and R. Lambiotte, Frontiers in Physics: Computational Social Science 3(79), (2015).


The UpshotPOWER OF FICTION

Why Rumors Outrace the Truth OnlineSEPT. 29, 2014

Photo

CreditTomi Um

Brendan Nyhan@BrendanNyhan

Continue reading the main storyShare This Page

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Information Diffusion in Twitter


tweets retweets (RT) mentions (@) replies (RE)

Tomi Um


Hashtag Diffusion in Twitter


hashtag

hashtag spike train

time

coun

t

Social dynamic behaviour patterns 1

I. Part:

II. Part: RT + @ RE

WHO WHOM


RT

@

RE

RT + @ RE


RT

@

RE

Spike Trains


time

coun

t

t t0 f

I. LOCAL VARIABLE OF A TIME SERIES

Time series in social system include interaction among agents. Considering online social

network such as Twitter, we address self-organized optimizing of popularity of information.

To this end, we create time series of #hashtag propogation, user activity, and user #hashtag

activity.

In a time series, if a time delay between successive events, inter-event interval , is a

resultant of independent events, the distrubution of inter-event interval is Poissonian. If not,

many bursty events are observed and therefore forward propogation of a signal is a function

of its temporal history. Thus, quantifying is crucial.

Local variable Lv is an alternative way to characterize whether a time series is Poissonian

or non-Poissonian. For a stationarly process, Lv is a ratio of the dierence between the

inter-event interval of forward event and the inter-event interval of backward event to the

sum of these inter-event intervals. Suppose that a signal propogates in distinct time such as

1 . . . , i1, i, i+1, . . . N . Then, at i, the inter-event interval of forward event is i+1 =

i+1 i and the inter-event interval of backward event is i = i i1. Consequently, Lvis

Lv =3

N 2

N1X

i=2

(i+1 i) (i i1)(i+1 i) + (i i1)

2=

i+1 ii+1 + i

2. (1)

Here, N is the total appearance of a time series in distinct times. Multiple activity in same

i is ignored.

If Lv = 1 the distribution of the inter-event interval of a time series is Poissonian. If a

time series considers significant amount of bursty activity, the distribution is non-Poissonian.

When N < 3 the distribution is automatically assumed to be Poissonian.

II. LIMITS OF Lv

Rank of a time series can be defined as how many activity proceeded in distinct times i.

If events occur in multiple dierent i, N 3, the signal has high rank. If a time serie is

too short, N 3, the signal has low rank.

2

100

102

104

106

0

50

100

150

200

250

300

rh

Fv

< rh>=11

< rh>= 2

Real activity(a)

FV = 1

100

102

104

106

0

50

100

150

200

250

300

rh

Fv

< rh>=11

< rh>= 2

(b) Random activity

FV = 1

FIG. 7. Local variation Lv of single #hashtag time series versus low rank rh of the corresponsing

#hashtag. (a) Real #hashtag propogation. (b) Randomly selected #hashtag activity from real

data set.

0 50 100 150 200 250 300 350

0

0.5

1

1.5

2

2.5

3

3.5

h (hour)

Lv

< r

h>=91127

< rh>=18553

< rh>= 1678

< rh>= 318

< rh>= 174

< rh>= 117

< rh>= 86

< rh>= 68

< rh>= 56

< rh>= 47

< rh>= 41

< rh>= 35

Real activity(a)

0 50 100 150 200 250 300 350

0

0.5

1

1.5

2

2.5

3

3.5

h (hour)

Lv

< rh>=91127

< rh>=18553

< rh>= 1678

< rh>= 318

< rh>= 174

< rh>= 117

< rh>= 86

< rh>= 68

< rh>= 56

< rh>= 47

< rh>= 41

< rh>= 35

FIG. 8. Local variation Lv of single #hashtag time series versus life time (h) of the corresponsing

#hashtag. (a) Real #hashtag propogation. (b) Randomly selected #hashtag activity from real

data set..

5

I. DAILY CYCLE OF #HASHTAGS

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 24:000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1 day (hour)

PD

F (

no

rma

lize

d p

rob

ab

ility

de

nsi

ty)

of

#h

ash

tag

s

total

rush hour

dead hour

FIG. 1. Daily activity of #hashtags: Normalized probability density (PDF) of the activity versus

day time.

II. HETEROGENEITY IN POPULARITY AND LIFE TIME OF #HASHTAGS

104

102

100

102

104

100

101

102

103

104

105

106

h (hour)

r h

r =2h

FIG. 2. Rank of #hashtag rh versus life time of #hashtag h.

2

. . .


00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 24:000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1 day (hour)

PD

F (

no

rma

lize

d p

rob

ab

ility

de

nsi

ty)

of

#h

ash

tag

s

total

rush hour

dead hour

FIG. 1. Daily activity of #hashtags: Normalized probability density (PDF) of the activity versus

day time.

II. HETEROGENEITY IN POPULARITY AND LIFE TIME OF #HASHTAGS

104

102

100

102

104

100

101

102

103

104

105

106

h (hour)

r h

r =2h

FIG. 2. Rank of #hashtag rh versus life time of #hashtag h.

2


00:0012:0000:0012:0000:0012:0000:0012:0000:0012:0000:0012:0000:000

10

20

30

40

50

60

70

80

hour

count/m

in.

#ledebat

#hollande

#sarkozy

#votehollande

#fh2012

#france2012

FIG. 1. ...

hpi =

p

2


= popularity


Local Analysis on Hashtag Spike Trains


hash

tag

coun

t

time

Populars are Regular


8

0

5

10

15

20

25

30

0 1 2 3 4 50

5

10

15

20

25

30

=91127 =18553 = 1678 = 318 = 174 = 117 = 86 = 68 = 56 = 47 = 41 = 35

=91127 =18553 = 1678 = 318 = 174 = 117 = 86 = 68 = 56 = 47 = 41 = 35

LV

P(

)L V

P(

)L V

Real activity(a)

Random activity(b)

FIG. 7. Probability density function (PDF) of the local vari-ation LV of real hashtag propagation (a) and random hash-tag time sequence (b). Two distinct shapes are visible: (a)From high p to low p, the peak position of P (LV ) shifts fromlow values of LV to higher values of LV . (b) P (LV ) alwayspeaks around 1 for the random sequences generated by arti-ficial hashtag spike trains. The same color coding is appliedas used in Fig. 6.

14 (ACM, New York, NY, USA, 2014) pp. 913924.[9] U. Frana, H. Sayama, C. McSwiggen, R. Daneshvar, and

Y. Bar-Yam, ArXiv e-prints (2014), arXiv:1411.0722[physics.soc-ph].

[10] A. Mollgaard and J. Mathiesen, ArXiv e-prints (2015),arXiv:1502.03224 [physics.soc-ph].

[11] J. Ratkiewicz, S. Fortunato, A. Flammini, F. Menczer,and A. Vespignani, Phys. Rev. Lett. 105, 158701 (2010).

[12] J. Borge-Holthoefer, A. Rivero, I. Garca, E. Cauh,A. Ferrer, D. Ferrer, D. Francos, D. Iiguez, M. P. Prez,G. Ruiz, F. Sanz, F. Serrano, C. Vias, A. Tarancn, andY. Moreno, PLoS ONE 6, e23883 (2011).

[13] S. Gonzlez-Bailn, J. Borge-Holthoefer, A. Rivero, andY. Moreno, Sci. Rep. 1, 197 (2011).

[14] K. Sasahara, Y. Hirata, M. Toyoda, M. Kitsuregawa, andK. Aihara, PLoS ONE 8, e61823 (2013).

[15] D. Y. Kenett, F. Morstatter, H. E. Stanley, and H. Liu,PLoS ONE 9, e102001 (2014).

[16] F. Deschtres and D. Sornette, Phys. Rev. E 72, 016112(2005).

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

LV (t1)

L V(t 2

)

101 102 103 104 1050

0.2

0.4

0.6

0.8

1

r (L V

(t 1),

L V(t 2

))

(a)

(b)

=91127 =18553 = 1678 = 318 = 174 = 117 = 86 = 68 = 56 = 47

bursty regular

FIG. 8. Linear correlation of LV through real hashtag spiketrains. (a) The linear relation of the first and the secondhalves of the empirical spike trains, LV (t1) and LV (t1), re-spectively, are investigated. The legend ranks hpi in dierentcolors and symbols. (b) The Pearson correlation coecientr(LV (t1), LV (t2)) between these quantities show that whilethe temporal correlation through moderately popular hashtagis maximum, r reaches the minimum values for both bursty(high LV and low p) and regular (low LV and high p) spiketrains.

[17] L. Weng, F. Menczer, and Y.-Y. Ahn, Sci. Rep. 3, 2522(2013).

[18] J. Cheng, L. Adamic, P. A. Dow, J. M. Kleinberg, andJ. Leskovec, in Proceedings of the 23rd International Con-ference on World Wide Web, WWW 14 (ACM, NewYork, NY, USA, 2014) pp. 925936.

[19] L. Weng, A. Flammini, A. Vespignani, and F. Menczer,Sci. Rep. 2, 335 (2012).

[20] J. P. Gleeson, J. A. Ward, K. P. OSullivan, and W. T.Lee, Phys. Rev. Lett. 112, 048701 (2014).

[21] U. Cetin and H. O. Bingol, Phys. Rev. E 90, 032801(2014).

[22] J. P. Gleeson, K. P. OSullivan, R. A. Baos, andY. Moreno, ArXiv e-prints (2015), arXiv:1501.05956[physics.soc-ph].

[23] S. Shinomoto, K. Shima, and J. Tanji, Neural Comput.15, 2823 (2003).

[24] S. Koyama and S. Shinomoto, Journal of Physics A:Mathematical and General 38, L531 (2005).

[25] K. Miura, M. Okada, and S. ichi Amari, Neural Comput.18, 2359 (2006).

8

0

5

10

15

20

25

30

0 1 2 3 4 50

5

10

15

20

25

30

=91127 =18553 = 1678 = 318 = 174 = 117 = 86 = 68 = 56 = 47 = 41 = 35

=91127 =18553 = 1678 = 318 = 174 = 117 = 86 = 68 = 56 = 47 = 41 = 35

LVP(

)

L VP(

)

L V

Real activity(a)

Random activity(b)











0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

LV (t1)

L V(t 2

)

101 102 103 104 1050

0.2

0.4

0.6

0.8

1

r (L V

(t 1),

L V(t 2

))

(a)

(b)

=91127 =18553 = 1678 = 318 = 174 = 117 = 86 = 68 = 56 = 47

bursty regular











8

0

5

10

15

20

25

30

0 1 2 3 4 50

5

10

15

20

25

30

=91127 =18553 = 1678 = 318 = 174 = 117 = 86 = 68 = 56 = 47 = 41 = 35

=91127 =18553 = 1678 = 318 = 174 = 117 = 86 = 68 = 56 = 47 = 41 = 35

LV

P(

)L V

P(

)L V

Real activity(a)

Random activity(b)











0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

LV (t1)

L V(t 2

)

101 102 103 104 1050

0.2

0.4

0.6

0.8

1

r (L V

(t 1),

L V(t 2

))

(a)

(b)

=91127 =18553 = 1678 = 318 = 174 = 117 = 86 = 68 = 56 = 47

bursty regular











hashtag dynamics artificial dynamics

ranking popularity



Bursty versus Regular


1 2 3 4 5 6

00.20.40.60.8

11.21.41.61.8

log ()

realrandom

(

) L V

10

real hashtags:decay in with increasing p

2010

01020304050

zva

lues (LV) = 1

realrandom

0 0 =

(a)

(b)

1 2 3 4 5 6

00.20.40.60.8

11.21.41.61.8

log ()

realrandom

(

) L V

10

real hashtags:decay in with increasing p

2010

01020304050

zva

lues (LV) = 1

realrandom

0 0 =

(a)

(b)

bursty

regular



KPI


Local Analysis on Communication Spike Trains


user

co

unt

time

Populars are Random

C. Sanli, CompleXity Networks, UNamur Social Dynamic Behavior Patterns 11

0

5

10

15

20

25

WH

O:

< aU>=190< aU>=112< aU>= 84< aU>= 44< aU>= 25< aU>= 17< aU>= 12

0 1 2 3 40

10

20

30

40

50

60

< pU>=4418< pU>=1037< pU>= 570< pU>= 193< pU>= 48< pU>= 18< pU>= 11

P(

)L V

WH

OM

: P(

) L V

LV

(a)

(b) popularityof the user increases, the patterns become regular

activityof the user plays no role

0

5

10

15

20

25

WH

O:

< aU>=190< aU>=112< aU>= 84< aU>= 44< aU>= 25< aU>= 17< aU>= 12

0 1 2 3 40

10

20

30

40

50

60

< pU>=4418< pU>=1037< pU>= 570< pU>= 193< pU>= 48< pU>= 18< pU>= 11

P(

)L V

WH

OM

: P(

) L V

LV

(a)



0

5

10

15

20

25

WH

O:

< aU>=190< aU>=112< aU>= 84< aU>= 44< aU>= 25< aU>= 17< aU>= 12

0 1 2 3 40

10

20

30

40

50

60

< pU>=4418< pU>=1037< pU>= 570< pU>= 193< pU>= 48< pU>= 18< pU>= 11

P(

)L V

WH

OM

: P(

) L V

LV

(a)



always bursty

RT + @ RE

WHO WHOM


RT

@

RE

RT + @ RE


RT

@

RE

KPI

Sanli et al. Temporal Pattern of Online Communication Spike Trains

1 1.5 2 2.5 3 3.5 4

log ()10 U

(d)

1 1.5 2 2.5 3 3.5 4

log ()10 U

WH

OM

: rik

k, (c)

0

0.2

0.4

0.6

0.8

1

1 1.5 2 2.5 3 3.5 4

log ()10 U

(b)

1 1.5 2 2.5 3 3.5 4

log ()10 U

WH

O: r

ikk,

(a)

0

0.2

0.4

0.6

0.8

1

r

r

full,RT

full,@

-RT

-@

U

U

r

r

full,RT

full,@

-RT

-@

U

U

Figure 7. Linear correlations of LV of the same users: The procedure and representation of the coef-ficients follow the same procedure as introduced in Fig. 6. However, we now impose the same users inthe same frequency classes. Even though (a, c) present the agreement in the temporal patterns of full andRT spike trains of the same users, with high correlation coefficients in almost all frequency ranges, (b)indicates lower consistency between RT and @ spike trains during entire activity aU and (d) providesa significant result. While less temporal coherence is observed between RT and @ spike trains in lowpopularity pU , the correlation drastically increases with pU .

Frontiers 17


Communication Habits of Users Linear (Pearson) correlations of :

0

5

10

15

20

25

WH

O:

< aU>=190< aU>=112< aU>= 84< aU>= 44< aU>= 25< aU>= 17< aU>= 12

0 1 2 3 40

10

20

30

40

50

60

< pU>=4418< pU>=1037< pU>= 570< pU>= 193< pU>= 48< pU>= 18< pU>= 11

P(

)L V

WH

OM

: P(

) L V

LV

(a)



C. Sanl and R. Lambiotte, Frontiers in Physics: Computational Social Science 3(79), (2015).

temporal patterns of @ and RT should be consisted

for popular users


Take Home Messages

Activity and Popularity of Users in Online Network: Our activity in Twitter is highly driven by the complex-decison making (large KPI set). On the other hand, our popularity is independent of that!

Structural versus Temporal in Network: Popularity of topics, e.g. hashtags, and users might be strongly influenced by temporal characteristics of the underlying network.

Ranking Hashtags by Temporal Parameters: Observing bursts in less popular hashtags, popular hashtags give regular signals.

social behavior patterns_short

Social Media