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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.
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
30
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
ive
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.
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
30
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
ive
Social Dynamic Behavior Patterns
@CeydaSanli
CompleXity Networks
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.
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
30
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
=2R
,t)
MM
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
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
C. Sanli, CompleXity Networks, UNamur
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"}
C. Sanli, CompleXity Networks, UNamur
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).
Social Dynamic Behavior Patterns 4
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
C. Sanli, CompleXity Networks, UNamur
tweets retweets (RT) mentions (@) replies (RE)
Tomi Um
Social Dynamic Behavior Patterns 5
Hashtag Diffusion in Twitter
C. Sanli, CompleXity Networks, UNamur
hashtag
hashtag spike train
time
coun
t
Social dynamic behaviour patterns 1
I. Part:
II. Part: RT + @ RE
WHO WHOM
aU : activity of users
RT
@
RE
RT + @ RE
pU : popularity of users
RT
@
RE
Spike Trains
C. Sanli, CompleXity Networks, UNamur
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
. . .
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
I. DAILY CYCLE OF #HASHTAGS
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
Social Dynamic Behavior Patterns 6
= popularity
C. Sanli, CompleXity Networks, UNamur
Local Analysis on Hashtag Spike Trains
Social Dynamic Behavior Patterns 7
hash
tag
coun
t
time
Populars are Regular
C. Sanli, CompleXity Networks, UNamur
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)
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
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].
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1
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2
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3
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L V(t 2
)
101 102 103 104 1050
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r (L V
(t 1),
L V(t 2
))
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(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.
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hashtag dynamics artificial dynamics
ranking popularity
C. Sanl and R. Lambiotte, PLoS ONE 10(7): e0131704 (2015).
Social Dynamic Behavior Patterns 8
Bursty versus Regular
C. Sanli, CompleXity Networks, UNamur
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Social Dynamic Behavior Patterns 9
C. Sanl and R. Lambiotte, PLoS ONE 10(7): e0131704 (2015).
KPI
C. Sanli, CompleXity Networks, UNamur
Local Analysis on Communication Spike Trains
Social Dynamic Behavior Patterns 10
user
co
unt
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C. Sanli, CompleXity Networks, UNamur Social Dynamic Behavior Patterns 11
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Sanli et al. Temporal Pattern of Online Communication Spike Trains
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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
C. Sanli, CompleXity Networks, UNamur Social Dynamic Behavior Patterns 12
Communication Habits of Users Linear (Pearson) correlations of :
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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
C. Sanli, CompleXity Networks, UNamur Social Dynamic Behavior Patterns 13
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.