Structural and geographic properties of online social ... · Tuenti Demographics: age pyramid by gender 50.6% female; 49.4% male. by age (average) female: 22 years; male: 28 years

Structural and geographic properties ofonline social interactions

Yana Volkovich

Barcelona Media - Innovation Center

in collaboration withA. Kaltenbrunner, D. Laniado, C. Mascolo, and S. Scellato

Yana Volkovich (Barcelona Media) Trento, 2012 1 / 40

References

Y. Volkovich, S. Scellato, D. Laniado, C. Mascolo, and A.Kaltenbrunner;“The length of bridge ties: structural and geographicproperties of online social interactions”ICWSM-12 (International AAAI Conference on Weblogs andSocial Media)A. Kaltenbrunner, S. Scellato, Y. Volkovich, D. Laniado, D. Currie,E. J. Jutemar, and C. Mascolo;“Far from the eyes, close on the Web: impact of geographicdistance on online social interactions”;WOSN ’12 (ACM SIGCOMM Workshop on Online SocialNetworks)


Introductionsocial graph

online social connections:explicit (articulated)e.g. friendship connectionsimplicit (behavioural)e.g. interactions


Motivationsocial graph: nodes and edges

social graph: nodes and edgesconnections could be more informative than nodesdifferent types of social connectionsdifferent ways to characterize social connections


Motivationsocial connections

different ways to characterize social connectionsinteraction strengthspatial distancestructural position in a social graph


Tuenti datasetTuenti dataset

Dataset


TuentiTuenti website

Tuenti is the “Spanish Facebook”a Spain-based, invitation-only social networking website


TuentiTuenti website


TuentiDataset

Tuenti dataset:

by Dec. 11, 2010;9.88 million registered users (anonymous profiles);more than 1 174 million friendship links;500 million messages exchanged during 3 months;


TuentiDemographics: age pyramid

age pyramid


TuentiDemographics: age pyramid

by gender

50.6% female;

49.4% male.

by age (average)

female: 22 years;

male: 28 years.

Tuenti users are very young45% of users are between 14 and 20 years;37.5% of users are between 21 and 30 years.1.35 more teenagers than official population (due to Tuenti signingrequirements).


Social connectionsimplicit vs. explicit connections

implicit vs. explicit social connectionsDunbar’s number: an alleged theoretical cognitive limit to thenumber of people with whom one can maintain stable socialrelationshipaverage fraction of friends and the average absolute number offriends a user interacts with as a function of the number of friends

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 10000

0.0250.05

0.0750.1

0.1250.15

0.1750.2

# friends

frac

tion

of

activ

e fr

iend

s

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 10000

255075

100125150

# friends

# a

ctiv

e fr

iend

s

in−degreeout−degree

in−degreeout−degree


Social connectionsSocial connections

Characteristics for social connections


Social connectionsspatial distance, related work

social ties and spatial distances:individuals try to minimize the efforts to maintain a friendship byinteracting more with their spatial neighborsprobability of a social interaction quickly decays as an inversepower of the relative geographic distance (Stewart [1941])


Social connectionsspatial distance, related work

online tools and long-distance travel might result in the ‘death ofdistance’probability of social connection between two individuals on onlinesocial networking services still decreases with their geographicdistance (Backstrom et al. [2010], Liben-Nowell et al. [2005]).


Social connectionsspatial distance

spatial distancedi ,j is the geographic distance between the cities of residence ofuser i and user j ;di ,j = 0 if users report the same city of residenceaverage geographic distances between users < D > is about oneorder of magnitude larger than the average geographic distancebetween friends < l >

average geographic distance between nodes, km 531.2average link length, km 79.9


Social connectionsspatial distance

spatially closer users are much more likely to engage in a socialconnection (e.g. become friends)about 50% of social links between users at a distance of 10 km orless

distance in km

% o

f frie

ndsh

ips,

inte

ract

ions

% of contacts at distance greater than x km

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103

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wall interactionsfriendshipspotential friendships


Social connectionsinteraction strength

interaction strengthclose friends or just acquaintancesquantitative estimation of a how much an online connection bindstwo users together


Social connectionsInteraction strength

interaction strengthwi ,j is the number of messages user i posted on the wall of user j ;wi ,j = 0 if user i has never left a message on user j ’s wall;

balanced interaction weight:


Social connectionsInteraction strength (log-log)

since non-reciprocated interactions may indicate spam:the minimum of the interaction weights to emphasize reciprocatedinteractions;for the non-reciprocated interactions we only add 1/2 no matterthe difference in the numbers of messages exchanged.

100

101

102

103

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

balanced interaction weight

frac

tion

of c

onne

ctio

ns

distribution of the balanced interaction weight


Social connectionsstructural properties

weak ties are more likely to connect together otherwise separatedportions of a network, playing an important role in informationdiffusion and resilience to network damage (Granovetter [1973])some social ties closing “structural holes” can be more powerful ormore innovative (Burt [1992])

Bakshy [2012]

100

101

102

103

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

balanced interaction weight

frac

tion

of c

onne

ctio

ns

distribution of the balanced interaction weight


Social connectionsStructural properties:social overlap

structural properties:local position: social overlap;social overlap of an edge ei ,j as oi ,j = |Γi ∩Γj |, where Γi is the setof users connected to user i


Social connectionsStructural properties:k-index of a node

structural properties:global position: k-index;k -core is the maximal subgraph in which each node is connectedto at least k other nodes of the subgraphk -index of a node is v if it belongs to the v -core but not to the(v + 1)-corek -index has been found to be an indicator of influential nodeswithin a social network (Kitsak et al. [2010])

k=1

k=3

k=2

central core/ smaller core in between/ peripheryYana Volkovich (Barcelona Media) Trento, 2012 23 / 40

Social connectionsStructural properties:k-index of an edge

k-index kij of an edge is the minimum of the k -indexes of twoendpointswe distinguish if an edge connects nodes inside a network core orlinks to a node in the periphery

0 20 40 60 80 100 120 140 160 18075

85

95

105

115

125

135

145

155

165

175180

average max k−index vs edge k−index

edge k−index

aver

age

max

k−

inde

x


Combined analysisCombined analysis

Combined analysis of social connections


Combined analysisCombined analysis of social connections

social connections


Combined analysisSocial overlap vs. k-index

social overlap and k -index allow network scenarios where links mayhave high k -index and low overlap, or the other way round


Combined analysisSocial overlap vs. k-index

social overlap ↑ ⇒ k -index grows quicklyk -index ↑ ⇒ the average social overlap grows slowlythere are inner cores where users are tightly connected to eachotherother parts of the network include more isolated users that tend tonot belong to any community

100

101

102

103

80

90

100

110

120

130

140

150

160average k−index vs. social overlap

social overlap

aver

age

k−in

dex

0 20 40 60 80 100 120 140 160 1800

20

40

60

80

100

120

140

160

180

200

220social overlap vs. k−index

k−index

soci

al o

verla

p


Combined analysisDistance vs. social overlap

the geographic distance between two connected users decreasesas they share more and more friendssocial connections which span less than 60-80 km exhibit highervalues of social overlap

100

101

102

103

0

20

40

60

80

100

120

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180

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220average distance vs. social overlap

social overlap

aver

age

dist

ance

101

102

103

5

10

15

20

25

30

35

40average social overlap vs. distance

distance

aver

age

soci

al o

verla

p


Combined analysisDistance vs. k -index

the average spatial length of social links decreases as theirk -index increasessocial links inside the core tend to be shorter than the onesreaching the periphery of the social network

0 20 40 60 80 100 120 140 160 1800

20

40

60

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160

180average distance vs. k−index

k−index

aver

age

dist

ance

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103

85

90

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120average k−index vs. distance

distance

aver

age

k−in

dex



kmax -core



kmax -core

Benidorm

Almería

Ojos-Albos

Eivissa

Arenys de Mar

Barcelona

Santa Eulàlia de Ronçana

Jerez de la Frontera

Trebujena

Coruña

Granada

Errezil

Huelva

Jaén

Madrid

Ronda

Pamplona

Las Palmas de GC

Abusejo

Salamanca

Adeje

Arahal

Dos Hermanas

Lebrija

Sevilla

Cuervo de Sevilla

Valencia

Bilbao

Pego

Zaragoza


Combined analysisDistance vs. interaction weight

the amount of interaction is uncorrelated to spatial distancenote that the likelihood that two individuals are connected isheavily dependent on distance

1

1.5

2

2.5

3

3.5# interactions as a function of distance

distance

# in

tera

ctio

ns

0 10 20 30 40 50 60 70 80 90 100

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100distance as a function of # interactions

dist

ance

# interactions

1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100

200

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1000


Combined analysisSocial overlap vs. interaction

the impact of social overlap remains fairly constantthe interaction weight only slowly increases the social overlapgrowsthe extremely high levels of interaction mainly take place betweenusers with several shared friends, which are likely to be in thenetwork core

100

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103

0

10

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social overlap

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age

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ght

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interaction weight

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Combined analysisk -index vs. interaction weight

ties in the inner cores have the highest levels of interactioninteraction weights are almost equally high for social ties with lowk -indexsocial ties with intermediate k -index, likely to bridge togetherdifferent portions of the network, experience the lowest interactionlevels

0 20 40 60 80 100 120 140 160 1801.5

2

2.5

3

3.5

4

4.5

5

5.5

6average iteraction weight vs. k−index

k−index

aver

age

inte

ract

ion

wei

ght


ConclusionsConclusions

Conclusions


Conclusions

social connections between users inside the core tend to haveshorter geographic spans than connections stretching outside thecoresocial ties outside the core tend to be much longer than the otherlinks: the length of these bridge ties is thus creating not onlynetwork shortcuts, but also spatial shortcutsthe amount of interactions appears independent of spatialdistanceinteraction levels appear higher inside well-connected cores andon links connecting to the fringe of the networkedges could be more informative than nodes


QuestionsQuestions


Bibliography I

L. Backstrom, E. Sun, and C. Marlow. Find me if you can: improvinggeographical prediction with social and spatial proximity. InProceedings of WWW 2010, Raleigh, North Carolina, USA, 2010.

E. Bakshy. Rethinking information diversity in networks, 2012. URLwww.facebook.com/notes/facebook-data-team/rethinking-information-diversity-in-networks/10150503499618859.

R. S. Burt. Structural holes: The social structure of competition.Harvard University Press, Cambridge, MA, 1992.

M. S. Granovetter. The strength of weak ties. The American Journal ofSociology, 78(6):1360–1380, 1973. doi: 10.2307/2776392.

M. Kitsak, L. K. Gallos, S. Havlin, F. Liljeros, L. Muchnik, H. E. Stanley,and H. A. Makse. Identification of influential spreaders in complexnetworks. Nature Physics, 6(11):888–893, Nov. 2010. URLhttp://dx.doi.org/10.1038/nphys1746.


www.facebook.com/notes/facebook-data-team/rethinking-information-diversity-in-networks/10150503499618859



http://dx.doi.org/10.1038/nphys1746

Bibliography II

D. Liben-Nowell, J. Novak, R. Kumar, P. Raghavan, and A. Tomkins.Geographic routing in social networks. PNAS, 102(33):11623–11628, Aug. 2005.

J. Q. Stewart. An inverse distance variation for certain socialinfluences. 93(2404):89–90, 1941.


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Structural and geographic properties of online social ... · Tuenti Demographics: age pyramid by gender 50.6% female; 49.4% male. by age (average) female: 22 years; male: 28 years