Structural and geographic properties of online social interactions - - PowerPoint PPT Presentation

Structural and geographic properties of

• nline social interactions

Yana Volkovich

Barcelona Media - Innovation Center

in collaboration with

• A. 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 geographic properties of online social interactions” ICWSM-12 (International AAAI Conference on Weblogs and Social 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 geographic distance on online social interactions”; WOSN ’12 (ACM SIGCOMM Workshop on Online Social Networks)

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Introduction

social graph

• nline social connections:

explicit (articulated) e.g. friendship connections implicit (behavioural) e.g. interactions

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Motivation

social graph: nodes and edges

social graph: nodes and edges connections could be more informative than nodes different types of social connections different ways to characterize social connections

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Motivation

social connections

different ways to characterize social connections interaction strength spatial distance structural position in a social graph

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Tuenti dataset

Tuenti dataset

Dataset

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Tuenti

Tuenti website

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

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Tuenti

Tuenti website

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Tuenti

Dataset

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;

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Tuenti

Demographics: age pyramid

age pyramid

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Tuenti

Demographics: age pyramid

by gender

50.6% female; 49.4% male.

by age (average)

female: 22 years; male: 28 years.

Tuenti users are very young 45% 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 signing requirements).

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Social connections

implicit vs. explicit connections

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

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2

# friends fraction of active friends

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 25 50 75 100 125 150

# friends # active friends in−degree

• ut−degree

in−degree

• ut−degree

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Social connections

Social connections

Characteristics for social connections

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Social connections

spatial distance, related work

social ties and spatial distances: individuals try to minimize the efforts to maintain a friendship by interacting more with their spatial neighbors probability of a social interaction quickly decays as an inverse power of the relative geographic distance (Stewart [1941])

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Social connections

spatial distance, related work

• nline tools and long-distance travel might result in the ‘death of

distance’ probability of social connection between two individuals on online social networking services still decreases with their geographic distance (Backstrom et al. [2010], Liben-Nowell et al. [2005]).

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Social connections

spatial distance

spatial distance di,j is the geographic distance between the cities of residence of user i and user j; di,j = 0 if users report the same city of residence average geographic distances between users < D > is about one

• rder of magnitude larger than the average geographic distance

between friends < l >

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

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Social connections

spatial distance

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

distance in km % of friendships, interactions % of contacts at distance greater than x km 10 10

1

10

2

10

3

10 20 30 40 50 60 70 80 90 100

wall interactions friendships potential friendships

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Social connections

interaction strength

interaction strength close friends or just acquaintances quantitative estimation of a how much an online connection binds two users together

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Social connections

Interaction strength

interaction strength wi,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:

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Social connections

Interaction strength (log-log)

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

10 10

1

10

2

10

3

10

−9

10

−8

10

−7

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10

balanced interaction weight fraction of connections distribution of the balanced interaction weight Yana Volkovich (Barcelona Media) Trento, 2012 20 / 40

Social connections

structural properties

weak ties are more likely to connect together otherwise separated portions of a network, playing an important role in information diffusion and resilience to network damage (Granovetter [1973]) some social ties closing “structural holes” can be more powerful or more innovative (Burt [1992]) Bakshy [2012]

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Social connections

Structural 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 set

• f users connected to user i

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Social connections

Structural properties:k-index of a node

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

k=1 k=3 k=2

central core/ smaller core in between/ periphery

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Social connections

Structural properties:k-index of an edge

k-index kij of an edge is the minimum of the k-indexes of two endpoints we distinguish if an edge connects nodes inside a network core or links to a node in the periphery

20 40 60 80 100 120 140 160 180 75 85 95 105 115 125 135 145 155 165 175 180

average max k−index vs edge k−index edge k−index average max k−index

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Combined analysis

Combined analysis

Combined analysis of social connections

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Combined analysis

Combined analysis of social connections

social connections

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Combined analysis

Social overlap vs. k-index

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

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Combined analysis

Social overlap vs. k-index

social overlap ↑ ⇒ k-index grows quickly k-index ↑ ⇒ the average social overlap grows slowly there are inner cores where users are tightly connected to each

• ther
• ther parts of the network include more isolated users that tend to

not belong to any community

10 10

1

10

2

10

3

80 90 100 110 120 130 140 150 160

average k−index vs. social overlap social overlap average k−index

20 40 60 80 100 120 140 160 180 20 40 60 80 100 120 140 160 180 200 220

social overlap vs. k−index k−index social overlap

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Combined analysis

Distance vs. social overlap

the geographic distance between two connected users decreases as they share more and more friends social connections which span less than 60-80 km exhibit higher values of social overlap

10 10

1

10

2

10

3

20 40 60 80 100 120 140 160 180 200 220

average distance vs. social overlap social overlap average distance

10

1

10

2

10

3

5 10 15 20 25 30 35 40

average social overlap vs. distance distance average social overlap

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Combined analysis

Distance vs. k-index

the average spatial length of social links decreases as their k-index increases social links inside the core tend to be shorter than the ones reaching the periphery of the social network

20 40 60 80 100 120 140 160 180 20 40 60 80 100 120 140 160 180

average distance vs. k−index k−index average distance

10

1

10

2

10

3

85 90 95 100 105 110 115 120

average k−index vs. distance distance average k−index

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Combined analysis

Distance vs. k-index

kmax-core

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Combined analysis

Distance vs. k-index

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

Pamplona Las Palmas de GC Abusejo

Adeje

Dos Hermanas

Lebrija Sevilla Cuervo de Sevilla

Valencia

Bilbao Pego Zaragoza

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Combined analysis

Distance vs. interaction weight

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

1 1.5 2 2.5 3 3.5

# interactions as a function of distance

distance # interactions

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 2 1 2 2 2 3 2 4 2 5

60 70 80 90 100

distance as a function of # interactions

distance # interactions

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1

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Combined analysis

Social overlap vs. interaction

the impact of social overlap remains fairly constant the interaction weight only slowly increases the social overlap grows the extremely high levels of interaction mainly take place between users with several shared friends, which are likely to be in the network core

10 10

1

10

2

10

3

10 20 30 40 50 60 70

average iteraction weight vs. social overlap social overlap average interaction weight

10 10

1

10

2

10

3

50 100 150 200 250 300 350

average social overlap vs. interaction weight interaction weight average social overlap

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Combined analysis

k-index vs. interaction weight

ties in the inner cores have the highest levels of interaction interaction weights are almost equally high for social ties with low k-index social ties with intermediate k-index, likely to bridge together different portions of the network, experience the lowest interaction levels

20 40 60 80 100 120 140 160 180 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

average iteraction weight vs. k−index k−index average interaction weight

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Conclusions

Conclusions

Conclusions

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Conclusions

social connections between users inside the core tend to have shorter geographic spans than connections stretching outside the core social ties outside the core tend to be much longer than the other links: the length of these bridge ties is thus creating not only network shortcuts, but also spatial shortcuts the amount of interactions appears independent of spatial distance interaction levels appear higher inside well-connected cores and

• n links connecting to the fringe of the network

edges could be more informative than nodes

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Questions

Questions

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Bibliography I

• L. Backstrom, E. Sun, and C. Marlow. Find me if you can: improving

geographical prediction with social and spatial proximity. In Proceedings of WWW 2010, Raleigh, North Carolina, USA, 2010.

• E. Bakshy. Rethinking information diversity in networks, 2012. URL

www.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 of

Sociology, 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 complex

• networks. Nature Physics, 6(11):888–893, Nov. 2010. URL

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

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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 social
• influences. 93(2404):89–90, 1941.

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