Social and Technological Network Analysis. Lecture 11: Spa;al and Social Network Analysis. Dr. Cecilia Mascolo

Transcription

1 Social and Technological Network Analysis Lecture 11: Spa;al and Social Network Analysis Dr. Cecilia Mascolo

2 In This Lecture In this lecture we will study spa;al networks and geo- social networks through examples from our work.

3 Places and Friends

4 Geo- social Network Analysis can lead to insights into social behaviour

5 Effect of Distance on Social Connec;ons LiveJournal (2005) Mobile phones (2008) Facebook (2010) P (d) d 1 + ɛ P (d) d 2 P (d) d 1

6 Effect of geography over social link forma6on

7 What do we see in Geo- social Networks? We have acquired data about the socio- spa;al network of 3 real- world loca6on- based services We design two randomized models of a socio- spa;al network to beoer understand which factors shape the real networks. We study how individual users create their social links and their social triangles over space.

8 Distance between Friends Friends tend to be much closer than random users: about 50% of social links span less than 100 km, while about 50% of users are more than 4,000 km apart. CDF Brightkite Foursquare Gowalla Friends Users Distance [km]

9 Probability of Friendship vs Distance Probability of friendship Brightkite Foursquare Gowalla Distance [km]

10 Network Randomiza;on Two randomized models, which capture either the geographic or the social properties of the original social networks and randomize everything else. Description Social properties Spatial properties Original data No modification.!! Geo model Fix node locations and reassign all links according to probability P(d). "! Social model Fix links and shuffle all node locations.! "

11 Users have heterogeneous w i = 1 k i Node degree j Γ i l ij friend distances Node neighborhood Link length CDF Original data Geo model Social model CDF Original data Geo model Social model CDF w [km] Original data Geo model Social model w [km] w [km]

12 Average triangle geographic length <lδ> is the average length of the triangles of a user CDF Original data Geo model Social model CDF Original data Geo model Social model CDF l [km] Original data Geo model Social model l [km] l [km]

13 Correla;on triangle length/degree Correla;on with degree: users with many friends belong to bigger triangles l Original data Geo model Social model Degree 10 4 l Original data Geo model Social model Degree l Original data Geo model Social model Degree

14 Effect of geography over interac6on

15 How does geography affect interac;on?

16 Tuen; Tuen; dataset (Nov 11) 9.88 million registered users ~1 174 million friendship links 500 million messages in 3 months

17 Geographic Proper;es 60% of social connec;ons are at a distance of 10km. Only 10% of all distances between users are below 100km % of friendships, interactions % of contacts at distance greater than x km wall interactions friendships potential friendships distance in km

18 Effect of geography on friendship Distance constrains social interac;on establishment but has a uniform effect on all interac;ons prob. of friendship 10 3 friendships δ ε; (ε=1.3e 06) wall directed δ ε; (ε=2.7e 07) interactions δ ε; (ε=5e 08) 5 interactions 10 5 δ ε; (ε=2.7e 08) 10 interactions δ ε; (ε=1.1e 08) distance δ in km

19 Effects of geography on interac;ons fraction of wall posts between friends Probability that a message is exchanged over a friendship link seems not to be very affected by distance prob. of interaction wall directed (all interactions) 3 interactions 5 interactions 10 interactions distance in km

20 Effect of Age Under 15 have 70% friends within 10km. They also have more friends and interact more.

21 Understanding human mobility

22 Foursquare Places (London)

23 Foursquare Dynamics

24 Samuel A. Stouffer Stouffer's law of intervening opportunities states, "The number of persons going a given distance is directly proportional to the number of opportunities at that distance and inversely proportional to the number of intervening opportunities." *! - Empirically proven using data for migrating families in the city of Cleveland." " - Is this true in our data?" * S. Stouffer (1940) Intervening opportunities: A theory relating mobility and distance, American Sociological Review 5, "

25 The importance of density Place density by far more important than city area size with respect to mean length of human movements (R 2 = 0.59 and 0.19 respec;vely).

26 Rank Distance u v

27 Rank universality three ci;es all ci;es The rank of all ci;es collapses to a single line. We have measured a power law exponent α = 0.84 ± 0.07

28 A new model for urban mobility

29 Simula;on Results...

30 Understanding communi6es and role of places

31 City- scale social networks We look at intra- city social networks People who have checked in at a place in a given city, and their friends who have also checked in at those places What do these place- based social networks look like?

32 City- scale social networks Degree: power- law distribu;on Atlanta Boston Chicago Minneapolis Seattle Number of people Number of friends

33 City- scale social networks Degree: power- law distribu;on Clustering coefficient: high (between 0.1 and 0.2, in random graph of the same size <0.001) Average shortest path length: small (about 4 hops), comparable to random graph (Clustering coeff. + average path length = small world ) Community structure (modularity > 0.4) Our city- level graphs have well- known structural proper;es of social networks.

34 The role of places Power- law distribu;on of place popularity like the degree distribu;on in the social network Number of places Atlanta Boston Chicago Minneapolis Seattle Number of visitors

35 Places vital for ;e forma;on Power- law distribu;on of place popularity Analyze triangles: >70% of triangles have one place shared between all three people à clustering around certain places These places could act as foci for 6e forma6on

36 Role of categories Probability of friendship What is the role of place categories? Atlanta Boston Chicago Minneapolis Seattle Probability of friendship between colocated people at places in each Foursquare category Some kinds of places are much more likely to reinforce friendship than others 0 Arts College Food Nightlife Outdoors Professional Residence Shop Transport Category

37 What can all this be used for? Friendship Recommenda6on: Exploi6ng Place Features in Link Predic6on on Loca6on- based Social Networks, Salvatore Scellato, Anastasios Noulas, Cecilia Mascolo. In Proceedings of 17th ACM Interna;onal Conference on Knowledge Discovery and Data Mining (KDD 2011). San Diego, USA. August Place Recommenda6on: Mining User Mobility Features for Next Place Predic6on in Loca6on- based Services. Anastasios Noulas, Salvatore Scellato, Neal Lathia and Cecilia Mascolo. In Proceedings of IEEE Interna;onal Conference on Data Mining (ICDM 2012). Short Paper. Brussels, Belgium. December A Random Walk Around the City: New Venue Recommenda6on in Loca6on- Based Social Networks. Anastasios Noulas, Salvatore Scellato, Neal Lathia and Cecilia Mascolo. In Proceedings of ASE/IEEE Interna;onal Conference on Social Compu;ng (SocialCom). Amsterdam, The Netherlands. September 2012.

38 What can all this used for? More Modelling: Talking Places: Modelling and Analysing Linguis6c Content in Foursquare. Sandro Bauer, Anastasios Noulas, Diarmuid Ó Séaghdha, Stephen Clark and Cecilia Mascolo. In Proceedings of ASE/IEEE Interna;onal Conference on Social Compu;ng (SocialCom). Amsterdam, The Netherlands. September Exploi6ng Foursquare and Cellular Data to Infer User Ac6vity in Urban Environments. Anastasios Noulas, Cecilia Mascolo and Enrique Frias- Mar;nez. In Proceedings of 14th Interna;onal Conference on Mobile Data Management (MDM 2013). Milan, Italy. June Evolu6on of a Loca6on- based Online Social Network: Analysis and Models. Mili;adis Allamanis, Salvatore Scellato and Cecilia Mascolo. In Proceedings of ACM Internet Measurement Conference (IMC 2012). Boston, MA. November 2012.

39 References The length of bridge 6es: structural and geographic proper6es of online social interac6ons. Yana Volkovich, Salvatore Scellato, David Laniado, Cecilia Mascolo and Andreas Kaltenbrunner. In Proceedings of Sixth Interna;onal AAAI Conference on Weblogs and Social Media (ICWSM 2012). Full Paper. Dublin, Ireland. June Far from the eyes, close on the Web: impact of geographic distance on online social interac6ons. Andreas Kaltenbrunner, Salvatore Scellato, Yana Volkovich, David Laniado, Dave Currie, Erik J. Jutemar, Cecilia Mascolo. In ACM SIGCOMM Workshop on Online Social Networks (WOSN 2012). Helsinki, Finland. August A tale of many ci6es: universal pawerns in human urban mobility. Anastasios Noulas, Salvatore Scellato, Renaud LambioOe, Massimiliano Pon;l, Cecilia Mascolo. In PLoS ONE. PLoS ONE 7(5): e doi: /journal.pone The Importance of Being Placefriends: Discovering Loca6on- focused Online Communi6es. Chloë Brown, Vincenzo Nicosia, Salvatore Scellato, Anastasios Noulas, Cecilia Mascolo. In ACM SIGCOMM Workshop on Online Social Networks (WOSN 2012). Helsinki, Finland. August 2012.