Social Network. Why they are different.Palo Alto, California. @gmiritello Giovanna Miritello...

Giovanna Miritello

@gmiritello

Social Network. Why they are different.

@gmiritello

Giovanna Miritello

data science at Zed

analytics at Telefonica I+D

2014

2009 2012

2012

2013digital products & data science at Telefonica I+D

PhD at Universidad Carlos III & Telefonica I+D

Research

Product/Development

Industry

University

University/MSc Physics, Catania Italy

Insight Data Science Palo Alto, California

@gmiritello

Giovanna Miritello

dani%villatorogiovanna%miritello

@gmiritello

marcelo%soria

@msoriaro@dani_agent

@gmiritello

What do you think when you think about social networks?

@gmiritello

When you think about social networks, you think about..

@gmiritello

Social Networks 6= Online Social Networks & Social Media

@gmiritello

Your family/friends network is a social network

mother

roommate

supervisor at work

friend at work

fiancee’s ex wife

fiancee

grandma

father

brother

old boyfriend

you

@gmiritello

What are Social Networks

.+ +

@gmiritello


.+ +

+ 2 .+ - -+

, 2 + + + 2

@gmiritello


.

+-

+ +

+ 2 .+ - -+

, 2 + + + 2

Moreno, 1930. .

.

@gmiritello

Examples of social networksmobile phone science collaboration

political network citation network

@gmiritello

The importance of graph theory in the real worldGoogle, uses a graph representation to store/retreive the semantic relationship between different entities, which they call it, Knowledge Graph as well as providing you with the top relevant webpages for your query, using PageRank algorithm

@gmiritello

LinkedIn uses the graph of connections (common friends/companies/etc) to recommend “people you might know”

The importance of graph theory in the real world

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Almost every recommendation system, including the ones used by Amazon for recommending you the relevant books to buy, or Netflix for recommending you what to watch use graph theoretic algorithms.


@gmiritello

social media management


@gmiritello

graph of flight connections to study epidemia propagation


@gmiritello

graph of ingredients based on common receipts


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graph of diseases based on the genes they have in common


@gmiritello


@gmiritello

The dimensions of social networks- + -

@gmiritello

The dimensions of social networks

( + -

- + -

@gmiritello

The dimensions of social networks

( + -

) ,

- + -

@gmiritello

Topological heterogeneity

@gmiritello


• degree distribution in real-world networks is very heterogeneous

• existence of hubs

@gmiritello




people with few connections

@gmiritello


people with few connectionspeople with average

number of connections



@gmiritello


hubshigh connected

people

people with few connectionspeople with average

number of connections



Random vs real networks

@gmiritello

Poisson

Power-law

k = hki± hki1/2

k = hki±1P (k) ⇠ k�� , 2 < � < 3

@gmiritello


Why does it matter?

- In a social network highly connected nodes can be fundamental to spread or stop information/innovation/epidemia diffusion

- In cities highly connected points can cause traffic congestions (metro stations or streets)

- The fact that the distribution of degree is so heterogeneous indicates that there is no a significant “average” value of the number of connections. No typical scale!

@gmiritello

Few tips to deal with power-laws• If you really have to chose one

value to define your data, use the median instead than the mean.

• Even better percentiles or box plots.

• Use a log-log plot for distributions instead than a linear scale

• Use log binning instead than linear

• Use cumulative distributions

@gmiritello

Assortativity and Homophily

@gmiritello

AssortativityAssortativity, or assortative mixing is a preference for a network's nodes to attach to others that are similar in some way.Assortativity in node’s degree: highly connected nodes tend to be connected with other high degree nodes. To measure assortativity in the degree, one usually measures the average nearest neighbors degree of a node i:

@gmiritello

Assortativity

• Depending on whether knn is an increasing or decreasing function of k, this properties is known as assortative or disassortative mixing.

• While in assortative networks nodes tend to connect with nodes with similar degree, in disassortative networks nodes with high degree are more likely connected with lowly connected ones.

Assortativity in node’s degree: highly connected nodes tend to be connected with other high degree nodes. To measure assortativity in the degree, one usually measures the average nearest neighbors degree of a node i:

Assortativity, or assortative mixing is a preference for a network's nodes to attach to others that are similar in some way.

@gmiritello

Homophily

Positive correlation can exist between many other features and behaviors.Assortativity is not observed only in the degree.

@gmiritello

Homophily 2007. Nicholas A. Christakis and James Fowler Obesity, rather than being individualistic, is causally correlated by contagion mechanisms that transmit these behaviors over long distances within social networks. [data:12,067 people with repeated measurements over a period of 32 years]

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Homophily

Social distance appears to be more important than geographic distance.

Increase of conditional probability of obesity in an individual if alter becomes obese

2007. Nicholas A. Christakis and James Fowler Obesity, rather than being individualistic, is causally correlated by contagion mechanisms that transmit these behaviors over long distances within social networks. [data:12,067 people with repeated measurements over a period of 32 years]

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HomophilySmocking cessation


Increase of conditional probability that an individual will smoke after alter smokes

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HomophilyHappiness


@gmiritello

What comes first?

?

Behavior

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What comes first?

?

or similar friends?

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Homophily or influence?

- very difficult to distinguish them - explore the causality/correlation relationship between similar behaviors using

the time dimension

@gmiritello


Data- online messaging data among 27.4 million Yahoo users - day-by-day adoption of a mobile service application (Go) and users' longitudinal

behavioral, demographic, and geographic data.

@gmiritello

Homophily or influence?Evolution of adopters of Go over time

@gmiritello


Homophily can, to a large extent, explain what seems at first to be a contagious process driven by peer influence. 50% of the cumulative adoption of treated users (those with at least one adopter friend) can be attributed to homophily effects

homophily is given by the percentage of neighbors that also adopt the product.

influence should depend on temporal order at which adoption happens.

@gmiritello

Your friends have more friends than you do

@gmiritello

(on average!)Your friends have more friends than you do

@gmiritello

The friendship paradox

@gmiritello


Scott L. Feld 1991 most people have fewer friends than their friends have, on average [“Why Your Friends Have More Friends Than You Do”]

2011 Pew survey the average Facebook user has 245 friends, but the average friend on Facebook has 359 friends. The average person on Facebook has fewer friends than their friends do.

@gmiritello

A concrete examplefriends A has1 friend. B has 3 friends. C and D each has 2 friends.

friends of friends A is friends with B who has 3 friends. B is friends with everyone, which makes for 5 friends of friends. C and D each has 5 friends of friends.


@gmiritello

friends A has1 friend. B has 3 friends. C and D each has 2 friends.


- average friends of friends column is higher for everyone but person B

- (a very popular person will have more friends than their friends do)

- there are 8 total friends amongst the 4 people: average is 2

- 18 friends of friends - 18/8 = 2.25!

let’s have a look at the math

The friendship paradoxA concrete example

@gmiritello

friends A has1 friend. B has 3 friends. C and D each has 2 friends.


the average person has 2 friends but the average friend has 2.25 friends! This is the friendship paradox!

let’s have a look at the math


- average friends of friends column is higher for everyone but person B

- (a very popular person will have more friends than their friends do)

- there are 8 total friends amongst the 4 people: average is 2

- 18 friends of friends - 18/8 = 2.25!

A concrete example

@gmiritello

The mathematical proof

Average number of friends for the entire graph:

Average number of friends of friends:

n number of people in the graph ki number of friends of person i

µ =

Pkin

which divided by the total number of friends which is- For all persons:X

(ki)2

Xki

Average number of friends of friends =

Pk2iPki

- For each person we look at their friends and add up the number of friends they have

- Trick: for a given person i, how many times will the term ki appear in the final summation? Each of the friends of person i (there are ki friends) will contribute the term ki to the final sum.

- So the final summation has the term: (ki)(ki) = k2i

@gmiritello


Pk2iPki

µ =

Pkin



We therefore have to compare:

But, from the formula for variance of a discrete random variable we know

�2 =

P(ki)2

n� µ2

X(ki)

2 = (µ2 + �2)n

and dividing by sum of ki:P

(ki)2

ki=

(µ2 + �2)n

µn= µ+

�2

µX

@gmiritello


Pk2iPki

µ =

Pkin



We therefore have to compare:

But, from the formula for variance of a discrete random variable we know

�2 =

P(ki)2

n� µ2

X(ki)

2 = (µ2 + �2)n

and dividing by sum of ki:P

(ki)2

ki=

(µ2 + �2)n

µn= µ+

�2

µX µ µ+

�2

µ

average number of friends average friends of friendsTA DA!!

@gmiritello

Generalization of the friendship paradox

On Facebook, your friends will have more friends than you have.

@gmiritello


On Twitter, your followers will have more followers than you do.

@gmiritello


And in real life, your sexual partners will have had more partners than you’ve had.

@gmiritello


And in real life, your sexual partners will have had more partners than you’ve had.

At least, on average.

@gmiritello

friends of your friends are likely to become your friends too

@gmiritello

Triadic ClosureIf two people in a social network have a friend in common, then there is an increased likelihood that they will become friends themselves at some point in the future

@gmiritello

If two people in a social network have a friend in common, then there is an increased likelihood that they will become friends themselves at some point in the future

Triadic Closure

Why triadic closure? if nodes B and C have a friend A in common, then the formation of an edge between B and C produces a situation in which all three nodes A, B, and C have edges connecting each other B-C edge has the effect of “closing” the third side of this triangle

triangle

@gmiritello

The basic role of triadic closure in social networks has motivated the formulation of metrics to capture its notion and prevalence. One of those metrics is clustering coefficient.

Clustering Coefficient

Clustering coefficient of a node A: probability that two randomly selected friends of A are friends with each other or also, the fraction of pairs of A’s friends that are connected to each other by edges

CA =1

6

There is only the single C-D edge among the six pairs of friends B-C, B-D, B-E, C-D, C-E, and D-E

0 Ci 1

@gmiritello

Reasons for Triadic Closure

1. Opportunity for B and C to meet: if A spends time with both B and C, then there is an increased chance that they will end up knowing each other and potentially becoming friends

2. In the process of forming a friendship, the fact that each of B and C is friends with A (provided they are mutually aware of this) gives them a basis for trusting each other that an arbitrary pair of unconnected people might lack.

3. Incentive A may have to bring B and C together: if A is friends with B and C, then it becomes a source of latent stress in these relationships if B and C are not friends with each other

@gmiritello

Triadic Closure in Recommendation SystemsMost people and product recommendation systems are based on triadic closure

@gmiritello

The strength of weak ties

1960, Granovetter as part of his Ph.D thesis interviewed people who had recently changed employers and asked: how did you discover your new job?

The Strength of Weak Ties

@gmiritello

1960, Granovetter as part of his Ph.D thesis interviewed people who had recently changed employers and asked: how did you discover your new job?


@gmiritello

• many people learned information leading to their current jobs through personal contacts.

• these personal contacts were often described by interview subjects as acquaintances rather than close friends

• when it comes to find a job, getting news, launching a restaurant, or spreading the last fad, our weak social ties are more important than our strong friendships.

Important findings

A has five friends in this picture, but one of her friendships is qualitatively different from the others: A’s links to C, D, and E connect her to a tightly-knit group of friends who all know each other, while the link to B or F seems to reach into a different part of the network.

There are differences in the role it plays in A’s everyday life: while the tightly-knit group of nodes A, C, D, and E will all tend to be exposed to similar opinions and similar sources of information, B offers her access to things she otherwise wouldn’t necessarily hear about.

Bridges and local bridges

@gmiritello

@gmiritello

Bridges and local bridges

@gmiritello


• 2007. Onnela et al. verified Granovetter’s thesis by using log phone data

• data undirected network of 4.6 × 106 nodes and 7.0 × 106 links

• strength of a tie so the duration of calls can naturally be interpreted as the

• to capture the structure of the neighborhood of a link, they measure the relative number of friends in common (topological overlap)

@gmiritello


Overlap, real dataOverlap, random dataBetweenness, real data

Stronger ties share a large fraction of contacts.

@gmiritello


real data random data

@gmiritello

6 degrees of separation

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1929, “Chains”, hungarian writer Frigyes Karinthy anyone on the planet can be connected to any other person on the planet through a chain of acquaintances that has no more than five intermediaries.

@gmiritello


1929, “Chains”, hungarian writer Frigyes Karinthy anyone on the planet can be connected to any other person on the planet through a chain of acquaintances that has no more than five intermediaries.

1990, “Chains”, play by John Guare inspired by the real-life story of David Hampton, a man who managed to convince a number of people in the 1980s that he was the son of actor Sidney Poitier

http://en.wikipedia.org/wiki/David_Hampton

http://en.wikipedia.org/wiki/Sidney_Poitier

@gmiritello


2001, Duncan Watts, professor at Columbia University, recreated Milgram's experiment on the Internet by using an e-mail message as the "package" that needed to be delivered. Watts found that the average number of intermediaries was indeed 6.

1967, american sociologist Stanley Milgram designed "the small-world problem”: randomly selected people in the mid-West had to send packages to a stranger located in Massachusetts.

Send the package to a person they knew on a first-name basis who they thought was most likely to know the target personally.

That person would do the same, and so on, until the package was personally delivered to its target recipient.

It took (on average) between 5 and 7 intermediaries.

http://en.wikipedia.org/wiki/Columbia_University

@gmiritello


Six degrees of Kevin Bacon game created in early 1994 by three Albright College students, Craig Fass, Brian Turtle, and Mike Ginelli. It is based on the "six degrees of separation" concept: find the shortest path between an arbitrary actor and Kevin Bacon.

http://en.wikipedia.org/wiki/Albright_College

http://en.wikipedia.org/wiki/Six_degrees_of_separation

@gmiritello


[Why Kevin Bacon? In 1994 he commented that he had worked with everybody in Hollywood or someone who's worked with them]

Six degrees of Kevin Bacon game created in early 1994 by three Albright College students, Craig Fass, Brian Turtle, and Mike Ginelli. It is based on the "six degrees of separation" concept: find the shortest path between an arbitrary actor and Kevin Bacon.

http://en.wikipedia.org/wiki/Hollywood

http://en.wikipedia.org/wiki/Albright_College

http://en.wikipedia.org/wiki/Six_degrees_of_separation

@gmiritello


2006, Eric Horvitz and Jure Leskovec, analyzed 30 billion conversations among 240 million people among Microsoft Messenger and also found that the average of steps was 6.

2011, Anatomy of Facebook, L. Backstrom, P. Boldi, M. Rosa, J. Ugander, S. Vigna examined all 721 million active Facebook users (more than 10% of the global population), with 69 billion friendships among them: “The average distance in 2008 was 5.28 hops, while now it is 4.74.”

Planetary-Scale Views on a Large Instant-Messaging Network (2008) by Jure Leskovec , Eric Horvitz

Four Degrees of Separation (2011) Lars Backstrom, Paolo Boldi, Marco Rosa, Johan Ugander, Sebastiano Vigna

http://citeseer.uark.edu:8080/citeseerx/viewdoc/summary;jsessionid=1E35949C5F7F88DD310BB0624AEB1B3C?cid=7454239

http://arxiv.org/find/cs/1/au:+Backstrom_L/0/1/0/all/0/1

http://arxiv.org/find/cs/1/au:+Boldi_P/0/1/0/all/0/1

http://arxiv.org/find/cs/1/au:+Rosa_M/0/1/0/all/0/1

http://arxiv.org/find/cs/1/au:+Ugander_J/0/1/0/all/0/1

http://arxiv.org/find/cs/1/au:+Vigna_S/0/1/0/all/0/1

@gmiritello

Dunbar number

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Dunbar number

1992, Robin Dunbar used the average human brain size and the correlation observed for non-human primates to predict a social group size for humans. Using a regression equation on data for 38 primate, Dunbar predicted a human "mean group size" of 148-150.Dunbar, R. I. M. (1992). "Neocortex size as a constraint on group size in primates". Journal of Human Evolution 22 (6): 469–493.

Dunbar's number is a suggested cognitive limit to the number of people with whom one can maintain stable social relationships.

http://en.wikipedia.org/wiki/Robin_Dunbar

@gmiritello

Dunbar numberMaintaining a social relationship has a cost (time, attention, money,..)

wij

tie weight = aggregated duration of calls (11 months)

wi =kiX

j

wij

ki=

siki

average aggregated time per contact (11 months)

i si total time (# calls or duration)

ki nro of contactsnode strength

social connectivity

0 100 200 300ki

10

20

30

40

50

60

< w

ij | k i>

ki

�wij|k

i⇥

11 months7 months

3 months

5 25 1250

10

20

30

40

50

60

REAL DATA

RANDOMIZED DATA

�wi|k

i⇥

@gmiritello

[..people with many connections dedicate on average less time to each of them]

Dunbar numberMaintaining a social relationship has a cost (time, attention, money,..)

wij

tie weight = aggregated duration of calls (11 months)

wi =kiX

j

wij

ki=

siki

average aggregated time per contact (11 months)

i si total time (# calls or duration)

ki nro of contactsnode strength

social connectivity

@gmiritello

temporal patterns. bursty behavior.

@gmiritello

time

Bursty behavior. What it is.

ki(

t)/k

i(�

)

t

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

x

coso

(x, 1

, 2)

Figure 1. Growth of the observed connectivity for exponential pdf for the inter event time

and gamma pdf for the average inter-event time. Parameters are k = 1 (exponential) and

theta = 2 (black line), k = 2 and ✓ = 1 (red line) and k = 4 and theta = 1/2 (blue

line). Note that in all cases the average �t = k✓ = 2.

(a)

(b)

i

j

i

j

i

j

i

j

i

j

i

j

i

j

�T1 �T2�tij

TI TF

tminij tmax

ij

TI TF T �0

T1 = 6 monthsT2 = T = 7 months

T3 = 6 months

T � = 19 months

{

Figure 2. (color online) (a) Schematic sketch of the time intervals blabla and (b) Schematic

view of communication events between i and j within the time period T2 = T under

consideration blabla.

10!5 10!3 10!1 101 103

10!7

10!4

10!1

102

�tij/�tij

P(�

t ij/�

t ij)

Figure 3. Rescaled inter-event time distribution for groups of edges with different average

inter-event time �tij

. Each curve is rescaled by the value of �tij

of the correspondent

bin.

Footline Author PNAS Issue Date Volume Issue Number 3

@gmiritello

Bursty behavior. What it is.The heterogeneity observed in real-world network topology is also a characteristic of temporal behavior: bursts of events are followed by periods of inactivity.Poissonian-like models fail to explain and describe human dynamics.

�tij

- circadian rhythms - task queue - decision making - correlations between actions - human nature

why we act bursty

@gmiritello

Bursty behavior. Examples.

Phone calls

Interaction patterns with our friends

File downloading

E-mail checking/sending

Neuron spike trains

Seismic signals

Sunspots

@gmiritello

Bursty behavior. Why does it matter?

Information spreading

Epidemic spreading

Digital viruses

Opinions/Influence/Innovation diffusion

@gmiritello

Other temporal processes

3020 C.A. Hidalgo, C. Rodriguez-Sickert / Physica A 387 (2008) 3017–3024

Fig. 2. Persistence across a cellular phone network (a) Distribution of persistence for all links (b) Fraction of surviving ties as a function of time.The inset shows the same plot in a double logarithmic scale. The continuous line is t�1/4.

Fig. 3. Network structure and the persistence of ties (a) A fragment of the network extracted by considering up to the second neighbour of arandomly chosen node (indicated by a black arrow). (b) Distribution of persistence divided into nine degree categories. (c) Number of persistentlinks defined as those with a persistence of, from top to bottom: 5/10, 6/10, 7/10, 8/10, 9/10 and 10/10. (d) Distribution of persistence dividedinto nine clustering categories. (e) Distribution of persistence divided into five different reciprocity segments.

correlations between persistence, perseverance and the topological attributes of the mobile call network. In particular,we find that these temporal attributes correlate with topological variables such as the number of connection or degreeki , the average reciprocity of a node r (fraction of ties containing both incoming and outgoing calls) and the clusteringcoefficient of a node Ci defined as

Ci = 2�ki (ki � 1)

, (3)

where � is the number of triads in which the node is involved. Fig. 3(b) shows a histogram of persistence split intonine different degree categories revealing that persistent links represent a large fraction of the connections for lowdegree nodes while transient links are more common for large degree nodes. The number of persistent ties however,grows as a function of degree, meaning that although on average the persistence of high degree nodes is lower, inabsolute terms their core is larger.

Hidalgo y Rodriguez-Sickert. Physica A (2008) data set except during natural spells of re-duced activity, such as winter break (Fig. 4C).On the other hand, as Fig. 4D illustrates, in-dividual ranks change substantially over theduration of the data set. Analogous results(27) apply to the concept of Bweak ties[ (13):The distribution of tie strength in the net-work is stable over time, and bridges are, onaverage, weaker than embedded ties Econsist-ent with (13)^. However, they do not retaintheir bridging function, or even remain weak,indefinitely.

Our results suggest that conclusionsrelating differences in outcome measuressuch as status or performance to differencesin individual network position (14) should betreated with caution. Bridges, for example,may indeed facilitate diffusion of informa-tion across entire communities (13). How-ever, their unstable nature suggests that theyare not Bowned[ by particular individualsindefinitely; thus, whatever advantages they

confer are also temporary. Furthermore, it isunclear to what extent individuals are ca-pable of strategically manipulating their po-sitions in a large network, even if that istheir intention (14). Rather, it appears thatindividual-level decisions tend to Baverage out,[yielding regularities that are simple functionsof physical and social proximity. Sharing focalactivities (10) and peers (26), for example,greatly increases the likelihood of individualsbecoming connected, especially when theseconditions apply simultaneously.

It may be the case, of course, that the in-dividuals in our population—mostly studentsand faculty—do not strategically manipulatetheir networks because they do not need to, notbecause it is impossible. Thus, our conclusionsregarding the relation between local and globalnetwork dynamics may be specific to theparticular environment that we have studied.Comparative studies of corporate or militarynetworks could help illuminate which features

of network evolution are generic and which arespecific to the cultural, organizational, andinstitutional context in question. We note thatthe methods we introduced here are generic andmay be applied easily to a variety of other set-tings. We conclude by emphasizing that under-standing tie formation and related processes insocial networks requires longitudinal data onboth social interactions and shared affiliations(4, 6, 10). With the appropriate data sets, theo-retical conjectures can be tested directly, andconclusions previously based on cross-sectionaldata can be validated or qualified appropriately.

References and Notes1. P. S. Dodds, D. J. Watts, C. F. Sabel, Proc. Natl. Acad. Sci.

U.S.A. 100, 12516 (2003).2. J. M. Kleinberg, Nature 406, 845 (2000).3. T. W. Valente, Network Models of the Diffusion of

Innovations (Hampton Press, Cresskill, NJ, 1995).4. P. Doreian, F. N. Stokman, Eds., Evolution of Social

Networks (Gordon and Breach, New York, 1997).5. P. Lazarsfeld, R. Merton, in Freedom and Control in

Modern Society, M. Berger, T. Abel, C. Page, Eds. (VanNostrand, New York, 1954), pp. 18–66.

6. M. McPherson, L. Smith-Lovin, J. M. Cook, Annu. Rev.Sociol. 27, 415 (2001).

7. J. A. Davis, Am. J. Sociology 68, 444 (1963).8. T. M. Newcomb, The Acquaintance Process (Holt Rinehart

and Winston, New York, 1961).9. P. M. Blau, J. E. Schwartz, Crosscutting Social Circles

(Academic Press, Orlando, FL, 1984).10. S. L. Feld, Am. J. Sociology 86, 1015 (1981).11. J. S. Coleman, Sociol. Theory 6, 52 (1988).12. A. Rapoport, Bull. Math. Biophys. 15, 523 (1953).13. M. S. Granovetter, Am. J. Sociology 78, 1360 (1973).14. R. S. Burt, Am. J. Sociology 110, 349 (2004).15. M. Hammer, Soc. Networks 2, 165 (1980).16. M. T. Hallinan, E. E. Hutchins, Soc. Forces 59, 225 (1980).17. M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 98, 404

(2001).18. S. Wasserman, K. Faust, Social Network Analysis: Methods

and Applications (Cambridge Univ. Press, Cambridge,1994).

19. M. E. J. Newman, SIAM Review 45, 167 (2003).20. J. P. Eckmann, E. Moses, D. Sergi, Proc. Natl. Acad. Sci.

U.S.A. 101, 14333 (2004).21. C. Cortes, D. Pregibon, C. Volinsky, J. Comp. Graph. Stat.

12, 950 (2003).22. P. Holme, C. R. Edling, F. Liljeros, Soc. Networks 26, 155

(2004).23. B. Wellman, C. Haythornthwaite, Eds., The Internet in

Everyday Life (Blackwell, Oxford, 2003).24. N. K. Baym, Y. B. Zhang, M. Lin, New Media Soc. 6, 299

(2004).25. Materials and methods are available as supporting

material on Science Online.26. H. Louch, Soc. Networks 22, 45 (2000).27. G. Kossinets, D. J. Watts, data not shown.28. M. E. J. Newman, S. H. Strogatz, D. J. Watts, Phys. Rev. E

6402, 026118 (2001).29. We thank P. Dodds and two anonymous reviewers for

helpful comments and B. Beecher and W. Bourne forassistance with data collection and anonymization. Thisresearch was supported by NSF (SES 033902), the James S.McDonnell Foundation, Legg Mason Funds, and theInstitute for Social and Economic Research and Policy atColumbia University.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/311/5757/88/DC1Materials and MethodsReferences

1 July 2005; accepted 29 November 200510.1126/science.1116869

Fig. 3. Network-levelproperties over time, forthree choices of smooth-ing window t 0 30 days(dashes), 60 days (solidlines), and 90 days(dots). (A) Mean vertexdegree bkÀ. (B) Fraction-al size of the largestcomponent S. (C) Meanshortest path length inthe largest componentL. (D) Clustering coeffi-cient C.

Fig. 4. Stability of de-gree distribution and in-dividual degree ranks. (A)Degree distribution inthe instantaneous net-work at day 61, logarith-mically binned. (B) Sameat day 270. (C) TheKolmogorov-Smirnovstatistic D comparing de-gree distribution in theinstantaneous network atday 61 and in subse-quent daily approxima-tions. (D) Dissimilaritycoefficient for degreeranks z 0 1 – rS

2, whererS is the Spearman rankcorrelation between indi-vidual degrees at day 61 and in subsequent approximations. z varies between 0 and 1 andmeasures the proportion of variance in degree ranks that cannot be predicted from the ranks inthe initial network.

REPORTS

6 JANUARY 2006 VOL 311 SCIENCE www.sciencemag.org90

Kossinets and Watts, Science (2006)

Most ties are not persistent in time. Only 30% of ties persists after 300 days!

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Human communication happens in groups (motifs)

Q. Zhao, and N. Oliver NetMob (2010)

Other temporal processes

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spatial patterns. mobility.

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How are distributed places in a city?

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Which and how many locations do you visit?Our mobility behavior is predictive: we repeatedly visit very few locations (home, work, leisure, ..).

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Human mobility and social tiesSocial relationships can explain about 10% to 30% of all human movements.

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Human mobility and social ties

Is a person with a stable job and family likely to be less exploratory and more predictable than a young college student with many acquaintances?

• bin nodes into groups based on two mobility metrics: a) the number of unique locations visited S and b) how predictable that user is (based on unique visited locations in time)

• compute the fraction of edges that belong to each classification for all nodes in each mobility bin.

• users who tend to visit more unique locations tend to have a higher fractions of acquaintances in their ego network

• less predictable individuals tend to have fewer contacts in this category.

The composition of a user’s ego network is correlated with mobility behavior

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Social networks and locations. Why does it matter?

recommendation transport systems

epidemic spreading

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Summary- Social networks are heterogeneous. Hubs.

- Your friends have more friends than you do, but it is not your fault. Blame the Friendship Paradox

- Between you and any other person on the planet there are only 5-6 other intermediates (on average)

- Friends of your friends are very likely to become your friends too

- We are very similar to our friends. But..influence or homophily?

- Dunbar number: cognitive limit to the number of people with whom one can maintain stable social relationships.

- The way we interact in time is not homogeneous, but bursty.

- Social relationships can explain about 10% to 30% of all human movements

Social Network. Why they are different.Palo Alto, California. @gmiritello Giovanna Miritello...

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