Internet Economicsכלכלת האינטרנט

Class 9 – social networks

(based on chapter 3 from Easely & Kleinberg’s books)

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Outline

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• A brief introduction

• Motivating example: job search

• Extending the model:– Bridges– Strong/weak ties– Properties and assumptions

• Real-world examples

history

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• Have been studied for a long time in sociology

• Now, an interdisciplinary field:– Economics, computer science, marketing, physics,

biology, medicine, and more…

• In the past: research on social networks with dozens of participants.Now: hundreds of millions users, well documented and electronically available data.

Modeling Social Networks

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• What is a social network? A graph.– Nodes … (participants)– Edges …. (meaning “friendship, know eachother,…)

G

E

F

D

C

B

AH

Non directed edge:“A and B are

friends”

A directed edge:“A is a friend of C”

modeling

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• We will make the graph modeling more complicated soon…

Example 1: high school romance

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• Nodes: high school students (male and female)• Edges: “have been in a romantic touch within the past 18 months”

Example 2: karate

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• Nodes: kids in a karate club• Edges: friendship

Example 3: Facebook

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• Nodes: Facebook accounts• Edges: (confirmed) friendships

Example 4: email

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• Nodes: 436 employees in a big firm (HP Research lab)• Edges: email between employees in the last 6 months

Example 4: blogs

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• Nodes: blogs• Edges: link to blog posts of other bloggers

Social network topics• We saw: structure.

• More issues:– Forming– Dynamics– Information– Strategic interactions– Influence– Behavior– “Riches Get Richer”, herding

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Outline

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• A brief introduction

Motivating example: job search

• Extending the model:– Bridges– Strong/weak ties– Properties and assumptions

• Real-world examples

Job search

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• In a famous experiment (late 1960’s), new employees were asked:

“how did you find your new job?”

• Most common observations:– “heard about it from a friend”– “this friend is more an acquaintance rather than a close

friend”

• Today we will try to model this phenomena:searching for information over social networks.

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Let’s define some new concepts…

Concept 1: Triadic Closure

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• “if A and B have a friend in common, there is an increase likelihood that they will become friends in the future”– Creating a “triangle”.

A

B

C

Triadic Closure – why?

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• More opportunities to meet– Social events, through the web,…

• Trust

• Incentives– “I want my friends to be friends”, Dating

• Homophily– People tend to be friends with similar others.

B says: “If C is my friend, he likes Star-wars, and most chances that A likes Star-wars too.”

A

B

C

Concept 2: Bridges

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Definition: An edge (A,B) is a bridge, if after deleting it A and B will lie in different components.– That is, (A,B) is the only path between them.

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E

F

B

C

D

HA

For node B: edge to A is different than other links.– Links him to parts of the network that he does not know.

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How many bridges do you expect to see in real networks?

Bridges – common?

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Remember the “small world” phenomenon?Kevin Bacon Game?

Bridges hardly exist in real networks!We need to refine this concept.

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E

F

B

C

D

HA

Concept 3: Local Bridges

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Local bridges: example: (A,B)

Connected pairs of nodes with no friends in common.– In other words, deleting the edge would increase the distance

between the nods to more than 2.– Conceptually opposite concept to triadic closure

(a local bridge is not a side of any triangle)

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E

F

B

C

D

HA

K

J L

M

I• In most cases, there are other social paths to friends— Probably harder to find.

Example 3: Facebook

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Local Bridges and job search

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G

E

F

B

C

D

HA

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J L

M

I

• Assume A is looking for a job.

• New information about jobs is likely to come via the local bridge.

• Why?The people close to you, although eager to help, know roughly the same things that you do.— And other paths are too long

Concept 4: Strong/weak ties

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• Remember the job-search example.• We need to distinguish between strengths of

friendships.

In our model, two types of friends:– Strong ties: mean “friends”.– Weak ties: mean “acquaintances”.

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E

F

B

C

D

HA

Solid lines:strong ties

Dashed lines:weak ties

The Strong Triadic Closure Property

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STC property:The following case does not occur:

– A has strong ties to B and C– B and C are not friends at all (neither strong or

weak)

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E

F

B

C

D

HA

G

E

F

B

C

D

HA

local bridges and weak ties

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We saw several definition so far:– Inter-personal (weak, strong ties)– Structural (local bridges)

The following claim connects them:

Local bridges and weak ties

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Assuming the STC property.

A (simple) claim:If node has at least 2 strong ties,

any local bridge it is involved in must be a weak tie.

Proof:

A

C B

Assume this is a local bridge and a strong tie.

But then this cannot be a bridge! Contradiction.

Job search - conclusion

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• When searching for information (job, for example) people want to collect new information.

• Users share knowledge with their group of close friends.– Who are also friends by the STC property

• For getting new information, users try their distance sources – via local bridges – to give them access to new information.

• Local bridges are accessed by weak ties – “acquaintances” – by the claim we proved.

• Therefore, people learn new information from “acquaintances” rather than from close friends.

Outline

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• A brief introduction

• Motivating example: job search

• Extending the model:– Bridges– Strong/weak ties– Properties and assumptions

Real-world examples

Evidence from Facebook

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• Social interaction moves online, and also the way we maintain our social networks.

• In online social networks, people maintain lists of friends– Friendship ties used to be more implicit.

• People have lists of hundreds of friends– Strong ties? (frequent contact)– Weak ties? (rare activity)

Friendship strengths in Facebook

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Classification by the extent the link was actually used.1. Reciprocal communication

the user both received and sent messages to this friend.

2. One-way communicationthe user sent a message (or more) to this friend

3. Maintained relationshipthe user followed information about this friend (visiting his profile, following content on News Feed Service etc.)

stronger

weaker

Real Data

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• Let’s have a look at real Facebook data.

• A network of some user’s friends (and links between them)

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Comments

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• We can see that the network becomes sparser as ties become stronger.

• Also, some parts thin out much faster than others:

• Consider the two clusters with large amount of “triadic closure”:– Cluster on the right becomes thinner quickly.

Possible explanation: bunch of old (highschool?) friends– Upper cluster survives

Possible explanation: more recent friends (co-workers?)

Evidence from Twitter

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• : micro-blogging web site, 140-characters messages (“Tweets”)

• Users can specify a set of other users they follow.For us: weak ties (it is easy to follow many users)

• A user can send messages directly to a certain user.For us: strong ties. – Definition: strong tie if at least two messages were

directed personally to the other user in the last month.

• How many strong ties can a user have?– Lets see real data…

Evidence from Twitter

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• We see: even users with many weak ties, only maintain few strong ties.• Stabilizes at about 40 for users with above 1000

followees.

Number of strong ties

Number of weak ties

Number of Strong Ties - conclusion

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• Even people with energies for maintaining many strong ties reach a limit.– Number of hours a day is limited….

• Weak ties do not need lots of maintenance….

Conclusions

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• Social interaction moves online.

• Explicit lists of friends, good opportunity for research

• We modeled social network by graphs, and added some properties like:– Weak and strong ties– Bridges and local bridges

• We raised some ideas on principles that should apply in networks– Triadic closure…