Internet Economics כלכלת האינטרנט Class 9 – social networks (based on chapter 3 from Easely & Kleinberg’s books) 1

Outline 2 A brief introduction Motivating example: job search Extending the model: – Bridges – Strong/weak ties – Properties and assumptions Real-world examples

history 3 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 4 What is a social network? A graph. – Nodes … (participants) – Edges …. (meaning “friendship, know eachother,…) G E F D C B A H Non directed edge: “A and B are friends” A directed edge: “A is a friend of C”

modeling 5 We will make the graph modeling more complicated soon…

Example 1: high school romance 6 Nodes: high school students (male and female) Edges: “have been in a romantic touch within the past 18 months”

Example 2: karate 7 Nodes: kids in a karate club Edges: friendship

Example 3: Facebook 8 Nodes: Facebook accounts Edges: (confirmed) friendships

Example 4: 9 Nodes: 436 employees in a big firm (HP Research lab) Edges: between employees in the last 6 months

Example 4: blogs 10 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 11

Outline 12 A brief introduction  Motivating example: job search Extending the model: – Bridges – Strong/weak ties – Properties and assumptions Real-world examples

Job search 13 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.

14 Let’s define some new concepts…

Concept 1: Triadic Closure 15 “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? 16 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 17 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. G E F B C D H A For node B: edge to A is different than other links. – Links him to parts of the network that he does not know.

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

Bridges – common? 19 Remember the “small world” phenomenon? Kevin Bacon Game? Bridges hardly exist in real networks! We need to refine this concept. G E F B C D H A

Concept 3: Local Bridges 20 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) G E F B C D H A K JL M I In most cases, there are other social paths to friends —Probably harder to find.

Example 3: Facebook 21

Local Bridges and job search 22 G E F B C D H A K JL 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 23 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”. G E F B C D H A Solid lines: strong ties Dashed lines: weak ties

The Strong Triadic Closure Property 24 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) G E F B C D H A G E F B C D H A

local bridges and weak ties 25 We saw several definition so far: – Inter-personal (weak, strong ties) – Structural (local bridges) The following claim connects them:

Local bridges and weak ties 26 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 CB Assume this is a local bridge and a strong tie. But then this cannot be a bridge! Contradiction.

Job search - conclusion 27 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 28 A brief introduction Motivating example: job search Extending the model: – Bridges – Strong/weak ties – Properties and assumptions  Real-world examples

Evidence from Facebook 29 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 30 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 communication the user sent a message (or more) to this friend 3.Maintained relationship the user followed information about this friend (visiting his profile, following content on News Feed Service etc.) stronger weaker

Real Data 31 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 36 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 37 : 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 38 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 39 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 40 Social interaction moves online.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…