Internet Economics כלכלת האינטרנט

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

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

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

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

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

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

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

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

Example 4: blogs • 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

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

Job search • 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.

Let’s define some new concepts…

Concept 1: Triadic Closure • “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”. B C A

Triadic Closure – why? B • 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.” C A

Concept 2: Bridges E D 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. A G B H F C For node B:edge to A is different than other links. • Links him to parts of the network that he does not know.

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

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

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

Example 3: Facebook

Local Bridges and job search • 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 K M I J L E D A G B H F C

Concept 4: Strong/weak ties • 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”. Solid lines:strong ties E D A G B H Dashed lines:weak ties F C

The Strong Triadic Closure Property STC property: The following case does not occur: • Ahas strong ties to B and C • B and C are not friends at all (neither strong or weak) E D A G B H E D F C A G B H F C

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

Local bridges and weak ties 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: C B Assume this is a local bridge and a strong tie. But then this cannot be a bridge! Contradiction. A

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

Evidence from Facebook • 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 Classification by the extent the link was actually used. • Reciprocal communicationthe user both received and sent messages to this friend. • One-way communicationthe user sent a message (or more) to this friend • Maintained relationshipthe user followed information about this friend (visiting his profile, following content on News Feed Service etc.) stronger weaker

Real Data • Let’s have a look at real Facebook data. • A network of some user’s friends (and links between them)

Comments • 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 survivesPossible explanation: more recent friends (co-workers?)

Evidence from Twitter • : 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…

Number of strong ties Evidence from Twitter Number of weak ties • 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 - conclusion • 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 • 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…

Internet Economics כלכלת האינטרנט