Download presentation

Presentation is loading. Please wait.

Published byPaulina Washington Modified about 1 year ago

1
Social Networks 101 P ROF. J ASON H ARTLINE AND P ROF. N ICOLE I MMORLICA

2
Last week… Overview of class Networks – why they have low diameter Game theory – dominant strategy/Nash equil. Markets – bidding in 1 st price auctions And in the blogsphere…

3
Blog Posts Week 1

4
Bush vs. Kerry Poster: Alexander Sheu About: Pure Nash and mixed Nash equilibria Link:

5
Difference Between Social Networking and Social Networks Difference between this course and Facebook. One is about connecting with your friends One is a group of theories about how things connect.

6
Difference Between Social Networking and Social Networks Difference between this course and Facebook. One is about connecting with your friends One is a group of theories about how things connect. One you will get points for posting about.

7
Difference Between Social Networking and Social Networks Difference between this course and Facebook. One is about connecting with your friends One is a group of theories about how things connect. One you will get points for posting about. The other is a good way of connecting with your friends.

8
“Very Useful Website” Power of “memes”

9
Conficker Worm

10
Next three weeks Social networks diameter, decentralized search, preferential attachment, PageRank, information cascades

11
Lecture Four: The diameter of a random graph.

12
Six degrees of separation Last time: The diameter of a social network is typically small.

13
Argument Each person has two new friends d2d + diameter = log n 2 d+1 - 1

14
Argument Each person has two new friends diameter = log n … but friends are likely to overlap.

15
Understanding social networks These networks are complex, … but they have a simple story for creation The interplay of fate and chance.

16
A random explanation Random links make short paths e.g., if you take a graph and “perturb” it, long paths are likely to reconnect

17
A random graph Each person knows 3 random others KEY: = a person = her rolodex

18
A random graph Each person knows 3 random others 1.People meet at random, write names into rolodexes. 2.Relationships are reciprocal. 3.Each rolodex has 3 distinct names.

19
A random graph Collapse big nodes to get graph.

20
A random graph Collapse big nodes to get graph.

21
Diameter of a random graph Consider growing tree while size of current tree is small enough Interior of current tree Leaves of current tree

22
Breadth-first search tree How many new leaves? Interior of current tree

23
Breadth-first search tree How many new leaves? Interior of current tree

24
Breadth-first search tree How many new leaves? Interior of current tree

25
Doubling argument When size of current tree is small enough # of leaves approximately doubles (doubling fails if new friend of a leaf node falls inside current tree or collides with new friend of another leaf node)

26
Doubling argument What is small enough? Suppose current tree T has size x. Pr[1 st new friend is in T] < x/n Pr[neither new friend is in T] > (1 – x/n) 2 Pr[all new friends outside of T] > [(1 – x/n) 2 ] x/2

27
Time for

28
Doubling argument What is small enough? Suppose current tree T has size x. Pr[all new friends outside of T] > (1 – x/n) x This is constant for x = √n.

29
Bounding number of steps Doubling number of leaves each time, it takes ? steps to reach √n nodes.

30
Bounding number of steps Doubling number of leaves each time, it takes log √n steps to reach √n nodes. But we still haven’t reached most nodes!

31
Good ideas are worth repeating To compute distance from some node 1 to another node 2, Idea: grow 2 trees! Each tree gets √n nodes in time log √n; argue that the trees intersect.

32
Growing two trees Random graph Tree 1 Tree 2 node 1 node 2

33
The birthday paradox Experiment: Your index card contains a random number between 1 and 100. Find someone in the same row as you that has your number and you will both earn a point. Find someone in an adjacent row that has your number and you will get ½ a point.

34
The birthday paradox Suppose you have d people, and each has a random number between 1 and n. Prob[no two people have same #] = = 1 x (1 – 1/n) x (1 – 2/n) x … x (1 – (d-1)/n) > (1 – d/n) d Constant for d = √n!

35
Good ideas are worth repeating Tree of size x has about x/2 leaves. Each leaf chooses two random neighbors. What is prob. two trees don’t intersect? Birthday paradox!

36
Intersecting trees Two trees of size √n (so √n/2 leaves each, or leaves in total √n).

37
Intersecting trees By birthday paradox, with constant probability 2 leaves pick same neighbor.

38
Intersecting trees With constant probability, these 2 leaves are from different trees, and so the trees intersect.

39
Bounding distance bt. two nodes Two trees of size √n intersect with constant probability, … and so we can combine the trees.

40
Diameter of a random graph Hence the expected distance between any two nodes … is about 2 log √n = log (√n) 2 = log n. Diameter of this class should be about 4!

41
Next time decentralized search

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google