6.207/14.15: Networks
Additional Problems
Friday, November 6, 2009
Problem 1. (Multitype Erd s- Rnyi)
o
e
Consider the following multitype generalization of the Erdos-R
enyi random graph model.
Nodes are of two types, type a and type b.
Fraction f of

6.207/14.15: Networks
Lecture 3: Erds-Renyi graphs and Branching processes
o
Daron Acemoglu and Asu Ozdaglar
MIT
September 16, 2009
1
Networks: Lecture 3
Introduction
Outline
Erds-Renyi random graph model
o
Branching processes
Phase transitions and thresh

6.207/14.15: Networks
Lecture 2: Graph Theory and Social Networks
Daron Acemoglu and Asu Ozdaglar
MIT
September 14, 2009
1
Networks: Lecture 2
Introduction
Outline
Types of networks
Graphs: notation and terminology
Properties of networks:
Diameter, averag

6.207/14.15: Networks
Lecture 1: Introduction
Daron Acemoglu and Asu Ozdaglar
MIT
September 9, 2009
1
Networks: Lecture 1
Introduction
Outline
What are networks?
Examples.
Small worlds.
Economic and social networks.
Network eects.
Networks as graphs.
Stro

6.207/14.15: Networks
Additional Problems
Friday, November 6, 2009
Problem 1. (Multitype Erd s- Rnyi) o e Consider the following multitype generalization of the Erdos-R enyi random graph model. Nodes are of two types, type a and type b. Fraction f of

6.207/14.15: Networks
Problem Set 5
Due: Wednesday, December 2, 2009
Problem 1. [Cooperation over social network]
Consider a social network, in which agents are matched pairwise at each date according to a matrix of
probabilities P (where all entries of

6.207/14.15: Networks
Problem Set 4
Due: Friday, November 6, 2009
Problem 1. [Sudoku as a game of cooperation] In the popular game of Sudoku, the number placement puzzle, the objective is to ll a 9 9 grid so that each column, each row, and each of the nin

6.207/14.15: Networks
Problem Set 3
Due: Wednesday, October 28, 2009
Problem 1 (Iterated Elimination of Strictly Dominated Strategies)
Consider the iterated elimination of strictly dominated strategies in the strategic form game I , (Si )i I , (ui )i I .

6.207/14.15: Networks
Problem Set 2
Due: Wednesday, October 14, 2009
Problem 1. Consider a growing random network model generated as follows: At each time step, k nodes (k > 1) each with degree k are born. All k of the newborn nodes connect to each o

6.207/14.15: Networks
Lecture 4: Erds-Renyi Graphs and Phase Transitions
o
Daron Acemoglu and Asu Ozdaglar
MIT
September 21, 2009
1
Networks: Lecture 4
Outline
Phase transitions
Connectivity threshold
Emergence and size of a giant component
An application

6.207/14.15: Networks
Lecture 5: Generalized Random Graphs and Small-World
Model
Daron Acemoglu and Asu Ozdaglar
MIT
September 23, 2009
1
Networks: Lecture 5
Outline
Generalized random graph models
Graphs with prescribed degrees Conguration model
Emergenc

6.207/14.15: Networks
Lecture 6: Growing Random Networks and Power Laws
Daron Acemoglu and Asu Ozdaglar
MIT
September 28, 2009
1
Networks: Lecture 6
Outline
Growing random networks
Power-law degree distributions: Rich-Get-Richer eects
Models:
Uniform atta

6.207/14.15: Networks
Problem Set 5
Due: Wednesday, December 2, 2009
Problem 1. [Cooperation over social network]
Consider a social network, in which agents are matched pairwise at each date according to a matrix of
probabilities P (where all entries of P

6.207/14.15: Networks
Problem Set 4
Due: Friday, November 6, 2009
Problem 1. [Sudoku as a game of cooperation]
In the popular game of Sudoku, the number placement puzzle, the objective is to ll a 9 9 grid so that each
column, each row, and each of the nin

6.207/14.15: Networks
Problem Set 3
Due: Wednesday, October 28, 2009
Problem 1 (Iterated Elimination of Strictly Dominated Strategies)
Consider the iterated elimination of strictly dominated strategies in the strategic form game I , (Si )i I , (ui )i I .

6.207/14.15: Networks
Problem Set 2
Due: Wednesday, October 14, 2009
Problem 1. Consider a growing random network model generated as follows:
At each time step, k nodes (k > 1) each with degree k are born.
All k of the newborn nodes connect to each o

6.207/14.15: Networks
Problem Set 1
Due: Monday, September 28, 2009
Problem 1.1 (Phase Transitions in the Erdos-Renyi Model)
Consider an Erdos-Renyi random graph G (n, p).
(a) Let A l denote the event that node 1 has at least l Z + neighbors. Do we obser

6.207/14.15: Networks
Midterm Exam
Monday, November 9, 2009
Problem 1. (Dying Links in Preferential Attachment) - 30 Points
Consider a preferential attachment process where at each step a single node with m links is born.
Suppose that each newborn agent

6.207/14.15: Networks
Lecture 8: Diusion through Networks
Daron Acemoglu and Asu Ozdaglar
MIT
October 7, 2009
1
Networks: Lecture 8
Outline
Spread of epidemics in networks
Models of diusion without network structure
Bass model
Models of diusion that expli

6.207/14.15: Networks
Lecture 7: Search on Networks: Navigation and Web
Search
Daron Acemoglu and Asu Ozdaglar
MIT
September 30, 2009
1
Networks: Lecture 7
Outline
Navigation (or decentralized search) in networks
Web search
Hubs and authorities: HITS algo

6.207/14.15: Networks
Problem Set 1
Due: Monday, September 28, 2009
Problem 1.1 (Phase Transitions in the Erdos-Renyi Model) Consider an Erdos-Renyi random graph G (n, p). (a) Let A l denote the event that node 1 has at least l Z + neighbors. Do we obser

School of Information University of Michigan
Unless otherwise noted, the content of this course material is licensed under a Creative Commons Attribution 3.0 License. http:/creativecommons.org/licenses/by/3.0/ Copyright 2008, Lada Adamic
You assume all re

6.207/14.15: Networks
Lecture 9: Introduction to Game Theory1
Daron Acemoglu and Asu Ozdaglar
MIT
October 13, 2009
1
Networks: Lecture 9
Introduction
Outline
Decisions, Utility Maximization Games and Strategies Best Responses and Dominant Strategies Nas

6.207/14.15: Networks
Lecture 8: Diusion through Networks
Daron Acemoglu and Asu Ozdaglar
MIT
October 7, 2009
1
Networks: Lecture 8
Outline
Spread of epidemics in networks Models of diusion without network structure
Bass model
Models of diusion that exp

6.207/14.15: Networks
Lecture 7: Search on Networks: Navigation and Web
Search
Daron Acemoglu and Asu Ozdaglar
MIT
September 30, 2009
1
Networks: Lecture 7
Outline
Navigation (or decentralized search) in networks
Web search
Hubs and authorities: HITS

6.207/14.15: Networks
Lecture 6: Growing Random Networks and Power Laws
Daron Acemoglu and Asu Ozdaglar
MIT
September 28, 2009
1
Networks: Lecture 6
Outline
Growing random networks Power-law degree distributions: Rich-Get-Richer eects Models:
Uniform at

6.207/14.15: Networks
Lecture 5: Generalized Random Graphs and Small-World
Model
Daron Acemoglu and Asu Ozdaglar
MIT
September 23, 2009
1
Networks: Lecture 5
Outline
Generalized random graph models Graphs with prescribed degrees Conguration model Emerg

6.207/14.15: Networks
Lecture 4: Erds-Renyi Graphs and Phase Transitions
o
Daron Acemoglu and Asu Ozdaglar
MIT
September 21, 2009
1
Networks: Lecture 4
Outline
Phase transitions Connectivity threshold Emergence and size of a giant component An applicat

6.207/14.15: Networks
Lecture 3: Erds-Renyi graphs and Branching processes
o
Daron Acemoglu and Asu Ozdaglar
MIT
September 16, 2009
1
Networks: Lecture 3
Introduction
Outline
Erds-Renyi random graph model o Branching processes Phase transitions and thr

6.207/14.15: Networks
Lecture 2: Graph Theory and Social Networks
Daron Acemoglu and Asu Ozdaglar
MIT
September 14, 2009
1
Networks: Lecture 2
Introduction
Outline
Types of networks Graphs: notation and terminology Properties of networks:
Diameter, aver