Structural Properties of
Networks: Introduction
Networked Life
NETS 112
Fall 2016
Prof. Michael Kearns
Networks: Basic Definitions
A network (or graph) is:
a collection of individuals or entities, each called a vertex or node
a list of pairs of vertice
Trading in Networks:
I. Model
Prof. Michael Kearns
Networked Life
NETS 112
Fall 2014
Roadmap
Networked trading motivation
A simple model and its equilibrium
A detailed example
Networked Games vs. Trading
Models and experiments so far (coloring, consen
Internet Economics
Networked Life
NETS 112
Fall 2016
Prof. Michael Kearns
The Internet is an Economic System
(whether we like it or not)
Highly decentralized and diverse
allocation of scarce resources; conflicting incentives
Disparate network administr
Models of Network Formation
Networked Life
NETS 112
Fall 2016
Prof. Michael Kearns
Roadmap
Recently: typical large-scale social and other networks exhibit:
giant component with small diameter
sparsity
heavy-tailed degree distributions
high clustering coe
How Do Real Networks Look?
Networked Life
NETS 112
Fall 2016
Prof. Michael Kearns
Roadmap
Next several lectures: universal structural properties of networks
Each large-scale network is unique microscopically, but with appropriate
definitions, striking m
Incentives and Collective Behavior
Networked Life
NETS 112
Fall 2016
Prof. Michael Kearns
Game Theory for Fun and Profit
The Beauty Contest Game
Write your name and an integer between 0 and 100
Let X denote the average of all the numbers
Whoevers number i
Networked Games:
Coloring, Consensus and Voting
Prof. Michael Kearns
Networked Life
NETS 112
Fall 2016
Experimental Agenda
Human-subject experiments at the intersection of CS, economics, sociology, network science
Subjects simultaneously participate in gr
Contagion in Networks
Networked Life
NETS 112
Fall 2016
Prof. Michael Kearns
Two Models of Network Formation
Start with a grid, remove random fraction of vertices
local or geographic connectivity
Start with N isolated vertices, add random edges
long d
NETS 150 Homework 1
Due Feb 4, 2016 at 12.00pm
Part 1 Theory (20 points)
Please do the following problems:
1. Consider the graph shown below:
a. What is the in-degree and out-degree of each node? (2 points)
b. Show how Breadth-First Search wor
NETS150 Midterm
Graph: a way of representing relationships that exist between pairs of objects
Vertex (of a graph)/Nodes: Objects
Edge (of a graph)/Arc: Relationships
Degree (of a vertex): number of edges incident on the node
Path: sequence of alternating
Part 1: Theory
1. This statement is true. We can prove this by considering cases. The first two cases will be
if A or B are the starting node of the DFS. Case 1 is if the DFS starts with B, B will have
a starting time of 1. We know any finish time after t
Part 1:
1. What is a socket? What is the difference between a Socket object and a
ServerSocket object?
A socket is an endpoint of a two-way communication link between two
programs running on a network. It is bound to a port number. TCP is
used to identify
Part 2: Experimentation
1. We can choose the simple example representing how populations tend to self-segregate
even when not intentional. One way this is shown in the real world is with people of
different economic classes and their neighborhoods. In a n
Part 1 Theory
1.
a. 1: In-Degree of 2, Out-Degree of 1
2: In-Degree of 3, Out-Degree of 2
3: In-Degree of 1, Out-Degree of 2
4: In-Degree of 1, Out-Degree of 2
5: In-Degree of 2, Out-Degree of 1
6: In-Degree of 1, Out-Degree of 2
b. 2 1 4 5 3 6
c. 2 1 5 1
NETS150 Final
Adjacency list: collection of unordered lists used to represent a finite graph. Each list describes
the set of neighbors of a vertex in the graph.
Adjacency matrix: Square matrix used to represent a finite graph. The elements of the matrix
i
NETS HW#5 Theory
1. A)
Man
Women
L
L
NL
35, 35
45, 35
35, 45
50, 50
NL
B) The Best Response for the man would be NL if the women played NL, resulting in $50. The
Best Response for man would be NL if the women played L, resulting in $30. This means that th