basic network concepts - bilgisayar mühendisliği...

Basic Network Concepts

Alice

Bob

Chuck Nodes

Vertices

Edges

Links

Graph

Network

Basic Vocabulary

Alice

Bob

Chuck

Edges

Alice

Bob

Chuck

Edge Weights

Apollo 13 Movie Network

Main Actors in Apollo 13 the Movie:

Tom Hanks

Kevin Bacon

Gary Sinise

Bill Paxton

Ed Harris

Actors are nodes. Edges connect actors who were in a movie together.

Since all were in Apollo 13, this is not interesting. Let’s make a new network that connects them if they were in an additional movie together.

Tom

Hanks

Kevin

Bacon

Ed

Harris

Bill

Paxton

Gary

Sinise

Magnificent Desolation:

Walking on the Moon

Magnificent Desolation:

Walking on the Moon

The Green Mile

Beyond All Boundaries

The Human

Stain

Apollo 13 Movie Network

Tom

Hanks

Kevin

Bacon

Ed

Harris

Bill

Paxton

Gary

Sinise

Directed or Undirected?

TH,BP

TH,GS

BP,GS

GS,KB

GS,EH

Tom

Hanks

Kevin

Bacon

Ed

Harris

Bill

Paxton

Gary

Sinise

Adjacency List

TH BP GS EH KB

TH 1 2

BP 1 1

GS 2 1 1 1

EH 1

KB 1

Tom

Hanks

Kevin

Bacon

Ed

Harris

Bill

Paxton

Gary

Sinise

Adjacency Matrix

A

C

D

F

H B

G

E

Shortest Path Length and Cliques

Tom

Hanks

Kevin

Bacon

Ed

Harris

Bill

Paxton

Gary

Sinise

Cliques

Connectedness

Two nodes are connected if there is a path between them.

A graph is connected if there is a path between every pair of nodes.

In a directed graph, it is strongly connected if there is a directed path between each pair. It is weakly connected if there is a path between every pair if direction is ignored.

R

K

J

H G

F

N

M

L

I

O

P

Q A

B C

D E

Hubs and Bridges

Clusters

A cluster is a group of nodes that are tightly connected

“tightly” varies, but usually means they are more tightly connected than the network as a whole

Does not need to be a clique

Group in the lower left of previous graph is a cluster

O

P

Q A

B C

D E

Subnetworks

Q A

B C

D E

Egocentric Networks

Network Structure

Tom Hanks

Kevin

Bacon

Ed Harris

Bill Paxton

Gary Sinise

Degrees

Tom Hanks

Bill Paxton

Gary Sinise

Kevin Bacon

Ed Harris

2

2

4

1

1 Degree Distribution

0

0.5

1

1.5

2

2.5

1 2 3 4

Degree

Degree Distribution

3

2

3

4

3 3

4

2

Degree Distribution

0

1

2

3

4

5

1 2 3 4

Degree

Degree Distribution

Edges: 5

Tom Hanks

Kevin

Bacon

Ed Harris

Bill Paxton

Gary Sinise

Total Possible Edges: 10 Density: 5/10 = 0.5

Density

Nodes: 8

Edges: 12

Total Possible Edges: ??

# Nodes * (# Nodes -1)

2

(8*7)/2 = 56/2 = 28

Density: 12/28 = 0.43

Density

Clustering Coefficient

Density of a node’s 1.5 degree egocentric network (with the node itself excluded) is called its clustering coefficient.

An important measure we will see later on.

R

K

J H

G

F N

M

L

I

B

C

D

A

Q

P

O E

Which Node is Most Important?

R

K

J

H G

F

N

M

L

I

O

P

Q A

B C

D E

Which Node is Most Important?

R

J

H G

F

I

O

P

Q

C

D

P 1

O 1

D 3

C 2

Q 2

R 1

G 2

J 2

I 2

H 2

=18/10=1.8

Closeness Centrality

R

J

H G

F

I

O

P

Q

C

D

P 2

O 2

D 4

C 3

Q 3

F 1

G 1

J 1

I 1

H 1

=19/10 =1.9


R

J

H G

F

I

O

P

Q

C

D

F 1

O 1

D 2

C 2

Q 1

R 2

G 3

J 3

I 3

H 3

=21/10 =2.1


Degree Centrality

R=9

F=3

D=5

B=4

R

K

J

H G

F

N

M

L

I

O

P

Q A

B C

D E

Betweenness Centrality

Measure of a node’s influence

Percentage of shortest paths that include a given node

Betweenness Centrality

C

A

B

H

D

E

G

F

Eigenvector Centrality

Measure of a node’s importance

Iterative matrix computation that gives more weight to nodes if they are connected to influential nodes.

The backbone to techniques like Google’s PageRank which ranks web pages.

Connectivity and Cohesion

Minimum number of nodes to remove before the network becomes disconnected.

C

A B

H

D

E

G

F

Cohesion=1

B

E

F D A

C G

Cohesion=2

Network

Exercise

Open an assigned network in a network analysis tool like Gephi or NodeXL.

Run statistics to compute centrality.

Compare different centrality measures.

Visual Analysis of Networks

What is interesting about this network?

What makes a good visualization?

Every node is visible

For every node you can count its degree

For every link you can follow it from source to destination

Clusters and outliers are identifiable

(Dunne and Shneiderman, 2009)

We can’t always do all of this, but it’s a start

Is this a good visualization?

What about this one?

And this one?

And finally, this one?

Node Size and Color

Edge Weight

Visualization Issues

Scale

Too many nodes (~10,000 or more) or edges are almost impossible to visualize

Dense networks may not reveal patterns

Example: Senate Voting Records

Filtering

Visualization Tools

Gephi

All platforms

Stand alone program

NodeXL

Windows only

Plugin for Microsoft Excel

In Class Exercise

Load an assigned dataset into NodeXL or Gephi

Create a visualization, using color, size, layout, and other features to tell a story or provide an insight into the data.

Post your final visualization in a shared space

Tie Strength

Strong vs. Weak Ties

Strong ties

Trusted

Close friends and family

Weak ties

Often part of other social circles

Acquaintances, co-workers

We talk about “strong” or “weak” ties, but in reality, there is a continuous spectrum

Mark Granovetter

Foundational work in 1973, “The Strength of Weak Ties”

Strong ties had been considered most important

His work showed weak ties mattered

Getting a Job

Carl Y. was doing commission sales for an encyclopedia firm, but was not doing well. He decided he would have to find a different job; meanwhile, he started driving a cab to bring in extra money. One passenger asked to be taken to the train station where he had to meet a friend. This friend turned out to be an old friend of Carl Y.'s, and asked him "what're you doing driving a cab?" When Mr. Y. explained, the friend offered him the job he now holds—labor relations manager for a small company, owned by his friend. (Granovetter, 1974, p34)

Granovetter, M. 1974. Getting a Job: A Study of Contacts and Careers..

Getting a Job

George C. was working as a technician for an electrical firm, with a salary of about $8000, and little apparent chance for advancement. While courting his future wife, he met her downstairs neighbor, the manager of a candy shop, a concession leased from a national chain. After they were married, Mr. C. continued to see him when visiting his mother-in-law. The neighbor finally talked him into entering a trainee program for the chain, and arranged an interview for him. Within three years, Mr. C. was earning nearly $30,000 in this business. (Granovetter, 1974, p. 49).


Getting a Job

Edward A., during high school, went to a party given by a girl he knew. There, he met her older sister's boyfriend, who was ten years older than himself. Three years later, when he had just gotten out of the service, he ran into him in a local hangout. In conversation, the boyfriend mentioned to Mr. A. that his company had an opening for a draftsman. Mr. A. applied for this job and was hired. (Granovetter, 1974, p. 76)


Replicating Milgram’s Six Degrees

Send booklets from original participants to a target, unknown person

(Lin, et al) show that successful chains made heavy use of weak ties

Weak Ties in Use

Racial integration in schools

Job satisfaction in psych hospital

The benefits of weak ties

Connect people to different social circles, exposing them to more information

Many more of them in a person’s life than strong ties

The network of strong ties

Measuring Tie Strength

Time

Emotional Intensity

Intimacy

Reciprocal Services

Measuring Tie Strength

Additional Features

Social Distance

Structural

Emotional Support

Quantifying Measurements

Time

Emotional Intensity

Intimacy

Reciprocal Services

Social Distance

Structural

Emotional Support

Measurement Overlaps

Network Structure – Forbidden Triad

Network Structure - Bridges

Tie Strength and Propagation

Strong ties – more trusted

Weak ties – wider spread

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