Lecture 6 - Social Network Analysis

Question 1

Why analyse social networks?

Answer 1

Network influences behavior

If a person had a friend who became obese, chances of becoming obese increased by 57%.

Social interactions in youth, determine who are likely to commit a crime

Aids transmission, immigration, voting. behaviour, epidemics etc..

Question 2

Basic definitions - Nodes

Answer 2

Objects, individuals, players

Question 3

Basic definitions - Edges

Answer 3

Connections between nodes

Question 4

Basic definitions - Weighted edges

Answer 4

The intensity of a link

How many hours do two people spend together?

Question 5

Basic definitions - Unweighted edges

Answer 5

0 or 1

Question 6

Basic definitions - Directed edges

Answer 6

One way relationship

Question 7

Basic definitions - Undirected edges

Answer 7

Mutual relationships

Question 8

Degree of a node

Answer 8

Number of edges connected to a node

Question 9

Neighborhood

Answer 9

Two nodes are neighbours if they share an edge in-between

Question 10

Density of a network

Answer 10

Average degree of all the nodes in the network

Only tells a partial story

Question 11

Walks and Paths

Answer 11

•Walk
Sequence of  links connecting two nodes
•Cycle
A walk that starts and ends at the same node
•Path
A walk where a node appears at most once
•Geodesic
The shortest path between two nodes

Question 12

Connectedness

Answer 12

•A network is connected if
There is a path between every two nodes
•Diameter of  a network
The largest geodesic (the maximum length of  shortest paths)
•Average path length
What is the most likely
distance between any
nodes?

Question 13

Six degrees of separation

Answer 13

Academic co-authorship networks
•Math: mean 7.6
•Physics: mean 5.9
•Economics: mean 9.5
Facebook friendship network
•Mean 4.74 (721 million users)

Question 14

Clustering Coefficient

Answer 14

How many of your friends know each other?

Real world networks are highly clustered

Question 15

Betweeenness Centrality

Answer 15

Number of shortest path that passes through a node

- Represents the influence of a node for information flows

Question 16

Network Types to model real world cases

Answer 16

Random networks - Links between each node is random

Small world Networks - similar to social networks in real world, a group of people are closely related, a few people have far reaching connections

Scale free networks - start with 1 node, add a new node via a link. Rich get richer phenomenon

Question 17

Strong Ties and Weak Ties

Answer 17

Strong ties

• Close friendships
• Your friends are also friends with each other

Weak ties

• A distant friend
• Your friends do not know each other

Question 18

Strength of Weak Ties

Answer 18

•A is looking for a job
-C, D, E and F are close friends and want to help A
-But what they know is similar to what A knows
•B has access to a bunch of information
-That A cannot directly perceive
•Job leads, novel information, etc.