Notes on Network Science
Welcome
1
Introduction to Network Science
1.1
Intro to networks
1.1.1
Networks and complex systems
1.1.2
Driving forces behind network science’s emerging as a discipline
1.1.3
Key characteristics of network science
1.2
Definition and significance of networks
1.2.1
What is a network
1.2.2
Why should we care about networks?
1.2.3
Think for yourself
1.3
Python setup
1.4
Homework
2
Graph Theory and Some Basic Concepts
2.1
Königsberg bridge problem (Ch. 2.1)
2.2
Networks and graphs (Ch. 2.2)
2.3
Degree, average degree, and degree distribution (Ch. 2.3)
2.3.1
Degree
2.3.2
Average degree
2.3.3
Degree distribution
2.4
Adjacency matrix
2.5
Chapter 2 Homework
2.5.1
Task 2-1:
Networkx
Basics
2.5.2
Task 2-2: Friendship paradox example
2.5.3
Task 2-3: Generating random and scale-free networks
2.5.4
Task 2-4: Homework by Professor YY
3
Small World Phenomenon
3.1
Weight, paths, connectedness, and clustering
3.1.1
Weighted network
3.1.2
Shortest path, network diameter, and average path length
3.1.3
Connectedness
3.1.4
Clustering coefficient
3.2
Chapter 3 Homework
4
Weak Ties and Watts-Strogatz model
4.1
Random networks (Barabási Ch.3)
4.1.1
Generating a random network
4.1.2
Average degree, and the expected number of links in a random network
4.1.3
Degree distribution
4.1.4
Poisson distribution does not capture reality
4.2
Reading two seminal papers
4.2.1
The Strength of Weak Ties
by
Granovetter
(
1973
)
4.2.2
Watts-Strogatz model of small world
5
Scale-Free Networks
5.1
Power-Law Distributions
5.1.1
Differences between FB study and the Milgram study
5.1.2
Power law
5.1.3
Logarithmic scale
5.1.4
Properties of power-law distributions
5.2
Scale-free property
5.2.1
Hubs
5.2.2
Universality
5.2.3
Ultra-small property, and the role of degree exponent
5.3
The Barabási-Albert Model
5.3.1
Improving the BA model
References
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Notes on Network Science
3.2
Chapter 3 Homework
This part is based on Professor YY’s module 3 assignment of
shortest path length distribution
.
You can find the homework
here
.