Lecture 1: Introduction to Network Science
This course is about applying network thinking (and complex system thinking) to solve economic and
business problems.
What is network thinking?
1. A network-based paradigm is taking science by storm (Barabási, 2012). But businesses too.
2. Network analysis is a broad intellectual approach instead of a narrow set of methods
(Wellman, 1983)
3. A network-based paradigm shifts the unit of analysis from individuals and their attributes to
(the structure of) their relationships
An interesting patent: the Google PageRank algorithm (uses Eigenvector correctly, see lecture 3).
A more simple form: customers who bought this also bought this (Amazon), or people you may know
(Facebook).
Leonhard Euler’s solution to the Seven Bridges of Königsberg problem (1735): was groundbreaking
- Euler recognized that the specific paths taken within each landmass in the city of Königsberg
were not important when trying to solve the problem. What mattered were the connections
between the landmasses via the seven bridges.
- Euler focused on the patterns of connection between the landmasses (islands) and the
bridges, rather than the geographical details of the paths taken on those landmasses.
- Euler abstracted the problem by simplifying the landmasses into points or nodes, and the
bridges between them as edges or connections. This abstract representation turned the
problem into a graph theory problem.
- Euler approached the problem using graph theory, which is a branch of mathematics that
deals with the study of networks and connections between points. He transformed the
physical problem into a graph-based problem.
- Euler's key contribution was proving that there was no continuous path that would cross each
of the seven bridges of Königsberg only once. This was a significant result in the history of
graph theory.
- Euler's solution to the Seven Bridges problem laid the foundation for both graph theory and
mathematical topology. It marked the beginning of formal network analysis and paved the
way for the study of abstract networks and their properties.
1
, Lecture 2: Graph Theory and Complex Networks
- Networks are found in nature and society
- Graphs are the mathematical representation of these networks (like a map)
- In the literature, both are used interchangeably
An advice network:
- Emma (1) helps Mason (2)
- Emma (1) helps William (3)
- Mason (2) helps William (3)
- Mason (2) helps Sophia (4)
- N = number of nodes (size of the network)
- N=4
- The network is composed by the nodes i = 1, 2, …, N
- L = number of links
- L=4
- The connection between Mason and William [Mason (2) helps William (3)] is denoted as (2,3)
- A graph might be denoted as G, its vertex set as V(G), and its edge set as E(G)
Different types of networks:
Network representations:
2
This course is about applying network thinking (and complex system thinking) to solve economic and
business problems.
What is network thinking?
1. A network-based paradigm is taking science by storm (Barabási, 2012). But businesses too.
2. Network analysis is a broad intellectual approach instead of a narrow set of methods
(Wellman, 1983)
3. A network-based paradigm shifts the unit of analysis from individuals and their attributes to
(the structure of) their relationships
An interesting patent: the Google PageRank algorithm (uses Eigenvector correctly, see lecture 3).
A more simple form: customers who bought this also bought this (Amazon), or people you may know
(Facebook).
Leonhard Euler’s solution to the Seven Bridges of Königsberg problem (1735): was groundbreaking
- Euler recognized that the specific paths taken within each landmass in the city of Königsberg
were not important when trying to solve the problem. What mattered were the connections
between the landmasses via the seven bridges.
- Euler focused on the patterns of connection between the landmasses (islands) and the
bridges, rather than the geographical details of the paths taken on those landmasses.
- Euler abstracted the problem by simplifying the landmasses into points or nodes, and the
bridges between them as edges or connections. This abstract representation turned the
problem into a graph theory problem.
- Euler approached the problem using graph theory, which is a branch of mathematics that
deals with the study of networks and connections between points. He transformed the
physical problem into a graph-based problem.
- Euler's key contribution was proving that there was no continuous path that would cross each
of the seven bridges of Königsberg only once. This was a significant result in the history of
graph theory.
- Euler's solution to the Seven Bridges problem laid the foundation for both graph theory and
mathematical topology. It marked the beginning of formal network analysis and paved the
way for the study of abstract networks and their properties.
1
, Lecture 2: Graph Theory and Complex Networks
- Networks are found in nature and society
- Graphs are the mathematical representation of these networks (like a map)
- In the literature, both are used interchangeably
An advice network:
- Emma (1) helps Mason (2)
- Emma (1) helps William (3)
- Mason (2) helps William (3)
- Mason (2) helps Sophia (4)
- N = number of nodes (size of the network)
- N=4
- The network is composed by the nodes i = 1, 2, …, N
- L = number of links
- L=4
- The connection between Mason and William [Mason (2) helps William (3)] is denoted as (2,3)
- A graph might be denoted as G, its vertex set as V(G), and its edge set as E(G)
Different types of networks:
Network representations:
2
