Networks
- Brain
- Neurons and neural connections
- Social networks
- Users and following / friendships
When new users join e.g. Twitter / Instagram, who do they follow?
Celebrities? Politicians?
Accounts related to the interests of the users
Those with a huge following are more likely to be followed
To describe the phenomenon
To capture the essence of the data
Based on rules in mathematics and/or physics
Simulate data and compare to real-life observations
Rule 1: New nodes join the network one by one
Rule 2: Each new node brings in (approximately) the same number of new edges
Rule 3: Probability that an existing node gets an edge is proportional to their current degree
Degree = number of edges
| Node | Degree |
|---|---|
| A | 1 |
| B | 3 |
| C | 2 |
| D | 3 |
| E | 1 |
| Total | 10 |
Node A has probability of 1/10 of getting connected
Node B has probability of 3/10 of getting connected, and so on
| Node | Degree |
|---|---|
| A | 1 |
| B | 3 |
| C | 2 |
| D | 3 |
| E | 1 |
| Total | 10 |
Node A has probability of 1/10 of getting connected
Node B has probability of 3/10 of getting connected, and so on
| Node | Degree |
|---|---|
| A | 1 |
| C | 2 |
| D | 3 |
| E | 1 |
| Total | 7 |
Node A has probability of 1/7 of getting connected
Node C has probability of 2/7 of getting connected, and so on
| Node | Degree |
|---|---|
| A | 1 |
| C | 2 |
| D | 3 |
| E | 1 |
| Total | 7 |
Node A has probability of 1/7 of getting connected
Node C has probability of 2/7 of getting connected, and so on
| Node | Degree |
|---|---|
| A | 1 |
| B | 4 |
| C | 3 |
| D | 3 |
| E | 1 |
| F | 2 |
| Total | 14 |
The rich get richer (and the poor get poorer)
The 80-20 rule / Pareto principle
Cumulative inequality / disadvantage
The Matthew effect (of accumulated advantage)
The big picture stays the same
Which individual nodes will succeed may vary
Change involves an element of chance
