quinta-feira, 23 de outubro de 2025

Chapter 7 - Degree Correlations

Rodolfo was studying ant colonies. He keeps several ant farms of Brazilian species in his house. For each colony, he mapped every contact between ants, representing these interactions as a network. Even when two ants interacted multiple times, he recorded that relationship only once.

He noticed that these networks follow the Scale-Free Network Model with k_min=1, and that the queen ant consistently has the highest number of connections.

His summarized results are as follows

  • Formigas carpinteiras” farm: 1,000,000 ants; queen has 100 connections.
  • Formigas de fogo” farm: 1,000,000 ants; queen has 10,000 connections.
  • Formigas faraó” farm: 10,000 ants; queen has 1,000 connections.
  • Formigas louca” farm: 10,000 ants; queen has 10 connections.

Select the correct statement: 🐜

A. The “Formigas carpinteiras” farm is a disassortative network because the high number of queen’s connections indicates a hub-dominated topology.
B. Both the “Formigas de fogo” and “Formigas faraó” farms are disassortative networks because their degree exponent values are less than 3.
C. The “Formigas louca” farm is disassortative because its degree exponent is greater than 3.
D. All farms are assortative networks because larger populations tend to promote connections between similar-degree nodes.
E. None of the above.

Original idea by: Rodolfo Bitu

sexta-feira, 3 de outubro de 2025

Chapter 5 - Barabási-Albert Model

Bitu is an explorer who sets out to visit the mysterious Bara-Al islands — a chain of 96 islands. Each island is connected by a few bridges. Whenever a new island was settled, its bridges were built with a preference for linking to islands that already had many connections. In this way, the Bara-Al islands grew according to Barabási–Albert Model of networks.

So, he wonders: what is the expected maximum number of bridges he would need to cross, starting from one island and traveling to the farthest one?

Note 1: 96 ≈ e^4.5 
Note 2: 4.5 ≈ e^1.5 

A. 3

B. 5

C. 6

D. 8

E. None of the above

Original idea by: Rodolfo Bitu

Chapter 7 - Network Robustness

Imagine a tree standing tall in the forest. Its structure can be represented as a tree graph: the node labeled R stands for the roots , the...