Barabási-Albert model

Regarding the Barabási-Albert (BA) and Linearized Chord Diagram (LCD) models, analyze the following statements:

I. Both of these models can be used to generate scale-free networks

II. In the BA model, if a network starts with only one isolated node at \(t=1\), a new node at \(t=2\) cannot connect to it because the sum of all degrees \(\sum k_j\) is zero, resulting in an undefined probability function

III. By allowing self-loops, the LCD model provides a consistent initialization, allowing the network to grow from \(t=1\) without requiring a pre-existing graph

IV. In the LCD model, as the network size \(N\) increases, the occurrence of new self-loops becomes increasingly rare, as the probability of a node connecting to itself is \(\frac{1}{2t-1}\)

Which of the statements are TRUE

A) I, II, III, IV

B) I, II, III

C) I, II, IV

D) I, IV

E) None of the above

Original idea by: Fernando de Facio Rossetti

Comentários

  1. Joao Meidanis18 de abril de 2026 às 12:00

    Good question, but I'm concerned with statement I. If fact, they can be considered the same model, since the LCD is just one way to formalize the hypotheses of BA. This may mislead some people. I'll pass.

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