Degree distribution in a Barabási-Albert Tree

Consider a growing network constructed according to the Barabási-Albert (BA) model with the following parameters:

  • Linear preferential attachment: each new node connects to existing nodes with probability proportional to their current degree.
  • We start with a single node, and each new node adds a single edge ($m=1$), generating a tree.
  • The network is sufficiently large ($t \to \infty$), so that the asymptotic degree distribution is well-defined.

Under these conditions, what is the expected value of the degree distribution exponent $\gamma$, defined by $P(k) \sim k^{-\gamma}$?

a) $\gamma \leq 1$

b) $\gamma = 2$

c) $\gamma = 3$

d) There is not enough information to estimate $\gamma$

e) None of the above


Original idea: Daniel Gardin

Comments

  1. Joao MeidanisOctober 5, 2025 at 6:23 PM

    Questão interessante, mas bem fácil para quem estudou o básico do modelo B.A.

    ReplyDelete

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