Question: Degree Dynamics in the BA Model

In the Barabási–Albert (BA) model, which incorporates growth (continuous addition of new nodes) and preferential attachment (new nodes prefer to connect to more connected nodes), the time evolution of a node’s degree, $k_i(t)$, is a central aspect.

The degree growth for a node $i$, which entered the network at time $t_i$ with $m$ links, follows a power law in time $t$, characterized by the dynamic exponent $\beta$.

Which of the following formulas correctly represents the degree growth law $k_i(t)$ for a node $i$ in the BA model?

A.

$$k_i(t) = m \left( \frac{t}{t_i} \right)^{1/2}$$

B.

$$k_i(t) = m \frac{t}{t_i}$$

C.

$$k_i(t) = k^{-\gamma} \quad \text{where} \quad \gamma = 3$$

D.

$$k_i(t) = m \left( \frac{t}{t_i} \right)^{2}$$

E. None of the above

Original idea by: Matteus Vargas Simão da Silva