Carlos Trindade's Graph Algorithms Quiz Blog

 Consider a network that follows the Barabási-Albert Model growth with \(m_0 = m = 2\). A node \(i\) joined the network at time \(t_i = 375\) and has degree \(k(t) = 40\) at current time step \(t\). What is the expected diameter of this network? Round to two decimal places. A) \( \langle D \rangle \approx 4.20 \) B) \( \langle D \rangle \approx 4.81 \) C) \( \langle D \rangle \approx 2.80 \) D) \( \langle D \rangle \approx 3.81 \) E) None of the above. Original idea by: Carlos Trindade

 Consider a network with \( N = 10^4\) nodes. If the degree distribution \(p_k\) follows the power law \(p_k \sim k^{\gamma}\), with degree exponent \(\gamma = 3\) and a minimum degree \(k_{\text{min}} = 2\), which the following statements are true? I. The expected size of the largest hub is \(k_{\text{max}} = 200\). II. The first moment \(\langle k \rangle\) diverges, meaning the network has no scale. III. Doubling the number of nodes to \(N = 2 \times 10^4\) would double the expected size of the largest hub to \(k_{\text{max}} = 400\). IV. The second moment \(\langle k^2 \rangle\) diverges, meaning the network has no characteristic flutuation. a) I, II and IV b) I and IV c) Only I d) II and III e) None of the above. Original idea by: Carlos Trindade