Antonio DCDN - MO412

In the optimization model, if \( \delta \) is extremely large, what dominates the connection decision? Node degree Path length \(h_{ij}\) Distance \(d_{ij}\) Random choice None of the above Original idea by: Antonio De Cesare Del Nero

Using the continuum formalism, a scale-free network has \[ p(k)=Ck^{-\gamma}, \qquad k \geq 1, \] with \(\gamma = 2.5\). Which expression gives the second moment \(\langle k^2 \rangle\) for a finite network with cutoff \(k_{\max}\)? \(\langle k^2 \rangle = \int_1^{k_{\max}} k^{-0.5}\,dk\) \(\langle k^2 \rangle = C\int_1^{k_{\max}} k^{-0.5}\,dk\) \(\langle k^2 \rangle = C\int_1^{k_{\max}} k^{-2.5}\,dk\) \(\langle k^2 \rangle = \int_1^{k_{\max}} k^{2.5}\,dk\) None of the above Original idea by: Antonio De Cesare Del Nero