Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2025 / Paper 2 / 6 / c

No. A scale-free network is characterized by an approximately power-law tail in its degree distribution, $P(k)\propto k^{-\gamma }$ over a meaningful range. clustering coefficients and mean graph distances do not supply that distribution. One would need the degrees of vertices, enough observations over a substantial range, and a fitted power-law model assessed against alternatives. Four vertices cannot establish such a tail, even if their degrees were supplied. small-worldness alone does not imply a scale-free network.