A large, undirected network, with no self-loops or multi-links, is analyzed. It exhibits a scale-free degree distribution described by the formula \(p(k) = k^\gamma\) with an exponent \(\gamma=2.5\). Empirical measurement yields a degree correlation coefficient \(r = -0.15\). A plot of the average nearest-neighbor degree \(k_{nn}(k)\) shows relatively independency of the degree \(k\) for small \(k\), but it begins to decay for nodes with \(k > \sqrt{\langle k\rangle N}\), where \(N\) is the network size. What is the most precise classification of this network's degree correlations?
A) The network is intrinsically disassortative;
B) The network exhibits structural disassortativity, a phenomenon affecting scale-free networks with exponent \(\gamma < 3\) and the network's nature;
C) The network is neutral, as the average nearest-neighbor degree is independent of \(k\) for most nodes and \(r\) is close to 0;
D) The network is assortative, but the measurement is skewed by the high variance of high-degree nodes;
E) None of the above.
Original idea: Caio Rhoden
No comments:
Post a Comment