Question about Degree Correlations
Two undirected networks, Network A and Network B , have identical degree distributions p k p_k but distinct mixing patterns. For each, it is measured the average nearest-neighbor degree function k n n ( k ) k_{nn}(k) and the degree correlation matrix e j k e_{jk} . So: In Network A , k n n ( k ) k_{nn}(k) is approximately constant across k k , and e j k e_{jk} roughly factorizes into q j q k q_j q_k . In Network B , k n n ( k ) k_{nn}(k) decreases systematically with k k , and the e j k e_{jk} matrix shows high values in the upper-left and lower-right corners rather than along the diagonal. Consider the following statements: I. Network A is neutral, while Network B is disassortative. II. Network B is expected to have a negative value of Newman’s correlation coefficient r r . III. If a new Network C were highly assortative, its e j k e_{jk} would concentrate along the diagonal, and k n n ( k ) k_{nn}(k) would increase with k k . IV. Be...