Network coherence and eigentime identity on a family of weighted fractal networks

Then, all nonzero normalized Laplacian eigenvalues can be obtained by computing the roots of several small-degree polynomials defined recursively. The obtained results show that the scalings of the eigentime identity obey two laws according to the range of the weight factor. The first law is that the scaling obeys ln Nn (i.e., the logarithm of the network size), when 0 < r ≤ 1 and r≠1s; The second law is that the scaling obeys Nnln Nn (i.e., the product of network size and its logarithm), when r=1s.