Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence

We study the statistical properties of the network constructed from the energy dissipation rate time series in the three dimensional developed turbulence using the visibility algorithm. The degree distribution is found to have a power-law tail with the tail exponent $\alpha =3.0$. The exponential relationship between the number of the boxes $N_B$ and the box size $l_B$ in the edge-covering box-counting method illustrates that the network is not self-similar, which is also confirmed by the hub-hub attraction according to the visibility algorithm. In addition, it is found that the skeleton of the visibility network exhibits excellent allometric scaling with the scaling exponent $\eta =1.163\pm 0.005$.