Distribution of Node Characteristics in Transfractal Network Systems and Additive Scale Invariance

For studies of distribution of node characteristics, this paper supplies a random descriptive frame including assertive matrices and the bivariate Gaussian distribution of dyad variables. Based on the frame, we firstly find from numerical experiment that there exists the novel additive scale invariance in total (D,H)-phase diagrams of the Tran fractal network(DGM model), and compute the transfinite dimensionalities of semi major, semi minor axis and area in the region of (D,H)-phase diagram with an ellipse boundary. Additionally the compressive g-effect and the stationary T-effect of the total phase diagram in the Park-Barabasi´s network model systems are obtained.