By applying algorithm method

the maximal planar network with scale-free properties is employed. The cumulative degree distribution and edge-cumulative degree distribution are computed

and the equivalence between them is testified. Besides

the new statistical index

namely

the mix cumulative distribution between edge and vertex on the basis of different mixed method is provided. A conjecture: If the mixed mode is linear

the mix cumulative distribution is equivalent to cumulative distribution is proposed. This conjecture makes a contribution to discussing scale-free network by applying all-round and multi-angle standpoint.