Abstract
Information dimension is applied to quantify fractal, and the current methods are improved on the basis of information entropy. Although information entropy is always used to measure the information volume, it fails when dealing with complex and uncertain information. To solve this problem, in this paper, the information dimension is defined by using Deng entropy, due to the reason that Deng entropy as the extension of information entropy has the characteristic of being able to measure uncertain information better. In our method, Deng entropy is considered to measure the information volume in the information dimension. Besides, box coverage is also combined in the process of the box covering to define box coverage Deng entropy information dimension. In addition, the classical information dimension and box dimension of BA scale-free networks, WS and NW small-world networks and four real networks are calculated to compare with the proposed information dimension. The results show that the values of Deng entropy information dimension and box coverage Deng entropy information dimension are bigger than the classical information dimension and box dimension for the same network. Moreover, the information dimension of the networks does not increase linearly with the increase of nodes.
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