Fuzzy fractal dimension of complex networks

Graphical abstractDisplay Omitted HighlightsA new fractal dimensional model based on fuzzy sets theory is proposed.The complexity in our model reduced significantly from NP-hard problems.This model could obtain a deterministic fractal dimension for a certain network. Complex networks are widely used to describe the structure of many complex systems in nature and society. The box-covering algorithm is widely applied to calculate the fractal dimension, which plays an important role in complex networks. However, there are two open issues in the existing box-covering algorithms. On the one hand, to identify the minimum boxes for any given size belongs to a family of Non-deterministic Polynomial-time hard problems. On the other hand, there exists randomness. In this paper, a fuzzy fractal dimension model of complex networks with fuzzy sets is proposed. The results are illustrated to show that the proposed model is efficient and less time consuming.

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