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Urban rail transit networks have become the most important traffic modal and greatly improve the traffic environment and travel efficiency of metropolis, and the critical station identification and robustness assessment of urban rail transit networks have become more and more important. In this paper, we propose a comprehensive vote-rank (CVR) algorithm to identify the critical stations, and adopt mutual information and k -center clustering algorithm to analyze the similar characteristics of passenger flow on different dates of urban rail transit networks. Meanwhile, Shanghai metro network is chosen as the example and we find that the optimal classification of passenger flow on different dates is 2 categories, and the passenger flows have the significant differences between conventional day and unconventional day. The results show that the critical stations on unconventional day are farther from the city center than the critical stations on conventional day, and some critical stations locate in the suburbs on unconventional day. Moreover, we study the structural and functional robustness characteristics of urban rail transit networks subjected to continuous malicious attacks to the top critical nodes, and the results show that Shanghai metro network has the worse robustness subjected to malicious attacks. Compared with the existed methods, we can declare that the proposed CVR algorithm is the most effective method for critical station identification and robustness assessment among the discussed methods in this paper, and this study will provide theoretical and practical support for the safe operation of urban rail transit networks. [ABSTRACT FROM AUTHOR]

Multifractal analysis of complex networks has attracted increasing interest in various fields of science, because it can help us unfold the intricate structure of a variety of networks for better understanding the underlying mechanism of these networks. In this study, we propose a sandbox edge-based (SBEB) multifractal analysis algorithm, which introduces the idea of the sandbox algorithm into the existing edge-based box-counting (EBBC) algorithm. Instead of using boxes to cover the nodes of a given network, the SBEB algorithm uses boxes to cover the entries '1' in the adjacency matrix of the network, where these entries '1' represent the edges of the network. We apply the SBEB algorithm to model networks to verify its effectiveness and feasibility. The results show that the SBEB algorithm can effectively capture the multifractal nature of these model networks. Compared with the existing EBBC algorithm, our algorithm greatly improves the linearity and smoothness in estimating the mass exponents τ (q) and the generalized fractal dimensions D (q) , thereby resulting in more accurate estimates. In addition, the SBEB algorithm inherits the advantage of the existing EBBC algorithm on studying small-diameter networks which are difficult to be dealt with by the traditional node-based box-covering algorithms. In application, we apply the SBEB algorithm to several real-world networks, and results indicate that this algorithm can uncover their genuine multifractal behaviors. • A sandbox edge-based (SBEB) algorithm is proposed for multifractal analysis of complex networks. • The SBEB algorithm improves the linearity and smoothness in estimating the multifractal results. • The SBEB algorithm is capable of detecting the multifractal structure of networks with small diameters. • The effectiveness, feasibility, and applicability of the SBEB algorithm are verified by some model and real-world networks. [ABSTRACT FROM AUTHOR]