Betweenness centrality evaluates the importance of nodes and edges in networks and is one of the most pivotal indices in complex network analysis; for example, it is widely used in centrality ordering, failure cascading modeling, and path planning. Existing algorithms are based on single-source shortest paths technology, which cannot show the change of betweenness centrality with the growth of paths, and prevents deep analysis. We propose a novel algorithm that calculates betweenness centrality hierarchically and accelerates computing via GPUs. Based on the novel algorithm, we find that the distribution of shortest path has an intrinsic correlation with betweenness centrality. Furthermore, we find that the betweenness centrality indices of some nodes are 0, but these nodes are not edge nodes, and they characterize critical significance in real networks. Experimental evidence shows that betweenness centrality is closely related to the distribution of the shortest paths.
A pseudorandom sequence is a repeatable sequence with random statistical properties that is widely used in communication encryption, authentication and channel coding. The pseudorandom sequence generator based on the linear feedback shift register has the problem of a fixed sequence, which is easily tracked. Existing methods use the secret linear feedback shift register (LFSR) and built-in multiple LFSRs and is difficult to prevent cracking based on the hardware analysis. Since the plaintext depends on a specific language to be generated, using pseudo-random sequence encryption, it faces the problem that the encryptor cannot hide the characteristics of the plaintext data. Fractal functions have the following properties: chaotic, unpredictable and random. We propose a novel pseudorandom sequence generator based on the nonlinear chaotic systems, which is constructed by the fractal function. Furthermore, we design a data processing matrix to hide the data characteristics of the sequence and enhance the randomness. In the experiment, the pseudo-random sequences generator passed 16 rigorous test items from the National Institute of Standards and Technology (NIST), which means that the nonlinear pseudorandom sequence generator for the fractal function is effective and efficient.
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