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.

The shortest paths problem is a fundamental challenge in graph theory, with a broad range of potential applications. The algorithms based on matrix multiplication exhibits excellent parallelism and scalability, but is constrained by high memory consumption and algorithmic complexity. Traditional shortest paths algorithms are limited by priority queues, such as BFS and Dijkstra algorithm, making the improvement of their parallelism a focal issue. We propose a matrix operation-optimized algorithm, which offers improved parallelism, reduced time complexity, and lower memory consumption. The novel algorithm requires O(Ewcc(i)) and O(Swcc · Ewcc) times for single-source and all-pairs shortest paths problems, respectively, where Swcc and Ewcc denote the number of nodes and edges included in the largest weakly connected component in graph. To evaluate the effectiveness of the novel algorithm, we tested it using graphs from SuiteSparse Matrix Collection and Gunrock benchmark dataset. Our algorithm outperformed the BFS implementations from Gunrock and GAP (the previous state-of-the-art solution), achieving an average speedup of 3.769 × and 9.410 ×, respectively.

The robust evolution of informationization in human society, particularly with the proliferation of mobile Internet and Internet of Things (IoT), has led to a substantial increase in network complexity and device inter-connectivity. In order to deeply understand the network properties of the real-world networks, network scientists propose multiple centrality measurements of networks to analyze the network characteristics, which indicates the importance of nodes and edges in the networks. Betweenness centrality is a crucial centrality measurement in the network, however the traditional algorithm for computing betweenness centrality struggles with inefficiency in large networks. In this paper, we introduce an efficient algorithm for betweenness centrality, leveraging a sampling strategy to address the computational challenges due to the large networks. In order to evaluate the algorithm, we introduce the accuracy and efficiency for the proposed sampling algorithm. The experimental results show that the algorithm can make notable improvements in computational performance without significantly compromising accuracy, thereby offering an efficient and scalable algorithm for centrality measurement in complex networks, especially in the scale-free networks.