Multifractal analysis for core-periphery structure of complex networks

Liu, Jinlong; Yu, Zu-Guo; Anh, Vo

doi:10.1088/1742-5468/ab2906

Cited by 8 publications

(3 citation statements)

References 52 publications

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“…Xiang et al proposed a method to detect both single and multiple pairs of core-periphery structure in complex networks and the overlapping nodes [30]. Liu et al demonstrated the effectiveness of fractal analysis in revealing the properties of the core-periphery structure of complex networks [31]. Silva et al also proposed a core coefficient to evaluate the core-periphery structure of a metabolic network [16].…”

Section: Introductionmentioning

confidence: 99%

Finding Core-Periphery Structures With Node Influences

Shen

Aliko

Han

et al. 2022

IEEE Trans. Netw. Sci. Eng.

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Detecting core-periphery structures is one of the outstanding issues in complex network analysis. Various algorithms can identify core nodes and periphery nodes. Recent advances found that many networks from real-world data can be better modeled with multiple pairs of core-periphery nodes. In this study, we propose to use an influence propagation process to detect multiple pairs of core-periphery nodes. In this framework, we assume each node can emit a certain amount of influence and propagate it through the network. Then we identify nodes with large influences as core nodes, and we utilize a maximum influence chain to construct a node-pairing network to determine core-periphery pairs. This approach can take node interactions into consideration and can reduce noises in finding pairs. Experiments on randomly generated networks and real-world networks confirm the efficiency and accuracy of our algorithm.

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Section: Introductionmentioning

confidence: 99%

Finding Core-Periphery Structures With Node Influences

Shen

Aliko

Han

et al. 2022

IEEE Trans. Netw. Sci. Eng.

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“…In recent years, some studies have also focused on the MFA of complex networks. MFA has been shown to have better performance than fractal analysis in characterizing the complexity of model and real-world networks [8,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Thus, if a network possesses the multifractal property, we can use the generalized fractal dimensions D q , instead of a single fractal dimension D 0 , to unfold effectively the self-similar structure of the network, thus capturing the fluctuations of local node density in the network.…”

mentioning

confidence: 99%

“…This is because that the sandbox algorithm only randomly selects a number of nodes on a network as the center nodes of sandboxes and then counts the number of nodes in each sandbox within a given radius for MFA. Therefore, the existing sandbox algorithm and its improved versions have been widely used to the calculation of the mass exponents τ q or the generalized fractal dimensions D q of different types of complex networks [10,[26][27][28][30][31][32][33][34]. The calculated results are then used for the investigation into the fractal and multifractal properties of the networks.…”

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confidence: 99%

A computationally-efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

Ding,

Liu,

et al. 2020

Preprint

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The fractality of complex networks has attracted much attention with extensive investigations over the last 15 years. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful tool to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. One of the widely used methods for fractal analysis is box-covering. It uses the minimum number of covering boxes to calculate the fractal dimension of complex networks, and is known to be NP-hard. More severely, in comparison with fractal analysis algorithms, MFA algorithms have much higher computational complexity. Among various MFA algorithms for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive. Thus, so far it has only been applied to small-scale complex networks of the size of about tens of thousands of nodes. It becomes challenging to implement the MFA for large-scale networks with tens of millions of nodes. It is also not clear whether or not MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally-efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of complex networks, our CESA employs the breadth-first search (BFS) technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. Our CESA's input is a sparse data structure derived from the compressed sparse row (CSR) format designed for compressed storage of the adjacency matrix of large-scale network. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. MFA experiments are performed for typical complex networks to verify our CESA. The CESA is demonstrated to be effective, efficient and feasible through the MFA results of (u,v)-flower model networks from the 5th to the 12th generations. It enables us to study the multifractality of networks of the size of about 11 million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of (u,v)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.

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