Principal eigenvector localization and centrality in networks: Revisited

Pradhan, Priodyuti; Angeliya, C U; Jalan, Sarika

doi:10.1016/j.physa.2020.124169

Cited by 16 publications

(4 citation statements)

References 49 publications

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“…Eigenvector centrality stands out as a prevalent metric in network analysis utilized to evaluate the significance or impact of nodes within a network [66]. It derives from the connectivity patterns of nodes, accentuating connections with other pivotal nodes.…”

Section: Eigenvector Centralitymentioning

confidence: 99%

Research on the Carbon Sequestration Capacity of Forest Ecological Network Topological Features and Network Optimization Based on Modification Recognition in the Yellow River Basin Mining Area: A Case Study of Jincheng City

Li,

Yu,

et al. 2024

Remote Sensing

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Forests are vital for terrestrial ecosystems, providing crucial functions like carbon sequestration and water conservation. In the Yellow River Basin, where 70% of forest coverage is concentrated in the middle reaches encompassing Sichuan, Shaanxi, and Shanxi provinces, there exists significant potential for coal production, with nine planned coal bases. This study centered on Jincheng City, Shanxi Province, a representative coal mining area in the Yellow River Basin, and combined the MSPA analysis method and MCR model to generate the five-period forest ecological network of Jincheng City from 1985 to 2022 under the background of coal mining and calculate the degree centrality, closeness centrality, betweenness centrality, and eigenvector centrality; the correlation between the four centralities and carbon sequestration ability is further explored. Simultaneously, employing the RAND-ESU algorithm for motif identification within forest ecological networks, this study integrates the ecological policies of the research area with the specific conditions of the coal mining region to optimize the forest ecological network in Jincheng City. Findings reveal the following. (1) Forest ecological spatial networks: Forest ecological networks exhibit robust overall ecological connectivity in the study area, with potential ecological corridors spanning the region. However, certain areas with high ecological resistance hinder connectivity between key forest ecological nodes under the background of coal mining. (2) Correlation between topological indices and carbon sequestration ecological services: From 1985 to 2022, the carbon sequestration capacity of Jincheng City’s forest source areas increased year by year, and significant positive correlations were observed between degree centrality, betweenness centrality, eigenvector centrality with carbon sequestration ecological services, indicating a strengthening trend over time. (3) Motif Recognition and Ecological Network Optimization: During the study, four types of motifs were identified in the forest ecological network of Jincheng City based on the number of nodes and their connections using the RAND-ESU network motif algorithm. These motifs are 3a, 4a, 4b, and 4d (where the number represents the number of nodes and the letter represents the connection type). Among these, motifs 3a and 4b play a crucial role. Based on these motifs and practical considerations, network optimization was performed on the existing ecological source areas to enhance the robustness of the forest ecological network.

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Section: Eigenvector Centralitymentioning

confidence: 99%

Research on the Carbon Sequestration Capacity of Forest Ecological Network Topological Features and Network Optimization Based on Modification Recognition in the Yellow River Basin Mining Area: A Case Study of Jincheng City

Li,

Yu,

et al. 2024

Remote Sensing

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“…Centrality localization [14,41] describes the situation when a small number of nodes account for a large fraction of the total centrality. (This can be viewed as a generalization of Freeman's centralization metric [42].)…”

Section: Localizationmentioning

confidence: 99%

Adjustable reach in a network centrality based on current flows

Gurfinkel

Rikvold

2021

Phys. Rev. E

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Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of nodes. As there are many ways in which influence can be defined, many different centrality measures are in use. Parametrized centralities allow further flexibility and utility by tuning the centrality calculation to the regime most appropriate for a given purpose and network. Here we identify two categories of centrality parameters. Reach parameters control the attenuation of influence flows between distant nodes. Grasp parameters control the centrality's tendency to send influence flows along multiple, often nongeodesic paths. Combining these categories with Borgatti's centrality types [Borgatti, Soc. Networks 27, 55 ( 2005)], we arrive at a classification system for parametrized centralities. Using this classification, we identify the notable absence of any centrality measures that are radial, reach parametrized, and based on acyclic, conserved flows of influence. We therefore introduce the ground-current centrality, which is a measure of precisely this type. Because of its unique position in the taxonomy, the ground-current centrality differs significantly from similar centralities. We demonstrate that, compared to other conserved-flow centralities, it has a simpler mathematical description. Compared to other reach-parametrized centralities, it robustly preserves an intuitive rank ordering across a wide range of network architectures, capturing aspects of both the closeness and betweenness centralities. We also show that it produces a consistent distribution of centrality values among the nodes, neither trivially equally spread (delocalization) nor overly focused on a few nodes (localization). Other reach-parametrized centralities exhibit both of these behaviors on regular networks and hub networks, respectively. We compare the properties of the ground-current centrality with several other reach-parametrized centralities on four artificial networks and seven real-world networks.

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“…The localization of the eigenvector often indicates a densely connected subgraph. There has been a lot of effort in understanding the localization of the PEV in terms of the degrees and centralities of the nodes and structure of the graph theoretically 3,31,32 . The greedy algorithm provides an efficient numerical validation tool for these theoretical studies.…”

Section: Numerical Examplesmentioning

confidence: 99%

A greedy algorithm for computing eigenvalues of a symmetric matrix with localized eigenvectors

Hernandez

Beeumen

Caprio

et al. 2020

Numerical Linear Algebra App

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Summary We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix H that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs of H by computing eigenpairs of a submatrix extracted from the corresponding rows and columns of H. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied to H. We discuss a few possibilities for selecting important rows and columns of H and techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many‐body calculations, many‐body localization studies of quantum spin chains and road network analysis.

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Principal eigenvector localization and centrality in networks: Revisited

Cited by 16 publications

References 49 publications

Research on the Carbon Sequestration Capacity of Forest Ecological Network Topological Features and Network Optimization Based on Modification Recognition in the Yellow River Basin Mining Area: A Case Study of Jincheng City

Research on the Carbon Sequestration Capacity of Forest Ecological Network Topological Features and Network Optimization Based on Modification Recognition in the Yellow River Basin Mining Area: A Case Study of Jincheng City

Adjustable reach in a network centrality based on current flows

A greedy algorithm for computing eigenvalues of a symmetric matrix with localized eigenvectors

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