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A Set of Measures of Centrality Based on Betweenness

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Abstract

A Family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which a point falls on the shortest path between others and therefore has a potential for control of communication. They may be used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected.
... The aim is to analyze the structure of the systems by assuming the relationship between the single elements of the systems: each element is represented by a node, while the link connects two elements related to each other. The centrality metrics, first introduced by [11], represents the measure for better describing the structure of the network by ranking the importance of the nodes [12], such as degree, closeness [11], eigenvector [13], Katz centrality [14], or PageRank [15]. ...
... The aim is to analyze the structure of the systems by assuming the relationship between the single elements of the systems: each element is represented by a node, while the link connects two elements related to each other. The centrality metrics, first introduced by [11], represents the measure for better describing the structure of the network by ranking the importance of the nodes [12], such as degree, closeness [11], eigenvector [13], Katz centrality [14], or PageRank [15]. ...
...  Degree centrality. The degree centrality [11] is defined as the number of links incident upon a node and describes the local connectivity of the network. Considering a network N composed of V vertices and E edges, it can be expressed as: ...
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Water Distribution Networks (WDNs) are spatially organized infrastructures, whose hydraulic behavior greatly depends on their connectivity properties, i.e., the topological domain. The Complex Network Theory (CNT) provides a wide range of useful functions and metrics that have been tailored for identifying WDNs behavior, even before using hydraulic models. This work exploits the recent studies on the WDN domain, which couple the CNT metrics of centrality tailored for WDN with the intrinsic relevance of the spatial elements of the networks. The study accounts for various combinations of metrics and intrinsic relevance functions aimed at supporting WDN analysis for operational and management tasks. A Digital Water Service (DWS) is used to enable technicians and water companies to replicate the same domain analysis in the ongoing context of digital transformation in WDN sector.
... To counter this, researchers have also used global centrality measures like Betweenness Centrality, Closeness Centrality, and K-shell Decomposition, among others, to Influence Maximization. Freeman (1977) defined Betweenness for a specific node as the ratio of the shortest path which passes through the node and the total number of possible shortest paths in the network. Okamoto et al. (2008) proposed Closeness for a node as the inverse of the sum of the shortest path to all other nodes, thus determining the average closeness of a node to the rest of the graph. ...
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Over the last couple of decades, Social Networks have connected people on the web from across the globe and have become a crucial part of our daily life. These networks have also rapidly grown as platforms for propagating products, ideas, and opinions to target a wider audience. This calls for the need to find influential nodes in a network for a variety of reasons, including the curb of misinformation being spread across the networks, advertising products efficiently, finding prominent protein structures in biological networks, etc. In this paper, we propose Modified Community Diversity (MCD), a novel method for finding influential nodes in a network by exploiting community detection and a modified community diversity approach. We extend the concept of community diversity to a two-hop scenario. This helps us evaluate a node’s possible influence over a network more accurately and also avoids the selection of seed nodes with an overlapping scope of influence. Experimental results verify that MCD outperforms various other state-of-the-art approaches on eight datasets cumulatively across three performance metrics.
... The more edges a node has, the greater its direct influence in the network, and the more important the node is in the network. The calculation formula of the degree centrality of node i is (Freeman, 1977): ...
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Platinum is widely considered as a critical mineral. According to the most optimistic scenario, the demand for platinum could increase 240-fold globally by 2050 due to the enormous demand potential for green hydrogen and fuel cell vehicles. By integrating network analysis and evaluation indicators, this study develops a framework to visualize the global platinum upstream supply chain, pinpoint supply-related risk areas, and assess the position of various nations in the supply chain. We conclude that there is a significant risk of disruption to the global platinum upstream supply chain. Following is a summary of the main conclusions: First, the global platinum supply network and primary platinum product trade network are both relatively sparse, with poor network connectivity, and the overall network’s risk-resistance is weak. Second, at the non-geographical production country level, the global platinum mining countries, the countries of the producing companies, and the countries of the shareholders of the producing companies are all highly concentrated. Third, the global platinum supply and demand markets are significantly divided, and South Africa holds a significantly stronger national position in the platinum supply network than any other nation, except for the national level of producing companies’ shareholders. However, the national role of South Africa in the trade network is not as strong as that of consuming countries and transit countries. The study proposes that global platinum consuming countries can reduce supply risks by increasing domestic platinum mine production, building international large-scale integrated mining corporations, and raising global supply share by investing in overseas mines.
... A centralidade por intermediação é a propriedade de um espaço recair no caminho que liga outros dois, e sua hierarquia se dá pela quantidade total de vezes que ele aparece nos caminhos que ligam todos os pares de espaços de um sistema (FREEMAN, 1977). Krafta (1994) A Figura 8 apresenta a classificação por tamanho dos CRFs. ...
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Os condomínios residenciais fechados (CRFs) são uma das tipologias habitacionais mais difundidas na contemporaneidade e sua implantação é capaz de gerar impactos na estrutura espacial de cidades e regiões. O objetivo deste artigo é problematizar a localização dos CRFs na escala regional, tendo como estudo empírico a Região Metropolitana de Porto Alegre (RMPA). Pretende-se responder às seguintes questões: que tipo de crescimento da mancha urbanizada os CRFs tem gerado? Como se inserem na centralidade metropolitana? A metodologia utiliza análise espacial e modelagem urbana para analisar a localização de 318 CRFs com área acima de 2,0 hectares. Os dados foram obtidos junto à base da METROPLAN-RS e PMPA e por análise de imagens de satélite. Os resultados produzem um panorama da localização dos CRFs, evidenciando uma tendência de ocupação de áreas periféricas, em descontinuidade ao tecido urbano, porém mantendo proximidade aos eixos de maior centralidade da RMPA.
... The classic metrics and the corresponding ones tailored by [16], for a network N composed by V nodes and E links, are defined as follows: [20] is defined as the number of links incident upon a node and describes the local connectivity of the network. It can be expressed as: ...
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... Therefore for understating the functionality of the configuration in this large system a set of centrality measures such as closeness centrality (Sabidussi, 1966) and betweenness centrality (Freeman, 1977) were employed to assess the local and global depth and integration of the segments in relation to the overall configuration. This model consisting of almost 700k segments was analysed using DepthmapX 0.5 (Turner, et al., n.d.) and the centrality measures were derived from local radius r400m to global radius. ...
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Chapter
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