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- In a connected graph, closeness centrality (or closeness) of a node is a measure of centrality in a network, calculated as the reciprocal of the sum of the length of the shortest paths between the node and all other nodes in the graph. Thus, the more central a node is, the closer it is to all other nodes. Closeness was defined by Bavelas (1950) as the reciprocal of the farness, that is: where is the distance (length of the shortest path) between vertices and . This unnormalised version of closeness is sometimes known as status When speaking of closeness centrality, people usually refer to its normalized form which represents the average length of the shortest paths instead of their sum. It is generally given by the previous formula multiplied by , where is the number of nodes in the graph resulting in: The normalization of closeness simplifies the comparison of nodes in graphs of different sizes. For large graphs, the minus one in the normalisation becomes inconsequential and it is often dropped. As one of the oldest centrality measures, closeness is often given in general discussions of network centrality meaures in introductory texts or in articles comparing different centrality measures. The values produced by many centrality measaures can be highly correlated. In particular, closeness and degree have been shown to be related in many networks through an approximate relationship where is the degree of vertex while and β are parameters found by fitting closeness and degree to this formula. The z parameter represents the branching factor, the average degree of nodes (excluding the root node and leaves) of the shortest-path trees used to approximate networks when demonstrating this relationship. This is never an exact relationship but it captures a trend seen in many real-world networks. Closeness is related to other length scales used in network science. For instance, the average shortest path length , the average distance between vertices in a network, is simply the average of the inverse closeness values . Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing links, but low closeness centrality from incoming links). (en)
- En análisis de redes sociales, la centralidad de cercanía, o simplemente cercanía (en inglés, closeness), es una medida de centralidad basada en las ideas de , definida formalmente por y , con aplicaciones en redes de comunicación, y luego popularizada por . Es la más conocida y utilizada de las medidas radiales de longitud. Se basa en calcular la suma o bien el promedio de las distancias geodésicas (o longitudes de los caminos más cortos) desde un nodo hacia todos los demás. Note que mientras mayor sea la «distancia» entre dos vértices, menor será la «cercanía» entre estos. Por lo tanto, la cercanía se define como el inverso multiplicativo de la «lejanía» entre dos vértices. (es)
- Степень близости узла (к другим узлам) — это мера центральности в сети, вычисляемая как обратная величина суммы длин кратчайших путей между узлом и всеми другими узлами графа. Таким образом, чем более централен узел, тем ближе он ко всем другим узлам. (ru)
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- En análisis de redes sociales, la centralidad de cercanía, o simplemente cercanía (en inglés, closeness), es una medida de centralidad basada en las ideas de , definida formalmente por y , con aplicaciones en redes de comunicación, y luego popularizada por . Es la más conocida y utilizada de las medidas radiales de longitud. Se basa en calcular la suma o bien el promedio de las distancias geodésicas (o longitudes de los caminos más cortos) desde un nodo hacia todos los demás. Note que mientras mayor sea la «distancia» entre dos vértices, menor será la «cercanía» entre estos. Por lo tanto, la cercanía se define como el inverso multiplicativo de la «lejanía» entre dos vértices. (es)
- Степень близости узла (к другим узлам) — это мера центральности в сети, вычисляемая как обратная величина суммы длин кратчайших путей между узлом и всеми другими узлами графа. Таким образом, чем более централен узел, тем ближе он ко всем другим узлам. (ru)
- In a connected graph, closeness centrality (or closeness) of a node is a measure of centrality in a network, calculated as the reciprocal of the sum of the length of the shortest paths between the node and all other nodes in the graph. Thus, the more central a node is, the closer it is to all other nodes. Closeness was defined by Bavelas (1950) as the reciprocal of the farness, that is: The normalization of closeness simplifies the comparison of nodes in graphs of different sizes. For large graphs, the minus one in the normalisation becomes inconsequential and it is often dropped. . (en)
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- Centralidad de cercanía (es)
- Closeness centrality (en)
- Степень близости (теория графов) (ru)
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