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closenesse
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There are 10 letters in CLOSENESSE ( C3E1L1N1O1S1 )
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| Closenesse might refer to |
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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:* * * * C * ( * x * ) * = * * * 1 * * * ∑ * * y * * * d * ( * y * , * x * ) * * * * . * * * {\displaystyle C(x)={\frac {1}{\sum _{y}d(y,x)}}.} * where * * * * d * ( * y * , * x * ) * * * {\displaystyle d(y,x)} * is the distance between vertices * * * * x * * * {\displaystyle x} * and * * * * y * * * {\displaystyle y} * . 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 * * * * N * − * 1 * * * {\displaystyle N-1} * , where * * * * N * * * {\displaystyle N} * is the number of nodes in the graph. For large graphs this difference becomes inconsequential so the * * * * − * 1 * * * {\displaystyle -1} * is dropped resulting in: * * * * * C * ( * x * ) * = * * * N * * * ∑ * * y * * * d * ( * y * , * x * ) * * * * . * * * {\displaystyle C(x)={\frac {N}{\sum _{y}d(y,x)}}.} * This adjustment allows comparisons between nodes of graphs of different sizes. * 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 link, but low closeness centrality from incoming links). |