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Centrality Network

Centrality in a network refers to the measure of the importance or significance of a node (or sometimes an edge) within that network. It helps identify which nodes play crucial roles in various network processes such as information flow, influence propagation, or resource allocation. Centrality measures are commonly used in network analysis, including social networks, transportation networks, biological networks, and more. There are several types of centrality measures, including:

Degree Centrality: This is the simplest centrality measure and is based on the number of connections a node has. In a social network, it would represent how many friends a person has. Nodes with higher degrees are considered more central.
 
Closeness Centrality: This measure quantifies how quickly a node can reach all other nodes in the network. It is based on the length of the shortest paths from a node to all other nodes. Nodes with shorter average path lengths are considered more central.

Betweenness Centrality: This measures the extent to which a node lies on the shortest paths between other nodes. Nodes with high betweenness centrality act as bridges or bottlenecks in the network.
 
Eigenvector Centrality: It measures the influence of a node in the network, considering the influence of its neighbors. A node is considered central if it is connected to other central nodes.

PageRank: Originally developed for ranking web pages by Google, PageRank measures the importance of a node in a network by considering both the number of links to the node and the quality (centrality) of those linking nodes.

Katz Centrality: This measure is a generalization of eigenvector centrality and takes into account not just direct connections but also indirect connections through paths of varying lengths.

Closeness Prestige: Similar to closeness centrality, this measure considers the sum of the reciprocal of the lengths of the shortest paths to all other nodes in the network.

Eccentricity Centrality: It measures the eccentricity of a node, which is the maximum shortest path length from that node to any other node in the network. Nodes with lower eccentricity are more central.

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