központúság

Központúság, also known as centrality in English, is a concept in graph theory and network analysis that measures the relative importance of a vertex (node) within a graph. It is often used to identify the most influential or critical nodes in a network. There are several types of centrality measures, each providing a different perspective on a node's importance.

Degree centrality is the simplest form of centrality, calculated as the number of direct connections a node has. Nodes with high degree centrality are often considered important because they have many direct ties to other nodes.

Betweenness centrality measures the extent to which a node lies on the shortest paths between other nodes. Nodes with high betweenness centrality act as bridges, connecting different parts of the network. They are crucial for information flow and can be critical in maintaining network connectivity.

Closeness centrality evaluates how close a node is to all other nodes in the network. It is calculated as the reciprocal of the sum of the shortest path distances from the node to all other nodes. Nodes with high closeness centrality can quickly disseminate information to the entire network.

Eigenvector centrality, also known as Google's PageRank, measures the influence of a node based on the influence of its neighbors. Nodes connected to many influential nodes are considered more important.

Központúság is a fundamental concept in understanding the structure and dynamics of complex networks, such as social networks, transportation systems, and biological networks. By identifying central nodes, researchers and practitioners can gain insights into the network's functionality, resilience, and potential vulnerabilities.