Description: Betweenness centrality is a measure in graph theory that evaluates the importance of a vertex within a network based on the number of shortest paths that pass through it. This metric is used to identify nodes that act as bridges or intermediaries between other nodes, which can be crucial for understanding the dynamics of the network. A vertex with high betweenness centrality has the ability to influence communication and the flow of information, as it connects different parts of the network. This property is especially relevant in various types of networks, such as social networks, biological networks, and transportation networks, where certain nodes can play a critical role in facilitating interactions or coordinating processes. Betweenness centrality is calculated by summing the fraction of the shortest paths that pass through a specific vertex, relative to the total number of shortest paths between all pairs of nodes. Therefore, a vertex that appears in many shortest paths between other nodes will have a high betweenness centrality score, indicating its crucial role in the connectivity of the network. This measure helps identify key nodes in diverse applications where the structure of the network can influence the behavior and dynamics of the system as a whole.
