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Betweenness centrality. An directed graph colored based on the betweenness centrality of each vertex from least (red) to greatest (blue). In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph, there exists at least one shortest path between the ...
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. The number next to each node is the ...
An undirected graph colored based on the betweenness centrality of each vertex from least (red) to greatest (blue). In network theory, Brandes' algorithm is an algorithm for calculating the betweenness centrality of vertices in a graph. The algorithm was first published in 2001 by Ulrik Brandes. [1]
Graph center. A graph with central points colored red. These are the three vertices A such that d (A, B) ≤ 3 for all vertices B. Each black vertex is a distance of at least 4 from some other vertex. The center (or Jordan center [1]) of a graph is the set of all vertices of minimum eccentricity, [2] that is, the set of all vertices u where the ...
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks.
On a circle, a digon is a tessellation with two antipodal points, and two 180° arc edges. In geometry, a bigon, [1] digon, or a 2-gon, is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be ...
In graph theory, eigenvector centrality (also called eigencentrality or prestige score [1]) is a measure of the influence of a node in a connected network.Relative scores are assigned to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.
Vertices are aligned to the left. The legend on the right shows the names of the edges. An example of a directed hypergraph, with and . In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices.