In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to … See more

Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the … See more

Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing … See more

Betweenness is a centrality measure of a vertex within a graph (there is also edge betweenness, which is not discussed here). Betweenness centrality quantifies the number of times … See more

Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would … See more

In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between … See more

Eigenvector centrality (also called eigencentrality) is a measure of the influence of a node in a network. It assigns relative scores to all nodes in the network based on the … See more