Closeness centrality

Closeness centrality is a useful measure that estimates how fast the flow of information would be through a given node to other nodes.

Closeness centrality measures how short the shortest paths are from node i to all nodes. It is usually expressed as the normalised inverse of the sum of the topological distances in the graph (see equation at the top of Figure 28). This sum is also known as the farness of the nodes. Sometimes closeness centrality is also expressed simply as the inverse the farness (13, 14). In the example shown on the bottom half of the figure, you can see the distances matrix for the graph on the left and the calculations to get the closeness centrality on the right. Node B is the most central node according to these parameters.

Calculating the closeness centrality of nodes in a graph

Figure 28 Calculating the closeness centrality of nodes in a graph.