Centrality / Location in the network

The first measure of centrality was developed by König in 1936 and is called the König numberKi. Let s(i, j) denote the number of edges in the shortest path from vertex i to vertex j. Then the König number for vertex i is defined as:

where s(i, j) is the shortest edge distance between vertex i and vertex j. Therefore, Ki is the longest shortest path originating from vertex i. It is a measure of topological distance in terms of edges and suggests that vertices with a low König numbers occupy a central place in the network.

If you have determined the shortest edge distance between the nodes, then the largest value in a column in the König number (blue). In the example, the orange node is centrally located and the two green nodes are peripheral.
The method for determining the König number is also applicable to a distance matrix. The example of accessibility is shown again in the figure below. This time the matrix is used with the same values to calculate the König number.