A measure for a balanced workload and its extremal values

In order to measure the extent to which the distribution of workload between actors in the network can be equalized, a degree-weighted measure for a balanced workload based on betweenness centrality is introduced. The goal of this study is to determine the extremal values of the introduced measure, as well as the graph structures where the extremal values are attained. Several real world networks were used for evaluation of the new invariant. The obtained results are used for statistical comparison with standard measures of centrality to demonstrate validity of the introduced measure.