# Ranking-Betweenness Centrality

#### Definition

This centrality measure combines the idea behind the random-walk betweenness centrality measure
and the idea of ranking the nodes of a network produced by an adapted PageRank algorithm.

In some types of networks, as for example street networks, a node does not measure its importance only by its connectivity to other nodes; there are other factors that can and should be measured to be considered a true ranking of importance within the network.

The PageRank algorithm modified with the primary objective to introduce a data matrix representing some type of information of the network itself. This information allows us to obtain a ranking of the nodes of the network which is used in the random-walk betweenness algorithm. This centrality measure reduces the effect of the randomness present in the random-walk betweenness measure and takes into account, in a decisive way, the information we want to evaluate of the network.

The detailed example is presented at [AGRYZKOV, T., 2014].

In some types of networks, as for example street networks, a node does not measure its importance only by its connectivity to other nodes; there are other factors that can and should be measured to be considered a true ranking of importance within the network.

The PageRank algorithm modified with the primary objective to introduce a data matrix representing some type of information of the network itself. This information allows us to obtain a ranking of the nodes of the network which is used in the random-walk betweenness algorithm. This centrality measure reduces the effect of the randomness present in the random-walk betweenness measure and takes into account, in a decisive way, the information we want to evaluate of the network.

The detailed example is presented at [AGRYZKOV, T., 2014].

#### Software

#### References

- AGRYZKOV, T., OLIVER, J. L., TORTOSA, L. & VICENT, J. 2014. A new betweenness centrality measure based on an algorithm for ranking the nodes of a network. Applied Mathematics and Computation, 244, 467-478. DOI: 10.1016/j.amc.2014.07.026