# Current-Flow Betweenness Centrality

#### Definition

The current-flow betweenness of a vertex v is defined as the amount of current that flows through v in this setup, averaged over all vertex pairs s and t. The current-flow betweenness of a vertex v is the average of the current flow over all source–target pairs:
where n(n − 1)/2 is a normalizing constant, and I

Random-Walk Betweenness Centrality

Alpha Current-Flow Betweenness Centrality

Truncated Alpha Current-Flow Betweenness Centrality

Beta Current-Flow Betweenness Centrality

Distributed Current-Flow Betweenness Centrality

Bertolucci, M., Lulli, A. and Ricci, L., 2016. Current Flow Betweenness Centrality with Apache Spark. In Algorithms and Architectures for Parallel Processing (pp. 270-278). Springer International Publishing.

Agryzkov, T., Tortosa, L. and Vicent, J.F., 2019. A variant of the current flow betweenness centrality and its application in urban networks. Applied Mathematics and Computation, 347, pp.600-615.

_{v}^{(st)}is the current flow through node v between source s and sink t. Thus, current-flow betweenness measures the fraction of current flow passing through vertex v between all possible vertex pairs in the network. A simple random walk from s to t is a walk traveling from source s to target t by taking random intermediate vertices. Current-flow betweenness is shown to be the same as random-walk betweenness [BRANDES, U. 2005, NEWMAN, M. E. 2005].**See also:**Random-Walk Betweenness Centrality

Alpha Current-Flow Betweenness Centrality

Truncated Alpha Current-Flow Betweenness Centrality

Beta Current-Flow Betweenness Centrality

Distributed Current-Flow Betweenness Centrality

**Edge Current-Flow Betweenness Centrality****With Apache Spark**Bertolucci, M., Lulli, A. and Ricci, L., 2016. Current Flow Betweenness Centrality with Apache Spark. In Algorithms and Architectures for Parallel Processing (pp. 270-278). Springer International Publishing.

Agryzkov, T., Tortosa, L. and Vicent, J.F., 2019. A variant of the current flow betweenness centrality and its application in urban networks. Applied Mathematics and Computation, 347, pp.600-615.

#### Software

#### References

- Bertolucci, M., Lulli, A. and Ricci, L., 2016. Current Flow Betweenness Centrality with Apache Spark. In Algorithms and Architectures for Parallel Processing (pp. 270-278). Springer International Publishing.
- BRANDES, U. & FLEISCHER, D. 2005. Centrality measures based on current flow, Springer.
- NEWMAN, M. E. 2005. A measure of betweenness centrality based on random walks. Social networks, 27, 39-54.
- ZHANG, A. 2009. Protein Interaction Networks: Computational Analysis, Cambridge University Press.