# Θ-Kirchhoff Edge Centrality

#### Definition

In use the well-known Kirchhoff index as the measure of edge centrality in weighted

networks, called Θ-Kirchhoff edge centrality. The Kirchhoff index of a network is defined as the

sum of effective resistances over all vertex pairs. The centrality of an edge e is reflected in the

increase of Kirchhoff index of the network when the edge e is partially deactivated, characterized

by a parameter Θ.

networks, called Θ-Kirchhoff edge centrality. The Kirchhoff index of a network is defined as the

sum of effective resistances over all vertex pairs. The centrality of an edge e is reflected in the

increase of Kirchhoff index of the network when the edge e is partially deactivated, characterized

by a parameter Θ.

#### References

- Li H., Zhang Z., 2018. Kirchhoff index as a measure of edge centrality in weighted networks: Nearly linear time algorithms. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, , pp.2377-2396. DOI: 10.1137/1.9781611975031.153