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.

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