Residual Closeness Centrality

Let d_k(i, j) be the distance between vertices i and j in the graph, received from the original graph where all links of vertex k are deleted. We calculate the closeness after removing vertex k The vertex residual closeness (VRC) of the graph can be defined as: We can define analogously the graph link residual closeness (LRC)—the minimal of the closeness, calculated when only one link (k, p) is deleted. To calculate it we use d_(k,p)(i, j) — the distance between vertices i and j in the graph, received from the original graph where only the link (k, p) is deleted.

See Dangalchev Closeness Centrality

• DANGALCHEV, C. 2006. Residual closeness in networks. Physica A: Statistical Mechanics and its Applications, 365, 556-564. DOI: 10.1016/j.physa.2005.12.020