CentiServer - Centrality - Closeness Centrality

Definition

Freeman closeness centrality
Reciprocal of the total distance from a node v to all the other nodes in a network:

where dist(v, t) is the distance between node v and t.
Typically it is used as a measure of how fast information will spread from one node in a network to all other nodes, or, in a network planning situation which nodes are favorable starting points.

Variant closeness centrality
By definition of shortest-path distances, classic closeness centrality is ill-defined on unconnected networks.

This variant (sum of inversed distances to all other nodes instead of the inversed of the sum of distances to all other nodes) [OPSAHL, T. 2010] applicable to both connected and unconnected graphs.
See Harmonic Centrality

Latora closeness centrality
In networks with disconnected components
Latora V., Marchiori M., Efficient behavior of small-world networks, Physical Review Letters, V. 87, p. 19, 2001.

Fuzzy closeness centrality
A closeness centrality measure, with a fuzzy distance measure in the graph.
DAVIDSEN, S. A. & PADMAVATHAMMA, M. A fuzzy closeness centrality using andness-direction to control degree of closeness. Networks & Soft Computing (ICNSC), 2014 First International Conference on, 19-20 Aug. 2014 2014. 203-208.
See Fuzzy Closeness Centrality

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.
See Dangalchev Closeness Centrality

Residual 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.
See Residual Closeness Centrality

Closeness centrality for a set of nodes
Chen, C., Wang, W. and Wang, X., 2016, September. Efficient Maximum Closeness Centrality Group Identification. In Australasian Database Conference (pp. 43-55). Springer International Publishing. See Closeness Centrality Group Identification

Top-k closeness centrality on dynamic networks
Lin, Y., Zhang, J., Ying, Y., Hong, S. and Li, H., 2016, September. FVBM: A Filter-Verification-Based Method for Finding Top-k Closeness Centrality on Dynamic Social Networks. In Asia-Pacific Web Conference (pp. 389-392). Springer International Publishing.

Edge Closeness centrality
Bröhl, T. and Lehnertz, K., 2019. Centrality-based identification of important edges in complex networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(3), p.033115.

Ni, P., Hanai, M., Tan, W.J. and Cai, W., 2019, August. Efficient closeness centrality computation in time-evolving graphs. In Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (pp. 378-385).

Shukla, K., Regunta, S.C., Tondomker, S.H. and Kothapalli, K., 2020, June. Efficient parallel algorithms for betweenness-and closeness-centrality in dynamic graphs. In Proceedings of the 34th ACM International Conference on Supercomputing (pp. 1-12).

Requirements

Require connected and strongly connected network.

Software

References

FREEMAN, L. C. 1978. Centrality in social networks conceptual clarification. Social Networks, 1, 215-239. DOI: 10.1016/0378-8733(78)90021-7
OPSAHL, T., AGNEESSENS, F. & SKVORETZ, J. 2010. Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32, 245-251. DOI: 10.1016/j.socnet.2010.03.006
Chen, C., Wang, W. and Wang, X., 2016, September. Efficient Maximum Closeness Centrality Group Identification. In Australasian Database Conference (pp. 43-55). Springer International Publishing.
Lin, Y., Zhang, J., Ying, Y., Hong, S. and Li, H., 2016, September. FVBM: A Filter-Verification-Based Method for Finding Top-k Closeness Centrality on Dynamic Social Networks. In Asia-Pacific Web Conference (pp. 389-392). Springer International Publishing.
Saxena, A., Gera, R. and Iyengar, S.R.S., Fast Estimation of Closeness Centrality Ranking.