A fuzzy closeness centrality using andness-direction to control degree of closeness

Centrality measures have many practical uses in network analysis, where closeness centrality is one of the original measures introduced by Freeman. Closeness centrality is a measure of how close a node is to all other nodes. 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. In this paper we propose a novel parametric fuzzy closeness measure which allows relaxation on the condition of all other nodes. The measure is defined for unweighted networks, and evaluate both on an exemplary network and a real network with synthesized errors introduced. Evaluation indicate that the fuzzy network measure provides new information for closeness centrality in networks not provided by the classical measure, and that the measure is more robust to observation errors in the network. Finally, ideas for a measure for weighted networks is discussed.