The structural holes have been a key issue in fuzzy social network analysis. For undirected fuzzy social networks where edges are just present or absent undirected fuzzy relation and have no more information attached, many structural holes measures have been presented, such as key fuzzy structural holes, general fuzzy structural holes, strong fuzzy structural holes, and weak fuzzy structural holes. There has been a growing need to design structural holes measures for directed fuzzy social networks, because directed fuzzy social networks where edges are attached by directed fuzzy relation would contain rich information. In this paper, we extend structural holes theory to directed fuzzy social network and propose the algorithm of unidirectional fuzzy structural holes and bidirectional fuzzy structural holes, which unveil more structural information of directed fuzzy social networks. Furthermore, we investigate the validness of the algorithm by illustrating this method to a case called G-Y Research Team and obtain reliable results, which provide strong evidences of the new measure’s utility.
"Structural Holes in Directed Fuzzy Social Networks." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/452063