Directed closure measures for networks with reciprocity

@article{Comandur2017DirectedCM,
  title={Directed closure measures for networks with reciprocity},
  author={Seshadhri Comandur and Ali Pinar and Nurcan Durak and Tamara G. Kolda},
  journal={J. Complex Networks},
  year={2017},
  volume={5},
  pages={32-47}
}
The study of triangles in graphs is a standard tool in network analysis, leading to measures such as the \emph{transitivity}, i.e., the fraction of paths of length $2$ that participate in triangles. Real-world networks are often directed, and it can be difficult to "measure" this network structure meaningfully. We propose a collection of \emph{directed closure values} for measuring triangles in directed graphs in a way that is analogous to transitivity in an undirected graph. Our study of these… 

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