YonatanRosen/direct​ionality-package

Implementation of two algorithms that provide order centrality in directed networks

Directed acyclic graphs have clear order, where precedence relations among vertices are naturally defined. Many directed real world networks contain inherent order that may be masked by strong connectivity components or long circles. Two algorithms aim at uncover the inherent order in directed networks that contain cycles as well. This package contains implementation of algorithms that handle the directionality problem. The two algorithms receive a binary directed graph and return a centrality score where high score vertices precede lower score vertices in the graph hierarchy. The flow algorithm exploits the asymmetry in distances in the directed graph and its underlying undirected graph. The hierarchy energy algorithm minimizes an energy function that takes into consideration all ordered relations of unidirectional edges.
flow reference:
Yonatan Rosen and Yoram Louzoun, "Directionality of real world networks as predicted by path length in directed and undirected graphs." Physica A: Statistical Mechanics and its Applications 401 (2014): 118-129.
hierarchy energy reference:
Carmel Liran, David Harel, and Yehuda Koren. "Combining hierarchy and energy for drawing directed graphs." Visualization and Computer Graphics, IEEE Transactions on 10.1 (2004): 46-57.

Yoram Louzoun's lab: http://peptibase.cs.biu.ac.il/

The package includes the BFS function of Lev Muchnik's complex networks toolbox:
http://www.levmuchnik.net/Content/Networks/ComplexNetworksPackage.html