Directed or Undirected? A New Index to Check for Directionality of Relations in Socio-Economic Networks
This paper proposes a simple procedure to decide whether the empirically-observed adjacency or weights matrix, which characterizes the graph underlying a socio-economic network, is sufficiently symmetric (respectively, asymmetric) to justify an undirected (respectively, directed) network analysis. We introduce a new index that satisfies two main properties. First, it can be applied to both binary or weighted graphs. Second, once suitably standardized, it distributes as a standard normal over all possible adjacency/weights matrices. To test the index in practice, we present an application that employs a set of well-known empirically-observed social and economic networks.
Volume (Year): 3 (2006)
Issue (Month): 34 ()
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- Garlaschelli, Diego & Loffredo, Maria I., 2005. "Structure and evolution of the world trade network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 138-144.
- Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906, December.
- D. Garlaschelli & M. I. Loffredo, 2005. "Structure and Evolution of the World Trade Network," Papers physics/0502066, arXiv.org, revised May 2005.
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