Directed or Undirected? A New Index to Check for Directionality of Relations in Socio-Economic Networks

Abstract

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.

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• Structure and Evolution of the World Trade Network
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Cited by in corpus (7)

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• The $\beta$-model for Random Graphs --- Regression, Cramér-Rao Bounds, and Hypothesis Testing
• Interactions between financial and environmental networks in OECD countries
• Spanning trees of the World Trade Web: real-world data and the gravity model of trade