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

TL;DR

This paper introduces a new statistical index to determine whether socio-economic network relations are better modeled as directed or undirected, applicable to both binary and weighted graphs, and validated through empirical network data.

Contribution

The paper presents a novel index for assessing relation directionality in socio-economic networks, with a standard normal distribution property and applicability to various graph types.

Findings

Index effectively distinguishes directed from undirected relations.

Application on real networks demonstrates practical utility.

Index distribution approximates standard normal under null hypothesis.

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.