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In network theory, Pearson's correlation coefficients are most commonly usedto measure the degree assortativity of a network. We investigate the behaviorof these coefficients in the setting of directed networks with heavy-taileddegree sequences. We prove that for graphs where the in- and out-degreesequences satisfy a power law with realistic parameters, Pearson's correlationcoefficients converge to a non-negative number in the infinite network sizelimit. We propose alternative measures for degree-degree dependencies indirected networks based on Spearman's rho and Kendall's tau. Using examples andcalculations on the Wikipedia graphs for nine different languages, we show whythese rank correlation measures are more suited for measuring degreeassortativity in directed graphs with heavy-tailed degrees.

Degree-degree dependencies in directed networks with heavy-tailed degrees