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Preferential attachment models of network growth are bivariate heavy tailedmodels for in- and out-degree with limit measures which either concentrate on aray of positive slope from the origin or on all of the positive quadrantdepending on whether the model includes reciprocity or not. Concentration onthe ray is called full dependence. If there were a reliable way to distinguishfull dependence from not-full, we would have guidance about which model tochoose. This motivates investigating tests that distinguish between (i) fulldependence; (ii) strong dependence (support of the limit measure is a propersubcone of the positive quadrant); (iii) weak dependence (limit measureconcentrates on positive quadrant). We give two test statistics, analyze theirasymptotically normal behavior under full and not-full dependence, and discussapplicability using bootstrap methods applied to simulated and real data.

2RV+HRV and Testing for Strong VS Full Dependence