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

翻译：网络增长中的优先依附模型是入度和出度的二元重尾模型，其极限测度要么集中在以原点为起点的正斜率射线上，要么覆盖整个正象限，具体取决于模型是否包含互惠性。集中在射线上称为完全依赖性。如果存在可靠的方法区分完全依赖性与非完全依赖性，我们将能为模型选择提供指导。这促使我们研究能区分以下情形的检验方法：(i) 完全依赖性；(ii) 强依赖性（极限测度的支撑集是正象限的真子锥）；(iii) 弱依赖性（极限测度集中在正象限）。我们提出了两个检验统计量，分析了它们在完全依赖性和非完全依赖性下的渐近正态行为，并利用自举方法对模拟数据和真实数据讨论了其适用性。