一类合作-竞争二部网络的竞争能力对唯一性的依赖
Competition ability dependence on uniqueness in some collaboration-competition bipartite networks
摘要：
最近，我们的小组定量定义了两个量，“竞争力”和“独特性”（中国。Phys. Lett. 26（2009）058901）为一种合作-竞争的二分网络，其中“生产者”生产一些“产品”并将其“输出”到“市场”以进行竞争。工厂、大学或餐馆都可以作为例子。在信中，我们提出了一个分析结论，竞争能力线性依赖于在平凡的情况下，“输入质量”和“竞争增益”服从正态分布的唯一性。以中国区域大学之间的竞争为例进行了分析。本文讨论了竞争收益服从幂律分布的异常情形。此外，我们将研究扩展到所有的合作-竞争二部网络，从而重新定义了竞争能力。对15个现实世界中的合作竞争系统的竞争能力依赖唯一性进行了实证研究，其中14个属于一般的非平凡情形。我们发现，一般的依赖遵循所谓的“移幂律（SPL）”，但非常接近的幂律。并给出了竞争力分布和独特性分布的异质性指数。这些实证研究将作为未来论文的补充，对非正常合作竞争系统中竞争能力对唯一性的依赖性以及这种依赖性与竞争能力和唯一性异质性之间的关系进行比较和进一步讨论。
英文摘要：
Recently, our group quantitatively defined two quantities, "competition ability" and "uniqueness" (Chin. Phys. Lett. 26 (2009) 058901) for a kind of cooperation-competition bipartite networks, where "producers" produce some "products" and "output" them to a "market" to make competition. Factories, universities or restaurants can serve as the examples. In the letter we presented an analytical conclusion that the competition ability was linearly dependent on the uniqueness in the trivial cases, where both the "input quality" and "competition gain" obey normal distributions. The competition between Chinese regional universities was taken as examples. In this article we discuss the abnormal cases where competition gains show the distributions near to power laws. In addition, we extend the study onto all the cooperation-competition bipartite networks and therefore redefine the competition ability. The empirical investigation of the competition ability dependence on the uniqueness in 15 real world collaboration-competition systems is presented, 14 of which belong to the general nontrivial cases. We find that the dependence generally follows the so-called "shifted power law (SPL)", but very near to power laws. The empirically obtained heterogeneity indexes of the distributions of competition ability and uniqueness are also presented. These empirical investigations will be used as a supplementary of a future paper, which will present the comparison and further discussions about the competition ability dependence on the uniqueness in the abnormal collaboration-competition systems and the relationship between the dependence and the competition ability and uniqueness heterogeneity.
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