企业网络结构与无标度模型
Structure of Business Firm Networks and Scale-Free Models
摘要：
我们利用$k$ -壳分解方法研究了度分布为$P(q) \propto (q+c)^{-λ}$的企业网络和无标度模型的结构，发现生命科学产业网络由三个部分组成：一个“核”，它是一个小的良好连接的子图，“卷须”，它是一个小的子图，由小度节点只连接到核，以及由大多数节点组成的“主体”。与此同时，我们在信息和通信技术行业没有观察到上述结构。我们还对随机无标度网络中的这三个分量进行了系统的研究。我们的研究结果表明，随着$λ$的增加，细胞核和卷须的大小减小，而$λ\geq 3$则消失。我们比较了随机无标度模型网络的$k$壳结构与两个现实世界中的企业网络在生命科学和信息和通信技术部门。我们的研究结果表明，所观察到的行为的$k$壳结构在两个行业是一致的，最近提出的增长模型，假设共存的优惠和随机协议的产业网络的演变。
英文摘要：
We study the structure of business firm networks and scale-free models with degree distribution $P(q) \propto (q+c)^{-λ}$ using the method of $k$-shell decomposition.We find that the Life Sciences industry network consist of three components: a ``nucleus,'' which is a small well connected subgraph, ``tendrils,'' which are small subgraphs consisting of small degree nodes connected exclusively to the nucleus, and a ``bulk body'' which consists of the majority of nodes. At the same time we do not observe the above structure in the Information and Communication Technology sector of industry. We also conduct a systematic study of these three components in random scale-free networks. Our results suggest that the sizes of the nucleus and the tendrils decrease as $λ$ increases and disappear for $λ\geq 3$. We compare the $k$-shell structure of random scale-free model networks with two real world business firm networks in the Life Sciences and in the Information and Communication Technology sectors. Our results suggest that the observed behavior of the $k$-shell structure in the two industries is consistent with a recently proposed growth model that assumes the coexistence of both preferential and random agreements in the evolution of industrial networks.
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