有向网络的复制机制及其相关网络分析

鉴于有向网络比无向网络包含了更多的内在信息, 而复杂网络中的基本统计量往往仅适用于无向网络, 使得有向网络的研究相对缺少, 由此提出了一个有向网络的统计量, 并分析该统计量在相关有向网络研究中的有效性. 考虑到复制是有向网络增长的一个主要动力, 定义了有向网络结点复制率和有向网络复制率的概念, 并利用结点入度分布和复制率研究了有向规则网络、复制模型网络及自然数网络. 结果显示, 完全复制模型和自然数网络的入度具有无标度特性, 其入度分布的幂律指数 都为2, 2个有向网络的复制率 , 而部分复制模型的复制率 . 因此, 有向网络的入度分布、复制率都能很好地解释完全复制模型与自然数网络的相关性, 可作为重要统计量广泛应用于有向网络研究中.     

Degree sequences of <Emphasis Type="Italic">k</Emphasis>-multi-hypertournaments

Let n and k（n ≥ k 〉 1） be two non-negative integers.A k-multi-hypertournament on n vertices is a pair（V,A）,where V is a set of vertices with ｜V｜=n,and A is a set of k-tuples of vertices,called arcs,such that for any k-subset S of V,A contains at least one（at most k!） of the k! k-tuples whose entries belong to S.The necessary and suffcient conditions for a non-decreasing sequence of non-negative integers to be the out-degree sequence（in-degree sequence） of some k-multi-hypertournament are given.     

Structure and Connectivity Analysis of Financial Complex System Based on G-Causality Network

The recent financial crisis highlights the inherent weaknesses of the financial market. To explore the mechanism that maintains the financial market as a system, we study the interactions of U.S. financial market from the network perspective. Applied with conditional Granger causality network analysis, network density, in-degree and out-degree rankings are important indicators to analyze the conditional causal relationships among financial agents, and further to assess the stability of U.S. financial systems. It is found that the topological structure of G-causality network in U.S. financial market changed in diferent stages over the last decade, especially during the recent global financial crisis. Network density of the G-causality model is much higher during the period of 2007–2009 crisis stage, and it reaches the peak value in 2008, the most turbulent time in the crisis. Ranked by in-degrees and out-degrees, insurance companies are listed in the top of 68 financial institutions during the crisis. They act as the hubs which are more easily influenced by other financial institutions and simultaneously influence others during the global financial disturbance.     

供应链型网络中双幂律分布模型

考察了供应链网络的基本特征，提出了节点到达过程是更新过程、新增入边和出边数是具有Bernoulli分布随机变量的供应链型有向网络.研究了这类网络节点的瞬态度分布和稳态平均度分布.利用更新过程理论对这类网络进行了分析，获得了网络节点瞬态度分布和网络稳态平均度分布的解析表达式.分析表明, 虽然这类网络节点的稳态度分布不存在，但是网络的稳态平均度分布具有双向幂律性. 关键词： 复杂网络 入度 出度 度分布     

Structure and Connectivity Analysis of Financial Complex System Based on G-Causality Network

The recent financial crisis highlights the inherent weaknesses of the financial market. To explore the mechanism that maintains the financial market as a system, we study the interactions of U.S. financial market from the network perspective. Applied with conditional Granger causality network analysis, network density, in-degree and out-degree rankings are important indicators to analyze the conditional causal relationships among financial agents, and further to assess the stability of U.S. financial systems. It is found that the topological structure of G-causality network in U.S. financial market changed in different stages over the last decade, especially during the recent global financial crisis. Network density of the G-causality model is much higher during the period of 2007-2009 crisis stage, and it reaches the peak value in 2008, the most turbulent time in the crisis. Ranked by in-degrees and out-degrees, insurance companies are listed in the top of 68 financial institutions during the crisis. They act as the hubs which are more easily influenced by other financial institutions and simultaneously influence others during the global financial disturbance.