局部可观测复杂网络的结构与功能关系
The relationship between structure and function in locally observed complex networks
摘要：
最近，一些研究开始揭示在复杂网络中发生的小规模交互时，节点组之间发生的大量交互。这样的发现要求一个新的系统方法来量化，在节点级别，动态是如何被影响（或分化）的基础系统的结构。在这里，我们定义了一个新的措施，根据动力学特性获得了一个大的初始条件，比较系统中存在的节点的动力学行为。通过这种测量，我们发现地理模型和巴拉巴西-阿尔伯特模型具有很高的生成网络的能力，与网络的其他部分相比，这些网络显示出具有不同动态的节点组。我们的方法的应用说明与两个真正的系统。在第一，我们使用的线虫秀丽隐杆线虫的神经元网络，以表明，interneurons的腹索的线虫提出了一个非常大的动态分化相比，其余的网络。第二个应用涉及机场网络上的SIS流行病模型，在该模型中，我们量化了高度和低度节点的感染时间分布与网络预期值相比的差异。
英文摘要：
Recently, some studies started to unveil the wealthy of interactions that occur between groups of nodes when looking at the small scale of interactions taking place in complex networks. Such findings claim for a new systematic methodology to quantify, at node level, how a dynamics is being influenced (or differentiated) by the structure of the underlying system. Here we define a new measure that, based on dynamical characteristics obtained for a large set of initial conditions, compares the dynamical behavior of the nodes present in the system. Through this measure we find that the geographic and Barabási-Albert models have high capacity for generating networks that exhibit groups of nodes with distinct dynamics compared to the rest of the network. The application of our methodology is illustrated with respect of two real systems. In the first we use the neuronal network of the nematode Caenorhabditis elegans to show that the interneurons of the ventral cord of the nematode presents a very large dynamical differentiation when compared to the rest of the network. The second application concerns the SIS epidemic model on an airport network, where we quantify how different the distribution of infection times of high and low degree nodes can be, when compared to the expected value for the network.
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