复杂加权网络的多尺度主干提取
Extracting the multiscale backbone of complex weighted networks
摘要：
大量的复杂系统以加权网络的形式找到一种自然的抽象，其节点表示系统的元素，而加权边标识相互作用的存在及其相对强度。近年来，越来越多的大规模网络的研究已经突出了他们的相互作用模式的统计异质性，与度和权重分布的变化在许多数量级。这些特征，以及大量的元素和链接，使得提取形成网络主干的真正相关的连接成为一个非常具有挑战性的问题。更具体地说，粗粒度的方法和过滤技术正在与大规模系统的多尺度性质作斗争。在这里，我们定义了一个过滤方法，提供了一个实用的程序来提取相关的连接骨干在复杂的多尺度网络，保留的边缘，代表统计显着的偏差相对于一个空模型的局部分配的权重边缘。该方法的一个重要方面是，它不轻视小规模的相互作用，并在由重量分布定义的所有尺度上运行。我们将我们的方法应用到现实世界的网络实例中，并将所得结果与其他骨干提取技术进行比较。
英文摘要：
A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In recent years, the study of an increasing number of large scale networks has highlighted the statistical heterogeneity of their interaction pattern, with degree and weight distributions which vary over many orders of magnitude. These features, along with the large number of elements and links, make the extraction of the truly relevant connections forming the network's backbone a very challenging problem. More specifically, coarse-graining approaches and filtering techniques are at struggle with the multiscale nature of large scale systems. Here we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks, preserving the edges that represent statistical significant deviations with respect to a null model for the local assignment of weights to edges. An important aspect of the method is that it does not belittle small-scale interactions and operates at all scales defined by the weight distribution. We apply our method to real world network instances and compare the obtained results with alternative backbone extraction techniques.
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