Serrano M Angeles, Boguñá Marián, Vespignani Alessandro
Instituto de Física Interdisciplinar y Sistemas Complejos, Consejo Superior de Investigaciones Científicas-Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.
Proc Natl Acad Sci U S A. 2009 Apr 21;106(16):6483-8. doi: 10.1073/pnas.0808904106. Epub 2009 Apr 8.
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 that 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 come into conflict 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 statistically 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.
大量复杂系统可以自然地抽象为加权网络的形式，其中节点代表系统的元素，加权边则标识相互作用的存在及其相对强度。近年来，对越来越多的大规模网络的研究突出了其相互作用模式的统计异质性，其度分布和权重分布在多个数量级上变化。这些特征，连同大量的元素和链接，使得提取构成网络主干的真正相关连接成为一个极具挑战性的问题。更具体地说，粗粒化方法和过滤技术与大规模系统的多尺度性质相冲突。在这里，我们定义了一种过滤方法，该方法提供了一种实用的程序来提取复杂多尺度网络中的相关连接主干，保留那些相对于边权重的局部分配的零模型表示统计上显著偏差的边。该方法的一个重要方面是它不会轻视小规模相互作用，并且在由权重分布定义的所有尺度上运行。我们将我们的方法应用于实际网络实例，并将获得的结果与其他主干提取技术进行比较。
