网络中的多尺度混合模式
Multiscale mixing patterns in networks
摘要：
网络中的分类混合是具有相同属性或元数据的节点相互链接的趋势。这是一种经常在社交网络中发现的属性，表现为具有相同年龄、种族或政治信仰的人之间更高的链接倾向。量化链接性或分离性（链接到具有不同属性的节点的偏好）的水平可以揭示复杂网络中链接和传染过程形成的因素。在离散值元数据的情况下，通常的做法是根据可扩展性系数或模块性来测量可扩展性水平。这个全局值是整个网络的平均重复率水平，当混合模式是异构的时，它可能不是一个代表性的统计数据。例如，由于文化规范的差异，一个跨越全球的社交网络可能会在混合模式上表现出地方差异。在这里，我们介绍了一种方法来本地化这个全球性的措施，使我们可以描述跨多个尺度，在节点级别的可追溯性。因此，我们能够捕捉和定性评估网络中的混合模式的分布。我们发现，对于许多现实世界中的网络的不确定性的分布是偏斜的，过度分散和多模态的。我们的方法提供了一个更清晰的镜头，通过它我们可以更仔细地检查网络中的混合模式。
英文摘要：
Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with the same age, race, or political belief. Quantifying the level of assortativity or disassortativity (the preference of linking to nodes with different attributes) can shed light on the factors involved in the formation of links and contagion processes in complex networks. It is common practice to measure the level of assortativity according to the assortativity coefficient, or modularity in the case of discrete-valued metadata. This global value is the average level of assortativity across the network and may not be a representative statistic when mixing patterns are heterogeneous. For example, a social network spanning the globe may exhibit local differences in mixing patterns as a consequence of differences in cultural norms. Here, we introduce an approach to localise this global measure so that we can describe the assortativity, across multiple scales, at the node level. Consequently we are able to capture and qualitatively evaluate the distribution of mixing patterns in the network. We find that for many real-world networks the distribution of assortativity is skewed, overdispersed and multimodal. Our method provides a clearer lens through which we can more closely examine mixing patterns in networks.
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