Multiscale mixing patterns in networks.
Multiscale mixing patterns in networks.
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DOI：
10.1073/pnas.1713019115
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发表时间：
2018-04-17
影响因子：
11.1
通讯作者：
Lambiotte R
中科院分区：
文献类型：
--
作者：
Peel L;Delvenne JC;Lambiotte R
网络科学的一个中心主题是现实生活系统中存在的异质性，例如节点缺乏特征度。尽管网络具有小世界性，但它可能呈现其他类型的异构模式，网络的不同部分表现出不同的行为。在这里，我们专注于相关性，一个网络模拟的相关性，用于描述的存在和不存在的边缘如何与节点的属性协变。我们设计了一种方法来表征网络内的非均匀性和局部变化，并在各种经验数据中展示丰富的混合模式，这些模式将通过用单个统计量总结非均匀性而被掩盖。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。这是一种经常出现在社交网络中的属性，表现为相同年龄、种族或政治信仰的人之间更倾向于建立联系。量化节点间的连接性或分离性（连接不同属性节点的偏好）可以揭示复杂网络的组织。在分类元数据的情况下，通常的做法是根据可解释性系数或模块性来衡量可解释性水平。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，一个跨越地球仪的社会网络，由于文化规范的差异，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，在节点级别的可扩展性。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，对于许多现实世界的网络，不确定性的分布是偏斜的，过度分散的，多模态的。我们的方法提供了一个更清晰的透镜，通过它我们可以更仔细地检查网络中的混合模式。
A central theme of network science is the heterogeneity present in real-life systems, for instance through the absence of a characteristic degree for the nodes. Despite their small-worldness, networks may present other types of heterogeneous patterns, with different parts of the network exhibiting different behaviors. Here we focus on assortativity, a network analogue of correlation used to describe how the presence and absence of edges covaries with the properties of nodes. We design a method to characterize the heterogeneity and local variations of assortativity within a network and exhibit, in a variety of empirical data, rich mixing patterns that would be obscured by summarizing assortativity with a single statistic. 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 of 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 organization of complex networks. It is common practice to measure the level of assortativity according to the assortativity coefficient, or modularity in the case of categorical 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 localize 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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