Multiscale mixing patterns in networks

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.