Multiscale mixing patterns in networks

Abstract

Assortative mixing in networks is the tendency for nodes with thesame attributes, or metadata, to link to each other. It is a propertyoften found in social networks, manifesting as a higher tendencyof links occurring between people of the same age, race, or politi-cal belief. Quantifying the level of assortativity or disassortativity(the preference of linking to nodes with different attributes) canshed light on the organization of complex networks. It is com-mon practice to measure the level of assortativity according tothe assortativity coefficient, or modularity in the case of categori-cal metadata. This global value is the average level of assortativityacross the network and may not be a representative statistic whenmixing patterns are heterogeneous. For example, a social networkspanning the globe may exhibit local differences in mixing pat-terns as a consequence of differences in cultural norms. Here, weintroduce an approach to localize this global measure so that wecan describe the assortativity, across multiple scales, at the nodelevel. Consequently, we are able to capture and qualitatively eval-uate the distribution of mixing patterns in the network. We findthat, for many real-world networks, the distribution of assorta-tivity is skewed, overdispersed, and multimodal. Our method pro-vides a clearer lens through which we can more closely examinemixing patterns in networks