Standardized local assortativity in networks and systemic risk in financial markets.

The study of assortativity allows us to understand the heterogeneity of networks and the implication of network resilience. While a global measure has been predominantly used to characterize this network feature, there has been little research to suggest a local coefficient to account for the presence of local (dis)assortative patterns in diversely mixed networks. We build on existing literature and extend the concept of assortativity with the proposal of a standardized scale-independent local coefficient to observe the assortative characteristics of each entity in networks that would otherwise be smoothed out with a global measure. This coefficient provides a lens through which the granular level of details can be observed, as well as capturing possible pattern (dis)formation in dynamic networks. We demonstrate how the standardized local assortative coefficient discovers the presence of (dis)assortative hubs in static networks on a granular level, and how it tracks systemic risk in dynamic financial networks.