The number of trading days out of 3333 days for which we accept the predictions in the RMSE assessments with extremes of 0.1%, 1%, and 2% in Eq (12).

The rows indicate the responses (loss and absolute return) to predict.</p

The time series plots of the smoothed average of the relative topological orders by sector, the daily closing price of the HSI and the number of variables in the networks from 2008 to 2021.

The time series plots of the smoothed average of the relative topological orders by sector, the daily closing price of the HSI and the number of variables in the networks from 2008 to 2021.</p

An overview of the methodology flow in our study.

An overview of the methodology flow in our study.</p

S1 File -

(ZIP)</p

Parameter setting for LFR benchmark network.

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.</div

The effects of standardizing the local assortativity, <i>LA</i>_<i>j</i> in Eq (3) to <i>SLA</i>_<i>j</i> in Eq (4), and their confidence intervals.

The results were obtained by constructing a dynamic financial network using daily financial returns from global markets.</p

Fig 8 -

Top panel: time series plot of the number of confirmed cases of COVID-19 and deaths due to COVID-19 (in log scale) from 2020 to 2021. Bottom panel: global assortativity (green line) and the median (red line), with its interquartile ranges highlighted by yellow regions of the dynamic pandemic networks in [30].</p

Network statistics of five randomly selected dates.

Network statistics of five randomly selected dates.</p

Global assortativity <i>GA</i> and the median and mean standardized local assortativity for the three static networks.

Global assortativity GA and the median and mean standardized local assortativity for the three static networks.</p

Density ridge plot of , where <i>k</i> = 1, ⋯, 10; the solid black line represents the median of each distribution.

Density ridge plot of , where k = 1, ⋯, 10; the solid black line represents the median of each distribution.</p