H2 norm based network volatility measures

Motivated by applications in biology and economics, we propose new volatility measures based on the H₂ system norm for linear networks stimulated by independent or correlated noise. We identify critical links in a network, where relatively small improvements can lead to large reductions in network volatility measures. We also examine volatility measures of individual nodes and their dependence on the topological position in the network. Finally, we investigate the dependence of the volatility on different network interconnections, weights of the edges and other network properties. Hence in an intuitive and efficient way, we can identify critical links, nodes and interconnections in network which can shed light in the network design to make it more robust.